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authorPeter Dettman <peter.dettman@bouncycastle.org>2022-12-03 17:25:25 +0700
committerPeter Dettman <peter.dettman@bouncycastle.org>2022-12-03 17:25:25 +0700
commite576a376b11268ca954b95e1d7e451e283c2ba15 (patch)
tree60ca57e1458c1b6c37a8ffdda3b0d42c551a4984
parentMissing file from commit (diff)
downloadBouncyCastle.NET-ed25519-e576a376b11268ca954b95e1d7e451e283c2ba15.tar.xz
Binary curve perf. opts.
-rw-r--r--crypto/src/math/ec/custom/sec/SecT113Field.cs190
-rw-r--r--crypto/src/math/ec/custom/sec/SecT131Field.cs289
-rw-r--r--crypto/src/math/ec/custom/sec/SecT163Field.cs280
-rw-r--r--crypto/src/math/ec/custom/sec/SecT163K1Point.cs4
-rw-r--r--crypto/src/math/ec/custom/sec/SecT193Field.cs220
-rw-r--r--crypto/src/math/ec/custom/sec/SecT233Field.cs26
-rw-r--r--crypto/src/math/ec/custom/sec/SecT233K1Point.cs4
-rw-r--r--crypto/src/math/ec/custom/sec/SecT233R1Point.cs24
-rw-r--r--crypto/src/math/ec/custom/sec/SecT239Field.cs268
-rw-r--r--crypto/src/math/ec/custom/sec/SecT239K1Point.cs4
-rw-r--r--crypto/src/math/ec/custom/sec/SecT283Field.cs326
-rw-r--r--crypto/src/math/ec/custom/sec/SecT283K1Point.cs4
-rw-r--r--crypto/src/math/ec/custom/sec/SecT409Field.cs234
-rw-r--r--crypto/src/math/ec/custom/sec/SecT409K1Point.cs4
-rw-r--r--crypto/src/math/ec/custom/sec/SecT571Field.cs284
-rw-r--r--crypto/src/math/ec/custom/sec/SecT571K1Point.cs4
-rw-r--r--crypto/src/math/ec/custom/sec/SecT571R1Point.cs8
-rw-r--r--crypto/src/math/raw/Nat128.cs12
-rw-r--r--crypto/src/math/raw/Nat192.cs13
-rw-r--r--crypto/src/math/raw/Nat320.cs15
-rw-r--r--crypto/src/math/raw/Nat448.cs17
-rw-r--r--crypto/src/math/raw/Nat576.cs19
22 files changed, 2084 insertions, 165 deletions
diff --git a/crypto/src/math/ec/custom/sec/SecT113Field.cs b/crypto/src/math/ec/custom/sec/SecT113Field.cs
index 2e99bdc4c..596d8070b 100644
--- a/crypto/src/math/ec/custom/sec/SecT113Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT113Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 #if NETCOREAPP3_0_OR_GREATER
+using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
 using System.Runtime.Intrinsics;
 using System.Runtime.Intrinsics.X86;
 #endif
@@ -9,18 +11,36 @@ using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
-    internal class SecT113Field
+    internal static class SecT113Field
     {
         private const ulong M49 = ulong.MaxValue >> 15;
         private const ulong M57 = ulong.MaxValue >> 7;
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Add(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ y[0];
             z[1] = x[1] ^ y[1];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
+        public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
+#endif
+        {
+            z[0] ^= x[0] ^ y[0];
+            z[1] ^= x[1] ^ y[1];
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
+#else
         public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+#endif
         {
             zz[0] = xx[0] ^ yy[0];
             zz[1] = xx[1] ^ yy[1];
@@ -28,13 +48,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[3] = xx[3] ^ yy[3];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddOne(ulong[] x, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ 1UL;
             z[1] = x[1];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddTo(ulong[] x, ulong[] z)
+#endif
         {
             z[0] ^= x[0];
             z[1] ^= x[1];
@@ -45,9 +73,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return Nat.FromBigInteger64(113, x);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void HalfTrace(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[4];
+#else
             ulong[] tt = Nat128.CreateExt64();
+#endif
 
             Nat128.Copy64(x, z);
             for (int i = 1; i < 113; i += 2)
@@ -60,15 +96,24 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Invert(ulong[] x, ulong[] z)
+#endif
         {
             if (Nat128.IsZero64(x))
                 throw new InvalidOperationException();
 
             // Itoh-Tsujii inversion
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> t0 = stackalloc ulong[2];
+            Span<ulong> t1 = stackalloc ulong[2];
+#else
             ulong[] t0 = Nat128.Create64();
             ulong[] t1 = Nat128.Create64();
+#endif
 
             Square(x, t0);
             Multiply(t0, x, t0);
@@ -89,21 +134,50 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Square(t1, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = new ulong[8];
+#endif
             ImplMultiply(x, y, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
         public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = new ulong[8];
+#endif
             ImplMultiply(x, y, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
+        public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
+        {
+            ImplMultiply(x, y, zz);
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
+#else
         public static void Reduce(ulong[] xx, ulong[] z)
+#endif
         {
             ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3];
 
@@ -125,7 +199,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[zOff + 1]  = z1 & M49;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Sqrt(ulong[] x, ulong[] z)
+#endif
         {
             ulong c0 = Interleave.Unshuffle(x[0], x[1], out ulong e0);
 
@@ -133,30 +211,58 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[1] =      (c0 >>  7) ^ (c0 >> 59); 
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Square(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[4];
+#else
             ulong[] tt = Nat128.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareAddToExt(ulong[] x, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[4];
+#else
             ulong[] tt = Nat128.CreateExt64();
+#endif
             ImplSquare(x, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareExt(ulong[] x, ulong[] zz)
+#endif
         {
             ImplSquare(x, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
+#else
         public static void SquareN(ulong[] x, int n, ulong[] z)
+#endif
         {
             Debug.Assert(n > 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[4];
+#else
             ulong[] tt = Nat128.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
 
@@ -167,16 +273,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static uint Trace(ReadOnlySpan<ulong> x)
+#else
         public static uint Trace(ulong[] x)
+#endif
         {
             // Non-zero-trace bits: 0
             return (uint)(x[0]) & 1U;
         }
 
-        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
         {
 #if NETCOREAPP3_0_OR_GREATER
-            if (Pclmulqdq.IsSupported)
+            if (Pclmulqdq.IsSupported && BitConverter.IsLittleEndian && Unsafe.SizeOf<Vector128<ulong>>() == 16)
             {
                 var X01 = Vector128.Create(x[0], x[1]);
                 var Y01 = Vector128.Create(y[0], y[1]);
@@ -186,10 +297,12 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                                    Pclmulqdq.CarrylessMultiply(X01, Y01, 0x10));
                 var Z23 =          Pclmulqdq.CarrylessMultiply(X01, Y01, 0x11);
 
-                zz[0] = Z01.GetElement(0);
-                zz[1] = Z01.GetElement(1) ^ Z12.GetElement(0);
-                zz[2] = Z23.GetElement(0) ^ Z12.GetElement(1);
-                zz[3] = Z23.GetElement(1);
+                Z01 = Sse2.Xor(Z01, Sse2.ShiftLeftLogical128BitLane(Z12, 8));
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftRightLogical128BitLane(Z12, 8));
+
+                Span<byte> zzBytes = MemoryMarshal.AsBytes(zz);
+                MemoryMarshal.Write(zzBytes[0x00..0x10], ref Z01);
+                MemoryMarshal.Write(zzBytes[0x10..0x20], ref Z23);
                 return;
             }
 #endif
@@ -206,6 +319,39 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             g1  = ((g0 >> 57) ^ (g1 << 7)) & M57;
             g0 &= M57;
 
+            Span<ulong> u = zz;
+            Span<ulong> H = stackalloc ulong[6];
+
+            ImplMulw(u, f0, g0, H[0..]);                // H(0)       57/56 bits                                
+            ImplMulw(u, f1, g1, H[2..]);                // H(INF)     57/54 bits                                
+            ImplMulw(u, f0 ^ f1, g0 ^ g1, H[4..]);      // H(1)       57/56 bits
+
+            ulong r  = H[1] ^ H[2];
+            ulong z0 = H[0],
+                  z3 = H[3],
+                  z1 = H[4] ^ z0 ^ r,
+                  z2 = H[5] ^ z3 ^ r;
+
+            zz[0] =  z0        ^ (z1 << 57);
+            zz[1] = (z1 >>  7) ^ (z2 << 50);
+            zz[2] = (z2 >> 14) ^ (z3 << 43);
+            zz[3] = (z3 >> 21);
+        }
+#else
+        private static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+        {
+            /*
+             * "Three-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
+             */
+
+            ulong f0 = x[0], f1 = x[1];
+            f1  = ((f0 >> 57) ^ (f1 << 7)) & M57;
+            f0 &= M57;
+
+            ulong g0 = y[0], g1 = y[1];
+            g1  = ((g0 >> 57) ^ (g1 << 7)) & M57;
+            g0 &= M57;
+
             ulong[] u = zz;
             ulong[] H = new ulong[6];
 
@@ -224,8 +370,13 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[2] = (z2 >> 14) ^ (z3 << 43);
             zz[3] = (z3 >> 21);
         }
+#endif
 
-        protected static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMulw(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
+#else
+        private static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#endif
         {
             Debug.Assert(x >> 57 == 0);
             Debug.Assert(y >> 57 == 0);
@@ -240,14 +391,14 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             u[7] = u[6] ^ y;
 
             uint j = (uint)x;
-            ulong g, h = 0, l = u[j & 7];
+            ulong g, h = 0, l = u[(int)j & 7];
             int k = 48;
             do
             {
                 j  = (uint)(x >> k);
-                g  = u[j & 7]
-                   ^ u[(j >> 3) & 7] << 3
-                   ^ u[(j >> 6) & 7] << 6;
+                g  = u[(int)j & 7]
+                   ^ u[(int)(j >> 3) & 7] << 3
+                   ^ u[(int)(j >> 6) & 7] << 6;
                 l ^= (g << k);
                 h ^= (g >> -k);
             }
@@ -257,11 +408,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             Debug.Assert(h >> 49 == 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            z[0] ^= l & M57;
+            z[1] ^= (l >> 57) ^ (h << 7);
+#else
             z[zOff    ] = l & M57;
             z[zOff + 1] = (l >> 57) ^ (h << 7);
+#endif
         }
 
-        protected static void ImplSquare(ulong[] x, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
+        private static void ImplSquare(ulong[] x, ulong[] zz)
+#endif
         {
 #if NETCOREAPP3_0_OR_GREATER
             if (Bmi2.X64.IsSupported)
@@ -274,7 +434,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
 #endif
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Interleave.Expand64To128(x[..2], zz[..4]);
+#else
             Interleave.Expand64To128(x, 0, 2, zz, 0);
+#endif
         }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/SecT131Field.cs b/crypto/src/math/ec/custom/sec/SecT131Field.cs
index f84fdd212..743fa6a5d 100644
--- a/crypto/src/math/ec/custom/sec/SecT131Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT131Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 #if NETCOREAPP3_0_OR_GREATER
+using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
 using System.Runtime.Intrinsics;
 using System.Runtime.Intrinsics.X86;
 #endif
@@ -9,21 +11,40 @@ using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
-    internal class SecT131Field
+    internal static class SecT131Field
     {
         private const ulong M03 = ulong.MaxValue >> 61;
         private const ulong M44 = ulong.MaxValue >> 20;
 
         private static readonly ulong[] ROOT_Z = new ulong[]{ 0x26BC4D789AF13523UL, 0x26BC4D789AF135E2UL, 0x6UL };
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Add(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ y[0];
             z[1] = x[1] ^ y[1];
             z[2] = x[2] ^ y[2];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
+        public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
+#endif
+        {
+            z[0] ^= x[0] ^ y[0];
+            z[1] ^= x[1] ^ y[1];
+            z[2] ^= x[2] ^ y[2];
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
+#else
         public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+#endif
         {
             zz[0] = xx[0] ^ yy[0];
             zz[1] = xx[1] ^ yy[1];
@@ -32,14 +53,22 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[4] = xx[4] ^ yy[4];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddOne(ulong[] x, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ 1UL;
             z[1] = x[1];
             z[2] = x[2];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddTo(ulong[] x, ulong[] z)
+#endif
         {
             z[0] ^= x[0];
             z[1] ^= x[1];
@@ -51,9 +80,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return Nat.FromBigInteger64(131, x);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void HalfTrace(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[5];
+#else
             ulong[] tt = Nat.Create64(5);
+#endif
 
             Nat192.Copy64(x, z);
             for (int i = 1; i < 131; i += 2)
@@ -66,15 +103,24 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Invert(ulong[] x, ulong[] z)
+#endif
         {
             if (Nat192.IsZero64(x))
                 throw new InvalidOperationException();
 
             // Itoh-Tsujii inversion
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> t0 = stackalloc ulong[3];
+            Span<ulong> t1 = stackalloc ulong[3];
+#else
             ulong[] t0 = Nat192.Create64();
             ulong[] t1 = Nat192.Create64();
+#endif
 
             Square(x, t0);
             Multiply(t0, x, t0);
@@ -95,21 +141,50 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Square(t0, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = new ulong[8];
+#endif
             ImplMultiply(x, y, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
         public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = new ulong[8];
+#endif
             ImplMultiply(x, y, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
+        public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
+        {
+            ImplMultiply(x, y, zz);
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
+#else
         public static void Reduce(ulong[] xx, ulong[] z)
+#endif
         {
             ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4];
 
@@ -135,9 +210,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[zOff + 2]  = z2 & M03;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Sqrt(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> odd = stackalloc ulong[3];
+#else
             ulong[] odd = Nat192.Create64();
+#endif
 
             odd[0] = Interleave.Unshuffle(x[0], x[1], out ulong e0);
             odd[1] = Interleave.Unshuffle(x[2]      , out ulong e1);
@@ -148,30 +231,58 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[1] ^= e1;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Square(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[5];
+#else
             ulong[] tt = Nat.Create64(5);
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareAddToExt(ulong[] x, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[5];
+#else
             ulong[] tt = Nat.Create64(5);
+#endif
             ImplSquare(x, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareExt(ulong[] x, ulong[] zz)
+#endif
         {
             ImplSquare(x, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
+#else
         public static void SquareN(ulong[] x, int n, ulong[] z)
+#endif
         {
             Debug.Assert(n > 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[5];
+#else
             ulong[] tt = Nat.Create64(5);
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
 
@@ -182,13 +293,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static uint Trace(ReadOnlySpan<ulong> x)
+#else
         public static uint Trace(ulong[] x)
+#endif
         {
             // Non-zero-trace bits: 0, 123, 129
             return (uint)(x[0] ^ (x[1] >> 59) ^ (x[2] >> 1)) & 1U;
         }
 
-        protected static void ImplCompactExt(ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplCompactExt(Span<ulong> zz)
+#else
+        private static void ImplCompactExt(ulong[] zz)
+#endif
         {
             ulong z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4], z5 = zz[5];
             zz[0] =  z0        ^ (z1 << 44);
@@ -201,10 +320,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[5] = 0;
         }
 
-        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
         {
 #if NETCOREAPP3_0_OR_GREATER
-            if (Pclmulqdq.IsSupported)
+            if (Pclmulqdq.IsSupported && BitConverter.IsLittleEndian && Unsafe.SizeOf<Vector128<ulong>>() == 16)
             {
                 var X01 = Vector128.Create(x[0], x[1]);
                 var X2_ = Vector128.CreateScalar(x[2]);
@@ -221,11 +341,16 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                                    Pclmulqdq.CarrylessMultiply(X2_, Y01, 0x10));
                 var Z4_ =          Pclmulqdq.CarrylessMultiply(X2_, Y2_, 0x00);
 
-                zz[0] = Z01.GetElement(0);
-                zz[1] = Z01.GetElement(1) ^ Z12.GetElement(0);
-                zz[2] = Z23.GetElement(0) ^ Z12.GetElement(1);
-                zz[3] = Z23.GetElement(1) ^ Z34.GetElement(0);
-                zz[4] = Z4_.GetElement(0) ^ Z34.GetElement(1);
+                Z01 = Sse2.Xor(Z01, Sse2.ShiftLeftLogical128BitLane(Z12, 8));
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftRightLogical128BitLane(Z12, 8));
+
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftLeftLogical128BitLane(Z34, 8));
+                Z4_ = Sse2.Xor(Z4_, Sse2.ShiftRightLogical128BitLane(Z34, 8));
+
+                Span<byte> zzBytes = MemoryMarshal.AsBytes(zz);
+                MemoryMarshal.Write(zzBytes[0x00..0x10], ref Z01);
+                MemoryMarshal.Write(zzBytes[0x10..0x20], ref Z23);
+                zz[4] = Z4_.ToScalar();
                 return;
             }
 #endif
@@ -244,6 +369,110 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             g1  = ((g0 >> 44) ^ (g1 << 20)) & M44;
             g0 &= M44;
 
+            Span<ulong> u = zz;
+            Span<ulong> H = new ulong[10];
+
+            ImplMulw(u, f0, g0, H[0..]);                // H(0)       44/43 bits
+            ImplMulw(u, f2, g2, H[2..]);                // H(INF)     44/41 bits
+
+            ulong t0 = f0 ^ f1 ^ f2;
+            ulong t1 = g0 ^ g1 ^ g2;
+
+            ImplMulw(u, t0, t1, H[4..]);                // H(1)       44/43 bits
+
+            ulong t2 = (f1 << 1) ^ (f2 << 2);
+            ulong t3 = (g1 << 1) ^ (g2 << 2);
+
+            ImplMulw(u, f0 ^ t2, g0 ^ t3, H[6..]);      // H(t)       44/45 bits
+            ImplMulw(u, t0 ^ t2, t1 ^ t3, H[8..]);      // H(t + 1)   44/45 bits
+
+            ulong t4 = H[6] ^ H[8];
+            ulong t5 = H[7] ^ H[9];
+
+            Debug.Assert(t5 >> 44 == 0);
+
+            // Calculate V
+            ulong v0 =      (t4 << 1) ^ H[6];
+            ulong v1 = t4 ^ (t5 << 1) ^ H[7];
+            ulong v2 = t5;
+
+            // Calculate U
+            ulong u0 = H[0];
+            ulong u1 = H[1] ^ H[0] ^ H[4];
+            ulong u2 =        H[1] ^ H[5];
+        
+            // Calculate W
+            ulong w0 = u0 ^ v0 ^ (H[2] << 4) ^ (H[2] << 1);
+            ulong w1 = u1 ^ v1 ^ (H[3] << 4) ^ (H[3] << 1);
+            ulong w2 = u2 ^ v2;
+
+            // Propagate carries
+            w1 ^= (w0 >> 44); w0 &= M44;
+            w2 ^= (w1 >> 44); w1 &= M44;
+
+            Debug.Assert((w0 & 1UL) == 0);
+
+            // Divide W by t
+
+            w0 = (w0 >> 1) ^ ((w1 & 1UL) << 43);
+            w1 = (w1 >> 1) ^ ((w2 & 1UL) << 43);
+            w2 = (w2 >> 1);
+
+            // Divide W by (t + 1)
+
+            w0 ^= (w0 << 1);
+            w0 ^= (w0 << 2);
+            w0 ^= (w0 << 4);
+            w0 ^= (w0 << 8);
+            w0 ^= (w0 << 16);
+            w0 ^= (w0 << 32);
+
+            w0 &= M44; w1 ^= (w0 >> 43);
+
+            w1 ^= (w1 << 1);
+            w1 ^= (w1 << 2);
+            w1 ^= (w1 << 4);
+            w1 ^= (w1 << 8);
+            w1 ^= (w1 << 16);
+            w1 ^= (w1 << 32);
+
+            w1 &= M44; w2 ^= (w1 >> 43);
+
+            w2 ^= (w2 << 1);
+            w2 ^= (w2 << 2);
+            w2 ^= (w2 << 4);
+            w2 ^= (w2 << 8);
+            w2 ^= (w2 << 16);
+            w2 ^= (w2 << 32);
+
+            Debug.Assert(w2 >> 42 == 0);
+
+            zz[0] = u0; 
+            zz[1] = u1 ^ w0      ^ H[2]; 
+            zz[2] = u2 ^ w1 ^ w0 ^ H[3]; 
+            zz[3] =      w2 ^ w1; 
+            zz[4] =           w2 ^ H[2]; 
+            zz[5] =                H[3]; 
+
+            ImplCompactExt(zz);
+        }
+#else
+        private static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+        {
+            /*
+             * "Five-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
+             */
+
+            ulong f0 = x[0], f1 = x[1], f2 = x[2];
+            f2  = ((f1 >> 24) ^ (f2 << 40)) & M44;
+            f1  = ((f0 >> 44) ^ (f1 << 20)) & M44;
+            f0 &= M44;
+
+            ulong g0 = y[0], g1 = y[1], g2 = y[2];
+            g2  = ((g1 >> 24) ^ (g2 << 40)) & M44;
+            g1  = ((g0 >> 44) ^ (g1 << 20)) & M44;
+            g0 &= M44;
+
             ulong[] u = zz;
             ulong[] H = new ulong[10];
 
@@ -331,8 +560,13 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             ImplCompactExt(zz);
         }
+#endif
 
-        protected static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMulw(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
+#else
+        private static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#endif
         {
             Debug.Assert(x >> 45 == 0);
             Debug.Assert(y >> 45 == 0);
@@ -347,20 +581,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             u[7] = u[6] ^  y;
 
             uint j = (uint)x;
-            ulong g, h = 0, l = u[j & 7]
-                              ^ u[(j >>  3) & 7] <<  3
-                              ^ u[(j >>  6) & 7] <<  6
-                              ^ u[(j >>  9) & 7] <<  9
-                              ^ u[(j >> 12) & 7] << 12;
+            ulong g, h = 0, l = u[(int)j & 7]
+                              ^ u[(int)(j >>  3) & 7] <<  3
+                              ^ u[(int)(j >>  6) & 7] <<  6
+                              ^ u[(int)(j >>  9) & 7] <<  9
+                              ^ u[(int)(j >> 12) & 7] << 12;
             int k = 30;
             do
             {
                 j  = (uint)(x >> k);
-                g  = u[j & 7]
-                   ^ u[(j >>  3) & 7] <<  3
-                   ^ u[(j >>  6) & 7] <<  6
-                   ^ u[(j >>  9) & 7] <<  9
-                   ^ u[(j >> 12) & 7] << 12;
+                g  = u[(int)j & 7]
+                   ^ u[(int)(j >>  3) & 7] <<  3
+                   ^ u[(int)(j >>  6) & 7] <<  6
+                   ^ u[(int)(j >>  9) & 7] <<  9
+                   ^ u[(int)(j >> 12) & 7] << 12;
                 l ^= (g << k);
                 h ^= (g >> -k);
             }
@@ -368,11 +602,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             Debug.Assert(h >> 25 == 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            z[0] ^= l & M44;
+            z[1] ^= (l >> 44) ^ (h << 20);
+#else
             z[zOff    ] = l & M44;
             z[zOff + 1] = (l >> 44) ^ (h << 20);
+#endif
         }
 
-        protected static void ImplSquare(ulong[] x, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
+        private static void ImplSquare(ulong[] x, ulong[] zz)
+#endif
         {
             zz[4] = Interleave.Expand8to16((byte)x[2]);
 
@@ -387,7 +630,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
 #endif
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Interleave.Expand64To128(x[..2], zz[..4]);
+#else
             Interleave.Expand64To128(x, 0, 2, zz, 0);
+#endif
         }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/SecT163Field.cs b/crypto/src/math/ec/custom/sec/SecT163Field.cs
index 1ba747681..d0f09cd8b 100644
--- a/crypto/src/math/ec/custom/sec/SecT163Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT163Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 #if NETCOREAPP3_0_OR_GREATER
+using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
 using System.Runtime.Intrinsics;
 using System.Runtime.Intrinsics.X86;
 #endif
@@ -9,21 +11,40 @@ using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
-    internal class SecT163Field
+    internal static class SecT163Field
     {
         private const ulong M35 = ulong.MaxValue >> 29;
         private const ulong M55 = ulong.MaxValue >> 9;
 
         private static readonly ulong[] ROOT_Z = new ulong[]{ 0xB6DB6DB6DB6DB6B0UL, 0x492492492492DB6DUL, 0x492492492UL };
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Add(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ y[0];
             z[1] = x[1] ^ y[1];
             z[2] = x[2] ^ y[2];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
+        public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
+#endif
+        {
+            z[0] ^= x[0] ^ y[0];
+            z[1] ^= x[1] ^ y[1];
+            z[2] ^= x[2] ^ y[2];
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
+#else
         public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+#endif
         {
             zz[0] = xx[0] ^ yy[0];
             zz[1] = xx[1] ^ yy[1];
@@ -33,14 +54,22 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[5] = xx[5] ^ yy[5];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddOne(ulong[] x, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ 1UL;
             z[1] = x[1];
             z[2] = x[2];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddTo(ulong[] x, ulong[] z)
+#endif
         {
             z[0] ^= x[0];
             z[1] ^= x[1];
@@ -52,9 +81,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return Nat.FromBigInteger64(163, x);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void HalfTrace(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[6];
+#else
             ulong[] tt = Nat192.CreateExt64();
+#endif
 
             Nat192.Copy64(x, z);
             for (int i = 1; i < 163; i += 2)
@@ -67,15 +104,24 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Invert(ulong[] x, ulong[] z)
+#endif
         {
             if (Nat192.IsZero64(x))
                 throw new InvalidOperationException();
 
             // Itoh-Tsujii inversion with bases { 2, 3 }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> t0 = stackalloc ulong[3];
+            Span<ulong> t1 = stackalloc ulong[3];
+#else
             ulong[] t0 = Nat192.Create64();
             ulong[] t1 = Nat192.Create64();
+#endif
 
             Square(x, t0);
 
@@ -108,21 +154,50 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Multiply(t0, t1, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = new ulong[8];
+#endif
             ImplMultiply(x, y, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
         public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = new ulong[8];
+#endif
             ImplMultiply(x, y, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
+        public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
+        {
+            ImplMultiply(x, y, zz);
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
+#else
         public static void Reduce(ulong[] xx, ulong[] z)
+#endif
         {
             ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4], x5 = xx[5];
 
@@ -148,9 +223,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[zOff + 2]  = z2 & M35;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Sqrt(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> odd = stackalloc ulong[3];
+#else
             ulong[] odd = Nat192.Create64();
+#endif
 
             odd[0] = Interleave.Unshuffle(x[0], x[1], out ulong e0);
             odd[1] = Interleave.Unshuffle(x[2]      , out ulong e1);
@@ -161,30 +244,58 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[1] ^= e1;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Square(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[6];
+#else
             ulong[] tt = Nat192.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareAddToExt(ulong[] x, ulong[] zz)
+#endif
         {
-            ulong[] tt = Nat192.CreateExt64();
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[6];
+#else
+            ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplSquare(x, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareExt(ulong[] x, ulong[] zz)
+#endif
         {
             ImplSquare(x, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
+#else
         public static void SquareN(ulong[] x, int n, ulong[] z)
+#endif
         {
             Debug.Assert(n > 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[6];
+#else
             ulong[] tt = Nat192.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
 
@@ -195,13 +306,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static uint Trace(ReadOnlySpan<ulong> x)
+#else
         public static uint Trace(ulong[] x)
+#endif
         {
             // Non-zero-trace bits: 0, 157
             return (uint)(x[0] ^ (x[2] >> 29)) & 1U;
         }
 
-        protected static void ImplCompactExt(ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplCompactExt(Span<ulong> zz)
+#else
+        private static void ImplCompactExt(ulong[] zz)
+#endif
         {
             ulong z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4], z5 = zz[5];
             zz[0] =  z0        ^ (z1 << 55);
@@ -212,10 +331,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[5] = (z5 >> 45);
         }
 
-        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
         {
 #if NETCOREAPP3_0_OR_GREATER
-            if (Pclmulqdq.IsSupported)
+            if (Pclmulqdq.IsSupported && BitConverter.IsLittleEndian && Unsafe.SizeOf<Vector128<ulong>>() == 16)
             {
                 var X01 = Vector128.Create(x[0], x[1]);
                 var X2_ = Vector128.CreateScalar(x[2]);
@@ -232,12 +352,16 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                                    Pclmulqdq.CarrylessMultiply(X2_, Y01, 0x10));
                 var Z45 =          Pclmulqdq.CarrylessMultiply(X2_, Y2_, 0x00);
 
-                zz[0] = Z01.GetElement(0);
-                zz[1] = Z01.GetElement(1) ^ Z12.GetElement(0);
-                zz[2] = Z23.GetElement(0) ^ Z12.GetElement(1);
-                zz[3] = Z23.GetElement(1) ^ Z34.GetElement(0);
-                zz[4] = Z45.GetElement(0) ^ Z34.GetElement(1);
-                zz[5] = Z45.GetElement(1);
+                Z01 = Sse2.Xor(Z01, Sse2.ShiftLeftLogical128BitLane (Z12, 8));
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftRightLogical128BitLane(Z12, 8));
+
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftLeftLogical128BitLane (Z34, 8));
+                Z45 = Sse2.Xor(Z45, Sse2.ShiftRightLogical128BitLane(Z34, 8));
+
+                Span<byte> zzBytes = MemoryMarshal.AsBytes(zz);
+                MemoryMarshal.Write(zzBytes[0x00..0x10], ref Z01);
+                MemoryMarshal.Write(zzBytes[0x10..0x20], ref Z23);
+                MemoryMarshal.Write(zzBytes[0x20..0x30], ref Z45);
                 return;
             }
 #endif
@@ -256,6 +380,110 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             g1  = ((g0 >> 55) ^ (g1 <<  9)) & M55;
             g0 &= M55;
 
+            Span<ulong> u = zz;
+            Span<ulong> H = stackalloc ulong[10];
+
+            ImplMulw(u, f0, g0, H[0..]);                // H(0)       55/54 bits
+            ImplMulw(u, f2, g2, H[2..]);                // H(INF)     55/50 bits
+
+            ulong t0 = f0 ^ f1 ^ f2;
+            ulong t1 = g0 ^ g1 ^ g2;
+
+            ImplMulw(u, t0, t1, H[4..]);                // H(1)       55/54 bits
+        
+            ulong t2 = (f1 << 1) ^ (f2 << 2);
+            ulong t3 = (g1 << 1) ^ (g2 << 2);
+
+            ImplMulw(u, f0 ^ t2, g0 ^ t3, H[6..]);      // H(t)       55/56 bits
+            ImplMulw(u, t0 ^ t2, t1 ^ t3, H[8..]);      // H(t + 1)   55/56 bits
+
+            ulong t4 = H[6] ^ H[8];
+            ulong t5 = H[7] ^ H[9];
+
+            Debug.Assert(t5 >> 55 == 0);
+
+            // Calculate V
+            ulong v0 =      (t4 << 1) ^ H[6];
+            ulong v1 = t4 ^ (t5 << 1) ^ H[7];
+            ulong v2 = t5;
+
+            // Calculate U
+            ulong u0 = H[0];
+            ulong u1 = H[1] ^ H[0] ^ H[4];
+            ulong u2 =        H[1] ^ H[5];
+        
+            // Calculate W
+            ulong w0 = u0 ^ v0 ^ (H[2] << 4) ^ (H[2] << 1);
+            ulong w1 = u1 ^ v1 ^ (H[3] << 4) ^ (H[3] << 1);
+            ulong w2 = u2 ^ v2;
+
+            // Propagate carries
+            w1 ^= (w0 >> 55); w0 &= M55;
+            w2 ^= (w1 >> 55); w1 &= M55;
+
+            Debug.Assert((w0 & 1UL) == 0UL);
+
+            // Divide W by t
+
+            w0 = (w0 >> 1) ^ ((w1 & 1UL) << 54);
+            w1 = (w1 >> 1) ^ ((w2 & 1UL) << 54);
+            w2 = (w2 >> 1);
+
+            // Divide W by (t + 1)
+
+            w0 ^= (w0 << 1);
+            w0 ^= (w0 << 2);
+            w0 ^= (w0 << 4);
+            w0 ^= (w0 << 8);
+            w0 ^= (w0 << 16);
+            w0 ^= (w0 << 32);
+
+            w0 &= M55; w1 ^= (w0 >> 54);
+
+            w1 ^= (w1 << 1);
+            w1 ^= (w1 << 2);
+            w1 ^= (w1 << 4);
+            w1 ^= (w1 << 8);
+            w1 ^= (w1 << 16);
+            w1 ^= (w1 << 32);
+
+            w1 &= M55; w2 ^= (w1 >> 54);
+
+            w2 ^= (w2 << 1);
+            w2 ^= (w2 << 2);
+            w2 ^= (w2 << 4);
+            w2 ^= (w2 << 8);
+            w2 ^= (w2 << 16);
+            w2 ^= (w2 << 32);
+
+            Debug.Assert(w2 >> 52 == 0);
+
+            zz[0] = u0; 
+            zz[1] = u1 ^ w0      ^ H[2]; 
+            zz[2] = u2 ^ w1 ^ w0 ^ H[3]; 
+            zz[3] =      w2 ^ w1; 
+            zz[4] =           w2 ^ H[2]; 
+            zz[5] =                H[3]; 
+
+            ImplCompactExt(zz);
+        }
+#else
+        private static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+        {
+            /*
+             * "Five-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
+             */
+
+            ulong f0 = x[0], f1 = x[1], f2 = x[2];
+            f2  = ((f1 >> 46) ^ (f2 << 18));
+            f1  = ((f0 >> 55) ^ (f1 <<  9)) & M55;
+            f0 &= M55;
+
+            ulong g0 = y[0], g1 = y[1], g2 = y[2];
+            g2  = ((g1 >> 46) ^ (g2 << 18));
+            g1  = ((g0 >> 55) ^ (g1 <<  9)) & M55;
+            g0 &= M55;
+
             ulong[] u = zz;
             ulong[] H = new ulong[10];
 
@@ -343,8 +571,13 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             ImplCompactExt(zz);
         }
+#endif
 
-        protected static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMulw(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
+#else
+        private static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#endif
         {
             Debug.Assert(x >> 56 == 0);
             Debug.Assert(y >> 56 == 0);
@@ -359,14 +592,14 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             u[7] = u[6] ^  y;
 
             uint j = (uint)x;
-            ulong g, h = 0, l = u[j & 3];
+            ulong g, h = 0, l = u[(int)j & 3];
             int k = 47;
             do
             {
                 j  = (uint)(x >> k);
-                g  = u[j & 7]
-                   ^ u[(j >> 3) & 7] << 3
-                   ^ u[(j >> 6) & 7] << 6;
+                g  = u[(int)j & 7]
+                   ^ u[(int)(j >> 3) & 7] << 3
+                   ^ u[(int)(j >> 6) & 7] << 6;
                 l ^= (g <<  k);
                 h ^= (g >> -k);
             }
@@ -374,11 +607,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             Debug.Assert(h >> 47 == 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            z[0] ^= l & M55;
+            z[1] ^= (l >> 55) ^ (h << 9);
+#else
             z[zOff    ] = l & M55;
             z[zOff + 1] = (l >> 55) ^ (h << 9);
+#endif
         }
 
-        protected static void ImplSquare(ulong[] x, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
+        private static void ImplSquare(ulong[] x, ulong[] zz)
+#endif
         {
 #if NETCOREAPP3_0_OR_GREATER
             if (Bmi2.X64.IsSupported)
@@ -393,7 +635,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
 #endif
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Interleave.Expand64To128(x[..3], zz[..6]);
+#else
             Interleave.Expand64To128(x, 0, 3, zz, 0);
+#endif
         }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/SecT163K1Point.cs b/crypto/src/math/ec/custom/sec/SecT163K1Point.cs
index 06855c50c..a93f0882b 100644
--- a/crypto/src/math/ec/custom/sec/SecT163K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecT163K1Point.cs
@@ -82,7 +82,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             SecT163FieldElement L1 = (SecT163FieldElement)this.RawYCoord, Z1 = (SecT163FieldElement)this.RawZCoords[0];
             SecT163FieldElement L2 = (SecT163FieldElement)b.RawYCoord, Z2 = (SecT163FieldElement)b.RawZCoords[0];
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt0 = stackalloc ulong[6];
+#else
             ulong[] tt0 = Nat192.CreateExt64();
+#endif
             ulong[] t1 = Nat192.Create64();
             ulong[] t2 = Nat192.Create64();
             ulong[] t3 = Nat192.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT193Field.cs b/crypto/src/math/ec/custom/sec/SecT193Field.cs
index 3d9937f75..b610bf554 100644
--- a/crypto/src/math/ec/custom/sec/SecT193Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT193Field.cs
@@ -9,12 +9,16 @@ using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
-    internal class SecT193Field
+    internal static class SecT193Field
     {
         private const ulong M01 = 1UL;
         private const ulong M49 = ulong.MaxValue >> 15;
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Add(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ y[0];
             z[1] = x[1] ^ y[1];
@@ -22,7 +26,23 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[3] = x[3] ^ y[3];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
+        public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
+#endif
+        {
+            z[0] ^= x[0] ^ y[0];
+            z[1] ^= x[1] ^ y[1];
+            z[2] ^= x[2] ^ y[2];
+            z[3] ^= x[3] ^ y[3];
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
+#else
         public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+#endif
         {
             zz[0] = xx[0] ^ yy[0];
             zz[1] = xx[1] ^ yy[1];
@@ -33,7 +53,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[6] = xx[6] ^ yy[6];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddOne(ulong[] x, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ 1UL;
             z[1] = x[1];
@@ -41,7 +65,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[3] = x[3];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddTo(ulong[] x, ulong[] z)
+#endif
         {
             z[0] ^= x[0];
             z[1] ^= x[1];
@@ -54,9 +82,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return Nat.FromBigInteger64(193, x);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void HalfTrace(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
 
             Nat256.Copy64(x, z);
             for (int i = 1; i < 193; i += 2)
@@ -69,15 +105,24 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Invert(ulong[] x, ulong[] z)
+#endif
         {
             if (Nat256.IsZero64(x))
                 throw new InvalidOperationException();
 
             // Itoh-Tsujii inversion with bases { 2, 3 }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> t0 = stackalloc ulong[4];
+            Span<ulong> t1 = stackalloc ulong[4];
+#else
             ulong[] t0 = Nat256.Create64();
             ulong[] t1 = Nat256.Create64();
+#endif
 
             Square(x, t0);
 
@@ -112,21 +157,55 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Multiply(t0, t1, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
         public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
+        public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
+        {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            zz[..8].Fill(0UL);
+#else
+            Array.Clear(zz, 0, 8);
+#endif
+            ImplMultiply(x, y, zz);
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
+#else
         public static void Reduce(ulong[] xx, ulong[] z)
+#endif
         {
             ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4], x5 = xx[5], x6 = xx[6];
 
@@ -157,7 +236,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[zOff + 3]  = z3 & M01;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Sqrt(ulong[] x, ulong[] z)
+#endif
         {
             ulong c0 = Interleave.Unshuffle(x[0], x[1], out ulong e0);
             ulong c1 = Interleave.Unshuffle(x[2]      , out ulong e1);
@@ -169,30 +252,58 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[3] =                                            (c1 >> 31);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Square(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareAddToExt(ulong[] x, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplSquare(x, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareExt(ulong[] x, ulong[] zz)
+#endif
         {
             ImplSquare(x, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
+#else
         public static void SquareN(ulong[] x, int n, ulong[] z)
+#endif
         {
             Debug.Assert(n > 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
 
@@ -203,13 +314,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static uint Trace(ReadOnlySpan<ulong> x)
+#else
         public static uint Trace(ulong[] x)
+#endif
         {
             // Non-zero-trace bits: 0
             return (uint)(x[0]) & 1U;
         }
 
-        protected static void ImplCompactExt(ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplCompactExt(Span<ulong> zz)
+#else
+        private static void ImplCompactExt(ulong[] zz)
+#endif
         {
             ulong z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4], z5 = zz[5], z6 = zz[6], z7 = zz[7];
             zz[0] =  z0        ^ (z1 << 49);
@@ -224,7 +343,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[7] = 0;
         }
 
-        protected static void ImplExpand(ulong[] x, ulong[] z)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplExpand(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
+        private static void ImplExpand(ulong[] x, ulong[] z)
+#endif
         {
             ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
             z[0] = x0 & M49;
@@ -233,7 +356,8 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[3] = ((x2 >> 19) ^ (x3 << 45));
         }
 
-        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
         {
 #if NETCOREAPP3_0_OR_GREATER
             if (Pclmulqdq.IsSupported)
@@ -277,6 +401,56 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             ulong[] u = new ulong[8];
 
+            ImplMulwAcc(u, f[0], g[0], zz[0..]);
+            ImplMulwAcc(u, f[1], g[1], zz[1..]);
+            ImplMulwAcc(u, f[2], g[2], zz[2..]);
+            ImplMulwAcc(u, f[3], g[3], zz[3..]);
+
+            // U *= (1 - t^n)
+            for (int i = 5; i > 0; --i)
+            {
+                zz[i] ^= zz[i - 1];
+            }
+
+            ImplMulwAcc(u, f[0] ^ f[1], g[0] ^ g[1], zz[1..]);
+            ImplMulwAcc(u, f[2] ^ f[3], g[2] ^ g[3], zz[3..]);
+
+            // V *= (1 - t^2n)
+            for (int i = 7; i > 1; --i)
+            {
+                zz[i] ^= zz[i - 2];
+            }
+
+            // Double-length recursion
+            {
+                ulong c0 = f[0] ^ f[2], c1 = f[1] ^ f[3];
+                ulong d0 = g[0] ^ g[2], d1 = g[1] ^ g[3];
+                ImplMulwAcc(u, c0 ^ c1, d0 ^ d1, zz[3..]);
+                Span<ulong> t = stackalloc ulong[3];
+                ImplMulwAcc(u, c0, d0, t[0..]);
+                ImplMulwAcc(u, c1, d1, t[1..]);
+                ulong t0 = t[0], t1 = t[1], t2 = t[2];
+                zz[2] ^= t0;
+                zz[3] ^= t0 ^ t1;
+                zz[4] ^= t2 ^ t1;
+                zz[5] ^= t2;
+            }
+
+            ImplCompactExt(zz);
+        }
+#else
+        private static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+        {
+            /*
+             * "Two-level seven-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
+             */
+
+            ulong[] f = new ulong[4], g = new ulong[4];
+            ImplExpand(x, f);
+            ImplExpand(y, g);
+
+            ulong[] u = new ulong[8];
+
             ImplMulwAcc(u, f[0], g[0], zz, 0);
             ImplMulwAcc(u, f[1], g[1], zz, 1);
             ImplMulwAcc(u, f[2], g[2], zz, 2);
@@ -314,8 +488,13 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             ImplCompactExt(zz);
         }
+#endif
 
-        protected static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMulwAcc(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
+#else
+        private static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#endif
         {
             Debug.Assert(x >> 49 == 0);
             Debug.Assert(y >> 49 == 0);
@@ -330,17 +509,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             u[7] = u[6] ^ y;
 
             uint j = (uint)x;
-            ulong g, h = 0, l = u[j & 7]
-                              ^ (u[(j >> 3) & 7] << 3);
+            ulong g, h = 0, l = u[(int)j & 7]
+                              ^ (u[(int)(j >> 3) & 7] << 3);
             int k = 36;
             do
             {
                 j  = (uint)(x >> k);
-                g  = u[j & 7]
-                   ^ u[(j >> 3) & 7] << 3
-                   ^ u[(j >> 6) & 7] << 6
-                   ^ u[(j >> 9) & 7] << 9
-                   ^ u[(j >> 12) & 7] << 12;
+                g  = u[(int)j & 7]
+                   ^ u[(int)(j >> 3) & 7] << 3
+                   ^ u[(int)(j >> 6) & 7] << 6
+                   ^ u[(int)(j >> 9) & 7] << 9
+                   ^ u[(int)(j >> 12) & 7] << 12;
                 l ^= (g <<  k);
                 h ^= (g >> -k);
             }
@@ -348,13 +527,22 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             Debug.Assert(h >> 33 == 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            z[0] ^= l & M49;
+            z[1] ^= (l >> 49) ^ (h << 15);
+#else
             z[zOff    ] ^= l & M49;
             z[zOff + 1] ^= (l >> 49) ^ (h << 15);
+#endif
         }
 
-        protected static void ImplSquare(ulong[] x, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
+        private static void ImplSquare(ulong[] x, ulong[] zz)
+#endif
         {
-            zz[6] = (x[3] & M01);
+            zz[6] = x[3] & M01;
 
 #if NETCOREAPP3_0_OR_GREATER
             if (Bmi2.X64.IsSupported)
@@ -369,7 +557,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
 #endif
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Interleave.Expand64To128(x[..3], zz[..6]);
+#else
             Interleave.Expand64To128(x, 0, 3, zz, 0);
+#endif
         }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/SecT233Field.cs b/crypto/src/math/ec/custom/sec/SecT233Field.cs
index 1e65b6112..00bbc0635 100644
--- a/crypto/src/math/ec/custom/sec/SecT233Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT233Field.cs
@@ -1,6 +1,7 @@
 using System;
 using System.Diagnostics;
 #if NETCOREAPP3_0_OR_GREATER
+using System.Runtime.CompilerServices;
 using System.Runtime.InteropServices;
 using System.Runtime.Intrinsics;
 using System.Runtime.Intrinsics.X86;
@@ -119,8 +120,8 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             // Itoh-Tsujii inversion
 
 #if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
-            Span<ulong> t0 = stackalloc ulong[8];
-            Span<ulong> t1 = stackalloc ulong[8];
+            Span<ulong> t0 = stackalloc ulong[4];
+            Span<ulong> t1 = stackalloc ulong[4];
 #else
             ulong[] t0 = Nat256.Create64();
             ulong[] t1 = Nat256.Create64();
@@ -377,7 +378,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
         private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
         {
 #if NETCOREAPP3_0_OR_GREATER
-            if (Pclmulqdq.IsSupported)
+            if (Pclmulqdq.IsSupported && BitConverter.IsLittleEndian && Unsafe.SizeOf<Vector128<ulong>>() == 16)
             {
                 var X01 = Vector128.Create(x[0], x[1]);
                 var X23 = Vector128.Create(x[2], x[3]);
@@ -461,7 +462,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                 ulong c0 = f[0] ^ f[2], c1 = f[1] ^ f[3];
                 ulong d0 = g[0] ^ g[2], d1 = g[1] ^ g[3];
                 ImplMulwAcc(u, c0 ^ c1, d0 ^ d1, zz[3..]);
-                ulong[] t = new ulong[3];
+                Span<ulong> t = stackalloc ulong[3];
                 ImplMulwAcc(u, c0, d0, t[0..]);
                 ImplMulwAcc(u, c1, d1, t[1..]);
                 ulong t0 = t[0], t1 = t[1], t2 = t[2];
@@ -577,14 +578,15 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 #if NETCOREAPP3_0_OR_GREATER
             if (Bmi2.X64.IsSupported)
             {
-                zz[7] = Bmi2.X64.ParallelBitDeposit(x[3] >> 32, 0x5555555555555555UL);
-                zz[6] = Bmi2.X64.ParallelBitDeposit(x[3]      , 0x5555555555555555UL);
-                zz[5] = Bmi2.X64.ParallelBitDeposit(x[2] >> 32, 0x5555555555555555UL);
-                zz[4] = Bmi2.X64.ParallelBitDeposit(x[2]      , 0x5555555555555555UL);
-                zz[3] = Bmi2.X64.ParallelBitDeposit(x[1] >> 32, 0x5555555555555555UL);
-                zz[2] = Bmi2.X64.ParallelBitDeposit(x[1]      , 0x5555555555555555UL);
-                zz[1] = Bmi2.X64.ParallelBitDeposit(x[0] >> 32, 0x5555555555555555UL);
-                zz[0] = Bmi2.X64.ParallelBitDeposit(x[0]      , 0x5555555555555555UL);
+                ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
+                zz[7] = Bmi2.X64.ParallelBitDeposit(x3 >> 32, 0x5555555555555555UL);
+                zz[6] = Bmi2.X64.ParallelBitDeposit(x3      , 0x5555555555555555UL);
+                zz[5] = Bmi2.X64.ParallelBitDeposit(x2 >> 32, 0x5555555555555555UL);
+                zz[4] = Bmi2.X64.ParallelBitDeposit(x2      , 0x5555555555555555UL);
+                zz[3] = Bmi2.X64.ParallelBitDeposit(x1 >> 32, 0x5555555555555555UL);
+                zz[2] = Bmi2.X64.ParallelBitDeposit(x1      , 0x5555555555555555UL);
+                zz[1] = Bmi2.X64.ParallelBitDeposit(x0 >> 32, 0x5555555555555555UL);
+                zz[0] = Bmi2.X64.ParallelBitDeposit(x0      , 0x5555555555555555UL);
                 return;
             }
 #endif
diff --git a/crypto/src/math/ec/custom/sec/SecT233K1Point.cs b/crypto/src/math/ec/custom/sec/SecT233K1Point.cs
index 0ed107d49..6599c1cc6 100644
--- a/crypto/src/math/ec/custom/sec/SecT233K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecT233K1Point.cs
@@ -82,7 +82,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             SecT233FieldElement L1 = (SecT233FieldElement)this.RawYCoord, Z1 = (SecT233FieldElement)this.RawZCoords[0];
             SecT233FieldElement L2 = (SecT233FieldElement)b.RawYCoord, Z2 = (SecT233FieldElement)b.RawZCoords[0];
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt0 = stackalloc ulong[8];
+#else
             ulong[] tt0 = Nat256.CreateExt64();
+#endif
             ulong[] t1 = Nat256.Create64();
             ulong[] t2 = Nat256.Create64();
             ulong[] t3 = Nat256.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT233R1Point.cs b/crypto/src/math/ec/custom/sec/SecT233R1Point.cs
index 44441b22a..c3a51a8bb 100644
--- a/crypto/src/math/ec/custom/sec/SecT233R1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecT233R1Point.cs
@@ -177,7 +177,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             SecT233FieldElement L1 = (SecT233FieldElement)this.RawYCoord, Z1 = (SecT233FieldElement)this.RawZCoords[0];
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt0 = stackalloc ulong[8];
+#else
             ulong[] tt0 = Nat256.CreateExt64();
+#endif
             ulong[] _X3 = Nat256.Create64();
             ulong[] _L3 = Nat256.Create64();
             ulong[] _Z3 = Nat256.Create64();
@@ -198,24 +202,28 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
             else
             {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+                Span<ulong> t1 = stackalloc ulong[4];
+#else
                 ulong[] t1 = Nat256.Create64();
-                ulong[] t2 = Nat256.Create64();
+#endif
 
                 SecT233Field.Multiply(L1.x, Z1.x, t1);      // L1Z1
                 SecT233Field.Square(Z1.x, tt0);             // Z1Sq
 
-                SecT233Field.Square(L1.x, t2);
-                SecT233Field.AddBothTo(t1, tt0, t2);        // T
+                SecT233Field.Square(L1.x, _X3);
+                SecT233Field.AddBothTo(t1, tt0, _X3);       // T
 
-                if (Nat256.IsZero64(t2))
-                    return new SecT233R1Point(curve, new SecT233FieldElement(t2), curve.B.Sqrt());
+                if (Nat256.IsZero64(_X3))
+                    return new SecT233R1Point(curve, new SecT233FieldElement(_X3), curve.B.Sqrt());
 
-                SecT233Field.Square(t2, _X3);
-                SecT233Field.Multiply(t2, tt0, _Z3);
+                SecT233Field.Multiply(_X3, tt0, _Z3);
                 SecT233Field.Multiply(X1.x, Z1.x, tt0);     // X1Z1
 
                 SecT233Field.SquareExt(tt0, tt0);
-                SecT233Field.MultiplyAddToExt(t2, t1, tt0);
+                SecT233Field.MultiplyAddToExt(_X3, t1, tt0);
+
+                SecT233Field.Square(_X3, _X3);
             }
 
             SecT233Field.Reduce(tt0, _L3);
diff --git a/crypto/src/math/ec/custom/sec/SecT239Field.cs b/crypto/src/math/ec/custom/sec/SecT239Field.cs
index d48e1ec2b..b90867b76 100644
--- a/crypto/src/math/ec/custom/sec/SecT239Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT239Field.cs
@@ -11,12 +11,16 @@ using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
-    internal class SecT239Field
+    internal static class SecT239Field
     {
         private const ulong M47 = ulong.MaxValue >> 17;
         private const ulong M60 = ulong.MaxValue >> 4;
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Add(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ y[0];
             z[1] = x[1] ^ y[1];
@@ -24,7 +28,23 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[3] = x[3] ^ y[3];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
+        public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
+#endif
+        {
+            z[0] ^= x[0] ^ y[0];
+            z[1] ^= x[1] ^ y[1];
+            z[2] ^= x[2] ^ y[2];
+            z[3] ^= x[3] ^ y[3];
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
+#else
         public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+#endif
         {
             zz[0] = xx[0] ^ yy[0];
             zz[1] = xx[1] ^ yy[1];
@@ -36,7 +56,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[7] = xx[7] ^ yy[7];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddOne(ulong[] x, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ 1UL;
             z[1] = x[1];
@@ -44,7 +68,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[3] = x[3];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddTo(ulong[] x, ulong[] z)
+#endif
         {
             z[0] ^= x[0];
             z[1] ^= x[1];
@@ -57,9 +85,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return Nat.FromBigInteger64(239, x);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void HalfTrace(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
 
             Nat256.Copy64(x, z);
             for (int i = 1; i < 239; i += 2)
@@ -72,15 +108,24 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Invert(ulong[] x, ulong[] z)
+#endif
         {
             if (Nat256.IsZero64(x))
                 throw new InvalidOperationException();
 
             // Itoh-Tsujii inversion
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> t0 = stackalloc ulong[4];
+            Span<ulong> t1 = stackalloc ulong[4];
+#else
             ulong[] t0 = Nat256.Create64();
             ulong[] t1 = Nat256.Create64();
+#endif
 
             Square(x, t0);
             Multiply(t0, x, t0);
@@ -109,21 +154,55 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Square(t0, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
         public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
+        public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
+        {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            zz[..8].Fill(0UL);
+#else
+            Array.Clear(zz, 0, 8);
+#endif
+            ImplMultiply(x, y, zz);
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
+#else
         public static void Reduce(ulong[] xx, ulong[] z)
+#endif
         {
             ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3];
             ulong x4 = xx[4], x5 = xx[5], x6 = xx[6], x7 = xx[7];
@@ -163,7 +242,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[zOff + 3]  = z3 & M47;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Sqrt(ulong[] x, ulong[] z)
+#endif
         {
             ulong c0 = Interleave.Unshuffle(x[0], x[1], out ulong e0);
             ulong c1 = Interleave.Unshuffle(x[2], x[3], out ulong e1);
@@ -173,9 +256,14 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c2  = (c0 >> 49) | (c1 << 15);
             c1 ^=              (c0 << 15);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+            Span<int> shifts = stackalloc int[] { 39, 120 };
+#else
             ulong[] tt = Nat256.CreateExt64();
-
             int[] shifts = { 39, 120 };
+#endif
+
             for (int i = 0; i < shifts.Length; ++i)
             {
                 int w = shifts[i] >> 6, s = shifts[i] & 63;
@@ -193,30 +281,58 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[1] ^= e1;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Square(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareAddToExt(ulong[] x, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplSquare(x, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareExt(ulong[] x, ulong[] zz)
+#endif
         {
             ImplSquare(x, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
+#else
         public static void SquareN(ulong[] x, int n, ulong[] z)
+#endif
         {
             Debug.Assert(n > 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[8];
+#else
             ulong[] tt = Nat256.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
 
@@ -227,13 +343,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static uint Trace(ReadOnlySpan<ulong> x)
+#else
         public static uint Trace(ulong[] x)
+#endif
         {
             // Non-zero-trace bits: 0, 81, 162
             return (uint)(x[0] ^ (x[1] >> 17) ^ (x[2] >> 34)) & 1U;
         }
 
-        protected static void ImplCompactExt(ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplCompactExt(Span<ulong> zz)
+#else
+        private static void ImplCompactExt(ulong[] zz)
+#endif
         {
             ulong z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4], z5 = zz[5], z6 = zz[6], z7 = zz[7];
             zz[0] =  z0        ^ (z1 << 60);
@@ -246,7 +370,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[7] = (z7 >> 28);
         }
 
-        protected static void ImplExpand(ulong[] x, ulong[] z)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplExpand(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
+        private static void ImplExpand(ulong[] x, ulong[] z)
+#endif
         {
             ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
             z[0] = x0 & M60;
@@ -255,10 +383,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[3] = ((x2 >> 52) ^ (x3 << 12));
         }
 
-        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
         {
 #if NETCOREAPP3_0_OR_GREATER
-            if (Pclmulqdq.IsSupported)
+            if (Pclmulqdq.IsSupported && BitConverter.IsLittleEndian && Unsafe.SizeOf<Vector128<ulong>>() == 16)
             {
                 var X01 = Vector128.Create(x[0], x[1]);
                 var X23 = Vector128.Create(x[2], x[3]);
@@ -272,35 +401,37 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                                    Pclmulqdq.CarrylessMultiply(X01, Y01, 0x10));
                 var Z23 =          Pclmulqdq.CarrylessMultiply(X01, Y01, 0x11);
 
+                Z01 = Sse2.Xor(Z01, Sse2.ShiftLeftLogical128BitLane (Z12, 8));
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftRightLogical128BitLane(Z12, 8));
+
                 var Z45 =          Pclmulqdq.CarrylessMultiply(X23, Y23, 0x00);
                 var Z56 = Sse2.Xor(Pclmulqdq.CarrylessMultiply(X23, Y23, 0x01),
                                    Pclmulqdq.CarrylessMultiply(X23, Y23, 0x10));
                 var Z67 =          Pclmulqdq.CarrylessMultiply(X23, Y23, 0x11);
 
+                Z45 = Sse2.Xor(Z45, Sse2.ShiftLeftLogical128BitLane (Z56, 8));
+                Z67 = Sse2.Xor(Z67, Sse2.ShiftRightLogical128BitLane(Z56, 8));
+
                 var K01 =          Pclmulqdq.CarrylessMultiply(X03, Y03, 0x00);
                 var K12 = Sse2.Xor(Pclmulqdq.CarrylessMultiply(X03, Y03, 0x01),
                                    Pclmulqdq.CarrylessMultiply(X03, Y03, 0x10));
                 var K23 =          Pclmulqdq.CarrylessMultiply(X03, Y03, 0x11);
 
-                K01 = Sse2.Xor(K01, Z01);
-                K12 = Sse2.Xor(K12, Z12);
-                K23 = Sse2.Xor(K23, Z23);
+                var T = Sse2.Xor(Z23, Z45);
 
-                K01 = Sse2.Xor(K01, Z45);
-                K12 = Sse2.Xor(K12, Z56);
-                K23 = Sse2.Xor(K23, Z67);
+                Z23 = Sse2.Xor(T, Z01);
+                Z45 = Sse2.Xor(T, Z67);
 
                 Z23 = Sse2.Xor(Z23, K01);
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftLeftLogical128BitLane (K12, 8));
+                Z45 = Sse2.Xor(Z45, Sse2.ShiftRightLogical128BitLane(K12, 8));
                 Z45 = Sse2.Xor(Z45, K23);
 
-                zz[0] = Z01.GetElement(0);
-                zz[1] = Z01.GetElement(1) ^ Z12.GetElement(0);
-                zz[2] = Z23.GetElement(0) ^ Z12.GetElement(1);
-                zz[3] = Z23.GetElement(1) ^ K12.GetElement(0);
-                zz[4] = Z45.GetElement(0) ^ K12.GetElement(1);
-                zz[5] = Z45.GetElement(1) ^ Z56.GetElement(0);
-                zz[6] = Z67.GetElement(0) ^ Z56.GetElement(1);
-                zz[7] = Z67.GetElement(1);
+                Span<byte> zzBytes = MemoryMarshal.AsBytes(zz);
+                MemoryMarshal.Write(zzBytes[0x00..0x10], ref Z01);
+                MemoryMarshal.Write(zzBytes[0x10..0x20], ref Z23);
+                MemoryMarshal.Write(zzBytes[0x20..0x30], ref Z45);
+                MemoryMarshal.Write(zzBytes[0x30..0x40], ref Z67);
                 return;
             }
 #endif
@@ -309,6 +440,56 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
              * "Two-level seven-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
              */
 
+            Span<ulong> f = stackalloc ulong[4], g = stackalloc ulong[4];
+            ImplExpand(x, f);
+            ImplExpand(y, g);
+
+            Span<ulong> u = stackalloc ulong[8];
+
+            ImplMulwAcc(u, f[0], g[0], zz[0..]);
+            ImplMulwAcc(u, f[1], g[1], zz[1..]);
+            ImplMulwAcc(u, f[2], g[2], zz[2..]);
+            ImplMulwAcc(u, f[3], g[3], zz[3..]);
+
+            // U *= (1 - t^n)
+            for (int i = 5; i > 0; --i)
+            {
+                zz[i] ^= zz[i - 1];
+            }
+
+            ImplMulwAcc(u, f[0] ^ f[1], g[0] ^ g[1], zz[1..]);
+            ImplMulwAcc(u, f[2] ^ f[3], g[2] ^ g[3], zz[3..]);
+
+            // V *= (1 - t^2n)
+            for (int i = 7; i > 1; --i)
+            {
+                zz[i] ^= zz[i - 2];
+            }
+
+            // Double-length recursion
+            {
+                ulong c0 = f[0] ^ f[2], c1 = f[1] ^ f[3];
+                ulong d0 = g[0] ^ g[2], d1 = g[1] ^ g[3];
+                ImplMulwAcc(u, c0 ^ c1, d0 ^ d1, zz[3..]);
+                Span<ulong> t = stackalloc ulong[3];
+                ImplMulwAcc(u, c0, d0, t[0..]);
+                ImplMulwAcc(u, c1, d1, t[1..]);
+                ulong t0 = t[0], t1 = t[1], t2 = t[2];
+                zz[2] ^= t0;
+                zz[3] ^= t0 ^ t1;
+                zz[4] ^= t2 ^ t1;
+                zz[5] ^= t2;
+            }
+
+            ImplCompactExt(zz);
+        }
+#else
+        private static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+        {
+            /*
+             * "Two-level seven-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
+             */
+
             ulong[] f = new ulong[4], g = new ulong[4];
             ImplExpand(x, f);
             ImplExpand(y, g);
@@ -352,8 +533,13 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             ImplCompactExt(zz);
         }
+#endif
 
-        protected static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMulwAcc(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
+#else
+        private static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#endif
         {
             Debug.Assert(x >> 60 == 0);
             Debug.Assert(y >> 60 == 0);
@@ -368,14 +554,14 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             u[7] = u[6] ^  y;
 
             uint j = (uint)x;
-            ulong g, h = 0, l = u[j & 7]
-                              ^ (u[(j >> 3) & 7] << 3);
+            ulong g, h = 0, l = u[(int)j & 7]
+                              ^ (u[(int)(j >> 3) & 7] << 3);
             int k = 54;
             do
             {
                 j  = (uint)(x >> k);
-                g  = u[j & 7]
-                   ^ u[(j >> 3) & 7] << 3;
+                g  = u[(int)j & 7]
+                   ^ u[(int)(j >> 3) & 7] << 3;
                 l ^= (g <<  k);
                 h ^= (g >> -k);
             }
@@ -385,28 +571,42 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             Debug.Assert(h >> 55 == 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            z[0] ^= l & M60;
+            z[1] ^= (l >> 60) ^ (h << 4);
+#else
             z[zOff    ] ^= l & M60;
             z[zOff + 1] ^= (l >> 60) ^ (h << 4);
+#endif
         }
 
-        protected static void ImplSquare(ulong[] x, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
+        private static void ImplSquare(ulong[] x, ulong[] zz)
+#endif
         {
 #if NETCOREAPP3_0_OR_GREATER
             if (Bmi2.X64.IsSupported)
             {
-                zz[7] = Bmi2.X64.ParallelBitDeposit(x[3] >> 32, 0x5555555555555555UL);
-                zz[6] = Bmi2.X64.ParallelBitDeposit(x[3]      , 0x5555555555555555UL);
-                zz[5] = Bmi2.X64.ParallelBitDeposit(x[2] >> 32, 0x5555555555555555UL);
-                zz[4] = Bmi2.X64.ParallelBitDeposit(x[2]      , 0x5555555555555555UL);
-                zz[3] = Bmi2.X64.ParallelBitDeposit(x[1] >> 32, 0x5555555555555555UL);
-                zz[2] = Bmi2.X64.ParallelBitDeposit(x[1]      , 0x5555555555555555UL);
-                zz[1] = Bmi2.X64.ParallelBitDeposit(x[0] >> 32, 0x5555555555555555UL);
-                zz[0] = Bmi2.X64.ParallelBitDeposit(x[0]      , 0x5555555555555555UL);
+                ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
+                zz[7] = Bmi2.X64.ParallelBitDeposit(x3 >> 32, 0x5555555555555555UL);
+                zz[6] = Bmi2.X64.ParallelBitDeposit(x3      , 0x5555555555555555UL);
+                zz[5] = Bmi2.X64.ParallelBitDeposit(x2 >> 32, 0x5555555555555555UL);
+                zz[4] = Bmi2.X64.ParallelBitDeposit(x2      , 0x5555555555555555UL);
+                zz[3] = Bmi2.X64.ParallelBitDeposit(x1 >> 32, 0x5555555555555555UL);
+                zz[2] = Bmi2.X64.ParallelBitDeposit(x1      , 0x5555555555555555UL);
+                zz[1] = Bmi2.X64.ParallelBitDeposit(x0 >> 32, 0x5555555555555555UL);
+                zz[0] = Bmi2.X64.ParallelBitDeposit(x0      , 0x5555555555555555UL);
                 return;
             }
 #endif
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Interleave.Expand64To128(x[..4], zz[..8]);
+#else
             Interleave.Expand64To128(x, 0, 4, zz, 0);
+#endif
         }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/SecT239K1Point.cs b/crypto/src/math/ec/custom/sec/SecT239K1Point.cs
index a57519d2b..36056744a 100644
--- a/crypto/src/math/ec/custom/sec/SecT239K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecT239K1Point.cs
@@ -82,7 +82,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             SecT239FieldElement L1 = (SecT239FieldElement)this.RawYCoord, Z1 = (SecT239FieldElement)this.RawZCoords[0];
             SecT239FieldElement L2 = (SecT239FieldElement)b.RawYCoord, Z2 = (SecT239FieldElement)b.RawZCoords[0];
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt0 = stackalloc ulong[8];
+#else
             ulong[] tt0 = Nat256.CreateExt64();
+#endif
             ulong[] t1 = Nat256.Create64();
             ulong[] t2 = Nat256.Create64();
             ulong[] t3 = Nat256.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT283Field.cs b/crypto/src/math/ec/custom/sec/SecT283Field.cs
index 332e47afe..498a72c81 100644
--- a/crypto/src/math/ec/custom/sec/SecT283Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT283Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 #if NETCOREAPP3_0_OR_GREATER
+using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
 using System.Runtime.Intrinsics;
 using System.Runtime.Intrinsics.X86;
 #endif
@@ -9,7 +11,7 @@ using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
-    internal class SecT283Field
+    internal static class SecT283Field
     {
         private const ulong M27 = ulong.MaxValue >> 37;
         private const ulong M57 = ulong.MaxValue >> 7;
@@ -17,7 +19,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
         private static readonly ulong[] ROOT_Z = new ulong[]{ 0x0C30C30C30C30808UL, 0x30C30C30C30C30C3UL,
             0x820820820820830CUL, 0x0820820820820820UL, 0x2082082UL };
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Add(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ y[0];
             z[1] = x[1] ^ y[1];
@@ -26,7 +32,24 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[4] = x[4] ^ y[4];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
+        public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
+#endif
+        {
+            z[0] ^= x[0] ^ y[0];
+            z[1] ^= x[1] ^ y[1];
+            z[2] ^= x[2] ^ y[2];
+            z[3] ^= x[3] ^ y[3];
+            z[4] ^= x[4] ^ y[4];
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
+#else
         public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+#endif
         {
             zz[0] = xx[0] ^ yy[0];
             zz[1] = xx[1] ^ yy[1];
@@ -39,7 +62,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[8] = xx[8] ^ yy[8];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddOne(ulong[] x, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ 1UL;
             z[1] = x[1];
@@ -48,7 +75,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[4] = x[4];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddTo(ulong[] x, ulong[] z)
+#endif
         {
             z[0] ^= x[0];
             z[1] ^= x[1];
@@ -62,9 +93,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return Nat.FromBigInteger64(283, x);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void HalfTrace(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[9];
+#else
             ulong[] tt = Nat.Create64(9);
+#endif
 
             Nat320.Copy64(x, z);
             for (int i = 1; i < 283; i += 2)
@@ -77,15 +116,24 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Invert(ulong[] x, ulong[] z)
+#endif
         {
             if (Nat320.IsZero64(x))
                 throw new InvalidOperationException();
 
             // Itoh-Tsujii inversion
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> t0 = stackalloc ulong[5];
+            Span<ulong> t1 = stackalloc ulong[5];
+#else
             ulong[] t0 = Nat320.Create64();
             ulong[] t1 = Nat320.Create64();
+#endif
 
             Square(x, t0);
             Multiply(t0, x, t0);
@@ -112,21 +160,55 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Square(t1, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[10];
+#else
             ulong[] tt = Nat320.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
         public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[10];
+#else
             ulong[] tt = Nat320.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
+        public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
+        {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            zz[..10].Fill(0UL);
+#else
+            Array.Clear(zz, 0, 10);
+#endif
+            ImplMultiply(x, y, zz);
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
+#else
         public static void Reduce(ulong[] xx, ulong[] z)
+#endif
         {
             ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4];
             ulong x5 = xx[5], x6 = xx[6], x7 = xx[7], x8 = xx[8];
@@ -158,9 +240,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[zOff + 4]  = z4 & M27;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Sqrt(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> odd = stackalloc ulong[5];
+#else
             ulong[] odd = Nat320.Create64();
+#endif
 
             odd[0] = Interleave.Unshuffle(x[0], x[1], out ulong e0);
             odd[1] = Interleave.Unshuffle(x[2], x[3], out ulong e1);
@@ -173,30 +263,58 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[2] ^= e2;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Square(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[9];
+#else
             ulong[] tt = Nat.Create64(9);
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareAddToExt(ulong[] x, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[9];
+#else
             ulong[] tt = Nat.Create64(9);
+#endif
             ImplSquare(x, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareExt(ulong[] x, ulong[] zz)
+#endif
         {
             ImplSquare(x, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
+#else
         public static void SquareN(ulong[] x, int n, ulong[] z)
+#endif
         {
             Debug.Assert(n > 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[9];
+#else
             ulong[] tt = Nat.Create64(9);
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
 
@@ -207,13 +325,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static uint Trace(ReadOnlySpan<ulong> x)
+#else
         public static uint Trace(ulong[] x)
+#endif
         {
             // Non-zero-trace bits: 0, 271
             return (uint)(x[0] ^ (x[4] >> 15)) & 1U;
         }
 
-        protected static void ImplCompactExt(ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplCompactExt(Span<ulong> zz)
+#else
+        private static void ImplCompactExt(ulong[] zz)
+#endif
         {
             ulong z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4];
             ulong z5 = zz[5], z6 = zz[6], z7 = zz[7], z8 = zz[8], z9 = zz[9];
@@ -229,7 +355,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             zz[9] = (z9 >> 63); // Zero!
         }
 
-        protected static void ImplExpand(ulong[] x, ulong[] z)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplExpand(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
+        private static void ImplExpand(ulong[] x, ulong[] z)
+#endif
         {
             ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4];
             z[0] = x0 & M57;
@@ -239,7 +369,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[4] = ((x3 >> 36) ^ (x4 << 28));
         }
 
-        //protected static void AddMs(ulong[] zz, int zOff, ulong[] p, params int[] ms)
+        //private static void AddMs(ulong[] zz, int zOff, ulong[] p, params int[] ms)
         //{
         //    ulong t0 = 0, t1 = 0;
         //    foreach (int m in ms)
@@ -252,10 +382,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
         //    zz[zOff + 1] ^= t1;
         //}
 
-        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
         {
 #if NETCOREAPP3_0_OR_GREATER
-            if (Pclmulqdq.IsSupported)
+            if (Pclmulqdq.IsSupported && BitConverter.IsLittleEndian && Unsafe.SizeOf<Vector128<ulong>>() == 16)
             {
                 var X01 = Vector128.Create(x[0], x[1]);
                 var X23 = Vector128.Create(x[2], x[3]);
@@ -290,16 +421,24 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                                    Pclmulqdq.CarrylessMultiply(X4_, Y23, 0x10));
                 var Z89 =          Pclmulqdq.CarrylessMultiply(X4_, Y4_, 0x00);
 
-                zz[0] = Z01.GetElement(0);
-                zz[1] = Z01.GetElement(1) ^ Z12.GetElement(0);
-                zz[2] = Z23.GetElement(0) ^ Z12.GetElement(1);
-                zz[3] = Z23.GetElement(1) ^ Z34.GetElement(0);
-                zz[4] = Z45.GetElement(0) ^ Z34.GetElement(1);
-                zz[5] = Z45.GetElement(1) ^ Z56.GetElement(0);
-                zz[6] = Z67.GetElement(0) ^ Z56.GetElement(1);
-                zz[7] = Z67.GetElement(1) ^ Z78.GetElement(0);
-                zz[8] = Z89.GetElement(0) ^ Z78.GetElement(1);
-                zz[9] = Z89.GetElement(1);
+                Z01 = Sse2.Xor(Z01, Sse2.ShiftLeftLogical128BitLane (Z12, 8));
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftRightLogical128BitLane(Z12, 8));
+
+                Z23 = Sse2.Xor(Z23, Sse2.ShiftLeftLogical128BitLane (Z34, 8));
+                Z45 = Sse2.Xor(Z45, Sse2.ShiftRightLogical128BitLane(Z34, 8));
+
+                Z45 = Sse2.Xor(Z45, Sse2.ShiftLeftLogical128BitLane (Z56, 8));
+                Z67 = Sse2.Xor(Z67, Sse2.ShiftRightLogical128BitLane(Z56, 8));
+
+                Z67 = Sse2.Xor(Z67, Sse2.ShiftLeftLogical128BitLane (Z78, 8));
+                Z89 = Sse2.Xor(Z89, Sse2.ShiftRightLogical128BitLane(Z78, 8));
+
+                Span<byte> zzBytes = MemoryMarshal.AsBytes(zz);
+                MemoryMarshal.Write(zzBytes[0x00..0x10], ref Z01);
+                MemoryMarshal.Write(zzBytes[0x10..0x20], ref Z23);
+                MemoryMarshal.Write(zzBytes[0x20..0x30], ref Z45);
+                MemoryMarshal.Write(zzBytes[0x30..0x40], ref Z67);
+                MemoryMarshal.Write(zzBytes[0x40..0x50], ref Z89);
                 return;
             }
 #endif
@@ -314,6 +453,131 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             ImplExpand(x, a);
             ImplExpand(y, b);
 
+            Span<ulong> u = zz;
+            Span<ulong> p = stackalloc ulong[26];
+
+            ImplMulw(u, a[0], b[0], p[0..]);                // m1
+            ImplMulw(u, a[1], b[1], p[2..]);                // m2
+            ImplMulw(u, a[2], b[2], p[4..]);                // m3
+            ImplMulw(u, a[3], b[3], p[6..]);                // m4
+            ImplMulw(u, a[4], b[4], p[8..]);                // m5
+
+            ulong u0 = a[0] ^ a[1], v0 = b[0] ^ b[1];
+            ulong u1 = a[0] ^ a[2], v1 = b[0] ^ b[2];
+            ulong u2 = a[2] ^ a[4], v2 = b[2] ^ b[4];
+            ulong u3 = a[3] ^ a[4], v3 = b[3] ^ b[4];
+
+            ImplMulw(u, u1 ^ a[3], v1 ^ b[3], p[18..]);     // m10
+            ImplMulw(u, u2 ^ a[1], v2 ^ b[1], p[20..]);     // m11
+
+            ulong A4 = u0 ^ u3  , B4 = v0 ^ v3;
+            ulong A5 = A4 ^ a[2], B5 = B4 ^ b[2];
+
+            ImplMulw(u, A4, B4, p[22..]);                   // m12
+            ImplMulw(u, A5, B5, p[24..]);                   // m13
+
+            ImplMulw(u, u0, v0, p[10..]);                   // m6
+            ImplMulw(u, u1, v1, p[12..]);                   // m7
+            ImplMulw(u, u2, v2, p[14..]);                   // m8
+            ImplMulw(u, u3, v3, p[16..]);                   // m9
+
+
+            // Original method, corresponding to formula (16)
+            //AddMs(zz, 0, p, 1);
+            //AddMs(zz, 1, p, 1, 2, 6);
+            //AddMs(zz, 2, p, 1, 2, 3, 7);
+            //AddMs(zz, 3, p, 1, 3, 4, 5, 8, 10, 12, 13);
+            //AddMs(zz, 4, p, 1, 2, 4, 5, 6, 9, 10, 11, 13);
+            //AddMs(zz, 5, p, 1, 2, 3, 5, 7, 11, 12, 13);
+            //AddMs(zz, 6, p, 3, 4, 5, 8);
+            //AddMs(zz, 7, p, 4, 5, 9);
+            //AddMs(zz, 8, p, 5);
+
+            // Improved method factors out common single-word terms
+            // NOTE: p1,...,p26 in the paper maps to p[0],...,p[25] here
+
+            zz[0]     = p[ 0];
+            zz[9]     = p[ 9];
+
+            ulong t1  = p[ 0] ^ p[ 1];
+            ulong t2  = t1    ^ p[ 2];
+            ulong t3  = t2    ^ p[10];
+        
+            zz[1]     = t3;
+
+            ulong t4  = p[ 3] ^ p[ 4];
+            ulong t5  = p[11] ^ p[12];
+            ulong t6  = t4    ^ t5;
+            ulong t7  = t2    ^ t6;
+
+            zz[2]     = t7;
+
+            ulong t8  = t1    ^ t4;
+            ulong t9  = p[ 5] ^ p[ 6];
+            ulong t10 = t8    ^ t9;
+            ulong t11 = t10   ^ p[ 8];
+            ulong t12 = p[13] ^ p[14];
+            ulong t13 = t11   ^ t12;
+            ulong t14 = p[18] ^ p[22];
+            ulong t15 = t14   ^ p[24];
+            ulong t16 = t13   ^ t15;
+
+            zz[3]     = t16;
+
+            ulong t17 = p[ 7] ^ p[ 8];
+            ulong t18 = t17   ^ p[ 9];
+            ulong t19 = t18   ^ p[17];
+
+            zz[8]     = t19;
+
+            ulong t20 = t18   ^ t9;
+            ulong t21 = p[15] ^ p[16];
+            ulong t22 = t20   ^ t21;
+
+            zz[7]     = t22;
+
+            ulong t23 = t22   ^ t3;
+            ulong t24 = p[19] ^ p[20];
+    //      ulong t25 = p[23] ^ p[24];
+            ulong t25 = p[25] ^ p[24];       // Fixes an error in the paper: p[23] -> p{25]
+            ulong t26 = p[18] ^ p[23];
+            ulong t27 = t24   ^ t25;
+            ulong t28 = t27   ^ t26;
+            ulong t29 = t28   ^ t23;
+
+            zz[4]     = t29;
+        
+            ulong t30 = t7    ^ t19;
+            ulong t31 = t27   ^ t30;
+            ulong t32 = p[21] ^ p[22];
+            ulong t33 = t31   ^ t32;
+
+            zz[5]     = t33;
+
+            ulong t34 = t11   ^ p[0];
+            ulong t35 = t34   ^ p[9];
+            ulong t36 = t35   ^ t12;
+            ulong t37 = t36   ^ p[21];
+            ulong t38 = t37   ^ p[23];
+            ulong t39 = t38   ^ p[25];
+
+            zz[6]     = t39;
+
+            ImplCompactExt(zz);
+        }
+#else
+        private static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+        {
+            /*
+             * Formula (17) from "Some New Results on Binary Polynomial Multiplication",
+             * Murat Cenk and M. Anwar Hasan.
+             * 
+             * The formula as given contained an error in the term t25, as noted below
+             */
+            ulong[] a = new ulong[5], b = new ulong[5];
+            ImplExpand(x, a);
+            ImplExpand(y, b);
+
             ulong[] u = zz;
             ulong[] p = new ulong[26];
 
@@ -426,8 +690,13 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             ImplCompactExt(zz);
         }
+#endif
 
-        protected static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMulw(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
+#else
+        private static void ImplMulw(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#endif
         {
             Debug.Assert(x >> 57 == 0);
             Debug.Assert(y >> 57 == 0);
@@ -442,14 +711,14 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             u[7] = u[6] ^  y;
 
             uint j = (uint)x;
-            ulong g, h = 0, l = u[j & 7];
+            ulong g, h = 0, l = u[(int)j & 7];
             int k = 48;
             do
             {
                 j  = (uint)(x >> k);
-                g  = u[j & 7]
-                   ^ u[(j >> 3) & 7] << 3
-                   ^ u[(j >> 6) & 7] << 6;
+                g  = u[(int)j & 7]
+                   ^ u[(int)(j >> 3) & 7] << 3
+                   ^ u[(int)(j >> 6) & 7] << 6;
                 l ^= (g <<  k);
                 h ^= (g >> -k);
             }
@@ -459,11 +728,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             Debug.Assert(h >> 49 == 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            z[0] ^= l & M57;
+            z[1] ^= (l >> 57) ^ (h << 7);
+#else
             z[zOff    ] = l & M57;
             z[zOff + 1] = (l >> 57) ^ (h << 7);
+#endif
         }
 
-        protected static void ImplSquare(ulong[] x, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
+        private static void ImplSquare(ulong[] x, ulong[] zz)
+#endif
         {
             zz[8] = Interleave.Expand32to64((uint)x[4]);
 
@@ -482,7 +760,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
 #endif
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Interleave.Expand64To128(x[..4], zz[..8]);
+#else
             Interleave.Expand64To128(x, 0, 4, zz, 0);
+#endif
         }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/SecT283K1Point.cs b/crypto/src/math/ec/custom/sec/SecT283K1Point.cs
index 440c5d348..00f7e1e83 100644
--- a/crypto/src/math/ec/custom/sec/SecT283K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecT283K1Point.cs
@@ -82,7 +82,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             SecT283FieldElement L1 = (SecT283FieldElement)this.RawYCoord, Z1 = (SecT283FieldElement)this.RawZCoords[0];
             SecT283FieldElement L2 = (SecT283FieldElement)b.RawYCoord, Z2 = (SecT283FieldElement)b.RawZCoords[0];
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt0 = stackalloc ulong[9];
+#else
             ulong[] tt0 = Nat.Create64(9);
+#endif
             ulong[] t1 = Nat320.Create64();
             ulong[] t2 = Nat320.Create64();
             ulong[] t3 = Nat320.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT409Field.cs b/crypto/src/math/ec/custom/sec/SecT409Field.cs
index c497d0223..6a5afb0dc 100644
--- a/crypto/src/math/ec/custom/sec/SecT409Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT409Field.cs
@@ -9,12 +9,16 @@ using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
-    internal class SecT409Field
+    internal static class SecT409Field
     {
         private const ulong M25 = ulong.MaxValue >> 39;
         private const ulong M59 = ulong.MaxValue >> 5;
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Add(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ y[0];
             z[1] = x[1] ^ y[1];
@@ -25,7 +29,26 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[6] = x[6] ^ y[6];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
+        public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
+#endif
+        {
+            z[0] ^= x[0] ^ y[0];
+            z[1] ^= x[1] ^ y[1];
+            z[2] ^= x[2] ^ y[2];
+            z[3] ^= x[3] ^ y[3];
+            z[4] ^= x[4] ^ y[4];
+            z[5] ^= x[5] ^ y[5];
+            z[6] ^= x[6] ^ y[6];
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
+#else
         public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+#endif
         {
             for (int i = 0; i < 13; ++i)
             {
@@ -33,7 +56,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddOne(ulong[] x, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ 1UL;
             z[1] = x[1];
@@ -44,7 +71,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[6] = x[6];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddTo(ulong[] x, ulong[] z)
+#endif
         {
             z[0] ^= x[0];
             z[1] ^= x[1];
@@ -60,9 +91,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return Nat.FromBigInteger64(409, x);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void HalfTrace(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[13];
+#else
             ulong[] tt = Nat.Create64(13);
+#endif
 
             Nat448.Copy64(x, z);
             for (int i = 1; i < 409; i += 2)
@@ -75,16 +114,26 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Invert(ulong[] x, ulong[] z)
+#endif
         {
             if (Nat448.IsZero64(x))
                 throw new InvalidOperationException();
 
             // Itoh-Tsujii inversion with bases { 2, 3 }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> t0 = stackalloc ulong[7];
+            Span<ulong> t1 = stackalloc ulong[7];
+            Span<ulong> t2 = stackalloc ulong[7];
+#else
             ulong[] t0 = Nat448.Create64();
             ulong[] t1 = Nat448.Create64();
             ulong[] t2 = Nat448.Create64();
+#endif
 
             Square(x, t0);
 
@@ -126,21 +175,55 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Multiply(t0, t2, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[14];
+#else
             ulong[] tt = Nat448.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
         public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[14];
+#else
             ulong[] tt = Nat448.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
+        public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
+        {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            zz[..14].Fill(0UL);
+#else
+            Array.Clear(zz, 0, 10);
+#endif
+            ImplMultiply(x, y, zz);
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
+#else
         public static void Reduce(ulong[] xx, ulong[] z)
+#endif
         {
             ulong x00 = xx[0], x01 = xx[1], x02 = xx[2], x03 = xx[3];
             ulong x04 = xx[4], x05 = xx[5], x06 = xx[6], x07 = xx[7];
@@ -193,7 +276,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[zOff + 6]  = z6 & M25;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Sqrt(ulong[] x, ulong[] z)
+#endif
         {
             ulong c0 = Interleave.Unshuffle(x[0], x[1], out ulong e0);
             ulong c1 = Interleave.Unshuffle(x[2], x[3], out ulong e1);
@@ -211,30 +298,58 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Debug.Assert((c3 >> 51) == 0);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Square(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[13];
+#else
             ulong[] tt = Nat.Create64(13);
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareAddToExt(ulong[] x, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[13];
+#else
             ulong[] tt = Nat.Create64(13);
+#endif
             ImplSquare(x, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareExt(ulong[] x, ulong[] zz)
+#endif
         {
             ImplSquare(x, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
+#else
         public static void SquareN(ulong[] x, int n, ulong[] z)
+#endif
         {
             Debug.Assert(n > 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[13];
+#else
             ulong[] tt = Nat.Create64(13);
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
 
@@ -245,13 +360,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static uint Trace(ReadOnlySpan<ulong> x)
+#else
         public static uint Trace(ulong[] x)
+#endif
         {
             // Non-zero-trace bits: 0
             return (uint)(x[0]) & 1U;
         }
 
-        protected static void ImplCompactExt(ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplCompactExt(Span<ulong> zz)
+#else
+        private static void ImplCompactExt(ulong[] zz)
+#endif
         {
             ulong z00 = zz[ 0], z01 = zz[ 1], z02 = zz[ 2], z03 = zz[ 3], z04 = zz[ 4], z05 = zz[ 5], z06 = zz[ 6];
             ulong z07 = zz[ 7], z08 = zz[ 8], z09 = zz[ 9], z10 = zz[10], z11 = zz[11], z12 = zz[12], z13 = zz[13];
@@ -272,7 +395,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             //zz[13] = 0;
         }
 
-        protected static void ImplExpand(ulong[] x, ulong[] z)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplExpand(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
+        private static void ImplExpand(ulong[] x, ulong[] z)
+#endif
         {
             ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6];
             z[0] = x0 & M59;
@@ -284,7 +411,72 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[6] = ((x5 >> 34) ^ (x6 << 30));
         }
 
-        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+        {
+            Span<ulong> a = stackalloc ulong[7], b = stackalloc ulong[7];
+            ImplExpand(x, a);
+            ImplExpand(y, b);
+
+            Span<ulong> u = stackalloc ulong[8];
+            for (int i = 0; i < 7; ++i)
+            {
+                ImplMulwAcc(u, a[i], b[i], zz[(i << 1)..]);
+            }
+
+            ulong v0 = zz[0], v1 = zz[1];
+            v0 ^= zz[ 2]; zz[1] = v0 ^ v1; v1 ^= zz[ 3];
+            v0 ^= zz[ 4]; zz[2] = v0 ^ v1; v1 ^= zz[ 5];
+            v0 ^= zz[ 6]; zz[3] = v0 ^ v1; v1 ^= zz[ 7];
+            v0 ^= zz[ 8]; zz[4] = v0 ^ v1; v1 ^= zz[ 9];
+            v0 ^= zz[10]; zz[5] = v0 ^ v1; v1 ^= zz[11];
+            v0 ^= zz[12]; zz[6] = v0 ^ v1; v1 ^= zz[13];
+
+            ulong w = v0 ^ v1;
+            zz[ 7] = zz[0] ^ w;
+            zz[ 8] = zz[1] ^ w;
+            zz[ 9] = zz[2] ^ w;
+            zz[10] = zz[3] ^ w;
+            zz[11] = zz[4] ^ w;
+            zz[12] = zz[5] ^ w;
+            zz[13] = zz[6] ^ w;
+
+            ImplMulwAcc(u, a[0] ^ a[1], b[0] ^ b[1], zz[ 1..]);
+
+            ImplMulwAcc(u, a[0] ^ a[2], b[0] ^ b[2], zz[ 2..]);
+
+            ImplMulwAcc(u, a[0] ^ a[3], b[0] ^ b[3], zz[ 3..]);
+            ImplMulwAcc(u, a[1] ^ a[2], b[1] ^ b[2], zz[ 3..]);
+
+            ImplMulwAcc(u, a[0] ^ a[4], b[0] ^ b[4], zz[ 4..]);
+            ImplMulwAcc(u, a[1] ^ a[3], b[1] ^ b[3], zz[ 4..]);
+
+            ImplMulwAcc(u, a[0] ^ a[5], b[0] ^ b[5], zz[ 5..]);
+            ImplMulwAcc(u, a[1] ^ a[4], b[1] ^ b[4], zz[ 5..]);
+            ImplMulwAcc(u, a[2] ^ a[3], b[2] ^ b[3], zz[ 5..]);
+
+            ImplMulwAcc(u, a[0] ^ a[6], b[0] ^ b[6], zz[ 6..]);
+            ImplMulwAcc(u, a[1] ^ a[5], b[1] ^ b[5], zz[ 6..]);
+            ImplMulwAcc(u, a[2] ^ a[4], b[2] ^ b[4], zz[ 6..]);
+
+            ImplMulwAcc(u, a[1] ^ a[6], b[1] ^ b[6], zz[ 7..]);
+            ImplMulwAcc(u, a[2] ^ a[5], b[2] ^ b[5], zz[ 7..]);
+            ImplMulwAcc(u, a[3] ^ a[4], b[3] ^ b[4], zz[ 7..]);
+
+            ImplMulwAcc(u, a[2] ^ a[6], b[2] ^ b[6], zz[ 8..]);
+            ImplMulwAcc(u, a[3] ^ a[5], b[3] ^ b[5], zz[ 8..]);
+
+            ImplMulwAcc(u, a[3] ^ a[6], b[3] ^ b[6], zz[ 9..]);
+            ImplMulwAcc(u, a[4] ^ a[5], b[4] ^ b[5], zz[ 9..]);
+
+            ImplMulwAcc(u, a[4] ^ a[6], b[4] ^ b[6], zz[10..]);
+
+            ImplMulwAcc(u, a[5] ^ a[6], b[5] ^ b[6], zz[11..]);
+
+            ImplCompactExt(zz);
+        }
+#else
+        private static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
         {
             ulong[] a = new ulong[7], b = new ulong[7];
             ImplExpand(x, a);
@@ -347,8 +539,13 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             ImplCompactExt(zz);
         }
+#endif
 
-        protected static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMulwAcc(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
+#else
+        private static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#endif
         {
             Debug.Assert(x >> 59 == 0);
             Debug.Assert(y >> 59 == 0);
@@ -361,8 +558,8 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                 var Z = Pclmulqdq.CarrylessMultiply(X, Y, 0x00);
                 ulong z0 = Z.GetElement(0);
                 ulong z1 = Z.GetElement(1);
-                z[zOff    ] ^= z0 & M59;
-                z[zOff + 1] ^= (z0 >> 59) ^ (z1 << 5);
+                z[0] ^= z0 & M59;
+                z[1] ^= (z0 >> 59) ^ (z1 << 5);
                 return;
             }
 #endif
@@ -377,14 +574,14 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             u[7] = u[6] ^  y;
 
             uint j = (uint)x;
-            ulong g, h = 0, l = u[j & 7]
-                              ^ (u[(j >> 3) & 7] << 3);
+            ulong g, h = 0, l = u[(int)j & 7]
+                              ^ (u[(int)(j >> 3) & 7] << 3);
             int k = 54;
             do
             {
                 j  = (uint)(x >> k);
-                g  = u[j & 7]
-                   ^ u[(j >> 3) & 7] << 3;
+                g  = u[(int)j & 7]
+                   ^ u[(int)(j >> 3) & 7] << 3;
                 l ^= (g << k);
                 h ^= (g >> -k);
             }
@@ -392,11 +589,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             Debug.Assert(h >> 53 == 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            z[0] ^= l & M59;
+            z[1] ^= (l >> 59) ^ (h << 5);
+#else
             z[zOff    ] ^= l & M59;
             z[zOff + 1] ^= (l >> 59) ^ (h << 5);
+#endif
         }
 
-        protected static void ImplSquare(ulong[] x, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
+        private static void ImplSquare(ulong[] x, ulong[] zz)
+#endif
         {
             zz[12] = Interleave.Expand32to64((uint)x[6]);
 
@@ -419,7 +625,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
 #endif
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Interleave.Expand64To128(x[..6], zz[..12]);
+#else
             Interleave.Expand64To128(x, 0, 6, zz, 0);
+#endif
         }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/SecT409K1Point.cs b/crypto/src/math/ec/custom/sec/SecT409K1Point.cs
index 86a02896c..0200de5df 100644
--- a/crypto/src/math/ec/custom/sec/SecT409K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecT409K1Point.cs
@@ -82,7 +82,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             SecT409FieldElement L1 = (SecT409FieldElement)this.RawYCoord, Z1 = (SecT409FieldElement)this.RawZCoords[0];
             SecT409FieldElement L2 = (SecT409FieldElement)b.RawYCoord, Z2 = (SecT409FieldElement)b.RawZCoords[0];
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt0 = stackalloc ulong[13];
+#else
             ulong[] tt0 = Nat.Create64(13);
+#endif
             ulong[] t1 = Nat448.Create64();
             ulong[] t2 = Nat448.Create64();
             ulong[] t3 = Nat448.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT571Field.cs b/crypto/src/math/ec/custom/sec/SecT571Field.cs
index b09a86ac3..e970027a5 100644
--- a/crypto/src/math/ec/custom/sec/SecT571Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecT571Field.cs
@@ -9,7 +9,7 @@ using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
-    internal class SecT571Field
+    internal static class SecT571Field
     {
         private const ulong M59 = ulong.MaxValue >> 5;
 
@@ -17,7 +17,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             0xCAF84657C232BE11UL, 0x657C232BE1195F08UL, 0xF84657C2308CAF84UL, 0x7C232BE1195F08CAUL,
             0xBE1195F08CAF8465UL, 0x5F08CAF84657C232UL, 0x784657C232BE119UL };
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Add(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Add(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             Nat.Xor64(9, x, y, z);
         }
@@ -27,7 +31,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Nat.Xor64(9, x, xOff, y, yOff, z, zOff);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddBothTo(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void AddBothTo(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
             for (int i = 0; i < 9; ++i)
             {
@@ -43,12 +51,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddExt(ReadOnlySpan<ulong> xx, ReadOnlySpan<ulong> yy, Span<ulong> zz)
+#else
         public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+#endif
         {
             Nat.Xor64(18, xx, yy, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddOne(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddOne(ulong[] x, ulong[] z)
+#endif
         {
             z[0] = x[0] ^ 1UL;
             for (int i = 1; i < 9; ++i)
@@ -57,7 +73,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void AddTo(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void AddTo(ulong[] x, ulong[] z)
+#endif
         {
             Nat.XorTo64(9, x, z);
         }
@@ -67,9 +87,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return Nat.FromBigInteger64(571, x);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void HalfTrace(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void HalfTrace(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
 
             Nat576.Copy64(x, z);
             for (int i = 1; i < 571; i += 2)
@@ -82,16 +110,26 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Invert(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Invert(ulong[] x, ulong[] z)
+#endif
         {
             if (Nat576.IsZero64(x))
                 throw new InvalidOperationException();
 
             // Itoh-Tsujii inversion with bases { 2, 3, 5 }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> t0 = stackalloc ulong[9];
+            Span<ulong> t1 = stackalloc ulong[9];
+            Span<ulong> t2 = stackalloc ulong[9];
+#else
             ulong[] t0 = Nat576.Create64();
             ulong[] t1 = Nat576.Create64();
             ulong[] t2 = Nat576.Create64();
+#endif
 
             Square(x, t2);
 
@@ -133,35 +171,85 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Multiply(t0, t2, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Multiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> z)
+#else
         public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyAddToExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
         public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
             ImplMultiply(x, y, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyExt(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+#else
+        public static void MultiplyExt(ulong[] x, ulong[] y, ulong[] zz)
+#endif
+        {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            zz[..18].Fill(0UL);
+#else
+            Array.Clear(zz, 0, 18);
+#endif
+            ImplMultiply(x, y, zz);
+        }
+
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyPrecomp(ReadOnlySpan<ulong> x, ulong[] precomp, Span<ulong> z)
+#else
         public static void MultiplyPrecomp(ulong[] x, ulong[] precomp, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
             ImplMultiplyPrecomp(x, precomp, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void MultiplyPrecompAddToExt(ReadOnlySpan<ulong> x, ulong[] precomp, Span<ulong> zz)
+#else
         public static void MultiplyPrecompAddToExt(ulong[] x, ulong[] precomp, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
             ImplMultiplyPrecomp(x, precomp, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static ulong[] PrecompMultiplicand(ReadOnlySpan<ulong> x)
+#else
         public static ulong[] PrecompMultiplicand(ulong[] x)
+#endif
         {
 #if NETCOREAPP3_0_OR_GREATER
             ulong[] z = Nat576.Create64();
@@ -173,7 +261,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
              */
             int len = 9 << 4;
             ulong[] t = new ulong[len << 1];
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            x[..9].CopyTo(t.AsSpan(9));
+#else
             Array.Copy(x, 0, t, 9, 9);
+#endif
             //Reduce5(t, 9);
             int tOff = 0;
             for (int i = 7; i > 0; --i)
@@ -193,7 +285,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 #endif
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Reduce(ReadOnlySpan<ulong> xx, Span<ulong> z)
+#else
         public static void Reduce(ulong[] xx, ulong[] z)
+#endif
         {
             ulong xx09 = xx[9];
             ulong u = xx[17], v = xx09;
@@ -225,9 +321,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[zOff + 8]  = z8 & M59;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Sqrt(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Sqrt(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> evn = stackalloc ulong[9], odd = stackalloc ulong[9];
+#else
             ulong[] evn = Nat576.Create64(), odd = Nat576.Create64();
+#endif
 
             odd[0] = Interleave.Unshuffle(x[0], x[1], out evn[0]);
             odd[1] = Interleave.Unshuffle(x[2], x[3], out evn[1]);
@@ -239,30 +343,58 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Add(z, evn, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Square(ReadOnlySpan<ulong> x, Span<ulong> z)
+#else
         public static void Square(ulong[] x, ulong[] z)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareAddToExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareAddToExt(ulong[] x, ulong[] zz)
+#endif
         {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
             ImplSquare(x, tt);
             AddExt(zz, tt, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareExt(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
         public static void SquareExt(ulong[] x, ulong[] zz)
+#endif
         {
             ImplSquare(x, zz);
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void SquareN(ReadOnlySpan<ulong> x, int n, Span<ulong> z)
+#else
         public static void SquareN(ulong[] x, int n, ulong[] z)
+#endif
         {
             Debug.Assert(n > 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
             ImplSquare(x, tt);
             Reduce(tt, z);
 
@@ -273,13 +405,103 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static uint Trace(ReadOnlySpan<ulong> x)
+#else
         public static uint Trace(ulong[] x)
+#endif
         {
             // Non-zero-trace bits: 0, 561, 569
             return (uint)(x[0] ^ (x[8] >> 49) ^ (x[8] >> 57)) & 1U;
         }
 
-        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiply(ReadOnlySpan<ulong> x, ReadOnlySpan<ulong> y, Span<ulong> zz)
+        {
+            //ulong[] precomp = PrecompMultiplicand(y);
+
+            //ImplMultiplyPrecomp(x, precomp, zz);
+
+            ulong[] u = new ulong[16];
+            for (int i = 0; i < 9; ++i)
+            {
+                ImplMulwAcc(u, x[i], y[i], zz[(i << 1)..]);
+            }
+
+            ulong v0 = zz[0], v1 = zz[1];
+            v0 ^= zz[ 2]; zz[1] = v0 ^ v1; v1 ^= zz[ 3];
+            v0 ^= zz[ 4]; zz[2] = v0 ^ v1; v1 ^= zz[ 5];
+            v0 ^= zz[ 6]; zz[3] = v0 ^ v1; v1 ^= zz[ 7];
+            v0 ^= zz[ 8]; zz[4] = v0 ^ v1; v1 ^= zz[ 9];
+            v0 ^= zz[10]; zz[5] = v0 ^ v1; v1 ^= zz[11];
+            v0 ^= zz[12]; zz[6] = v0 ^ v1; v1 ^= zz[13];
+            v0 ^= zz[14]; zz[7] = v0 ^ v1; v1 ^= zz[15];
+            v0 ^= zz[16]; zz[8] = v0 ^ v1; v1 ^= zz[17];
+
+            ulong w = v0 ^ v1;
+            zz[ 9] = zz[0] ^ w;
+            zz[10] = zz[1] ^ w;
+            zz[11] = zz[2] ^ w;
+            zz[12] = zz[3] ^ w;
+            zz[13] = zz[4] ^ w;
+            zz[14] = zz[5] ^ w;
+            zz[15] = zz[6] ^ w;
+            zz[16] = zz[7] ^ w;
+            zz[17] = zz[8] ^ w;
+
+            ImplMulwAcc(u, x[0] ^ x[1], y[0] ^ y[1], zz[ 1..]);
+
+            ImplMulwAcc(u, x[0] ^ x[2], y[0] ^ y[2], zz[ 2..]);
+
+            ImplMulwAcc(u, x[0] ^ x[3], y[0] ^ y[3], zz[ 3..]);
+            ImplMulwAcc(u, x[1] ^ x[2], y[1] ^ y[2], zz[ 3..]);
+
+            ImplMulwAcc(u, x[0] ^ x[4], y[0] ^ y[4], zz[ 4..]);
+            ImplMulwAcc(u, x[1] ^ x[3], y[1] ^ y[3], zz[ 4..]);
+
+            ImplMulwAcc(u, x[0] ^ x[5], y[0] ^ y[5], zz[ 5..]);
+            ImplMulwAcc(u, x[1] ^ x[4], y[1] ^ y[4], zz[ 5..]);
+            ImplMulwAcc(u, x[2] ^ x[3], y[2] ^ y[3], zz[ 5..]);
+
+            ImplMulwAcc(u, x[0] ^ x[6], y[0] ^ y[6], zz[ 6..]);
+            ImplMulwAcc(u, x[1] ^ x[5], y[1] ^ y[5], zz[ 6..]);
+            ImplMulwAcc(u, x[2] ^ x[4], y[2] ^ y[4], zz[ 6..]);
+
+            ImplMulwAcc(u, x[0] ^ x[7], y[0] ^ y[7], zz[ 7..]);
+            ImplMulwAcc(u, x[1] ^ x[6], y[1] ^ y[6], zz[ 7..]);
+            ImplMulwAcc(u, x[2] ^ x[5], y[2] ^ y[5], zz[ 7..]);
+            ImplMulwAcc(u, x[3] ^ x[4], y[3] ^ y[4], zz[ 7..]);
+
+            ImplMulwAcc(u, x[0] ^ x[8], y[0] ^ y[8], zz[ 8..]);
+            ImplMulwAcc(u, x[1] ^ x[7], y[1] ^ y[7], zz[ 8..]);
+            ImplMulwAcc(u, x[2] ^ x[6], y[2] ^ y[6], zz[ 8..]);
+            ImplMulwAcc(u, x[3] ^ x[5], y[3] ^ y[5], zz[ 8..]);
+
+            ImplMulwAcc(u, x[1] ^ x[8], y[1] ^ y[8], zz[ 9..]);
+            ImplMulwAcc(u, x[2] ^ x[7], y[2] ^ y[7], zz[ 9..]);
+            ImplMulwAcc(u, x[3] ^ x[6], y[3] ^ y[6], zz[ 9..]);
+            ImplMulwAcc(u, x[4] ^ x[5], y[4] ^ y[5], zz[ 9..]);
+
+            ImplMulwAcc(u, x[2] ^ x[8], y[2] ^ y[8], zz[10..]);
+            ImplMulwAcc(u, x[3] ^ x[7], y[3] ^ y[7], zz[10..]);
+            ImplMulwAcc(u, x[4] ^ x[6], y[4] ^ y[6], zz[10..]);
+
+            ImplMulwAcc(u, x[3] ^ x[8], y[3] ^ y[8], zz[11..]);
+            ImplMulwAcc(u, x[4] ^ x[7], y[4] ^ y[7], zz[11..]);
+            ImplMulwAcc(u, x[5] ^ x[6], y[5] ^ y[6], zz[11..]);
+
+            ImplMulwAcc(u, x[4] ^ x[8], y[4] ^ y[8], zz[12..]);
+            ImplMulwAcc(u, x[5] ^ x[7], y[5] ^ y[7], zz[12..]);
+
+            ImplMulwAcc(u, x[5] ^ x[8], y[5] ^ y[8], zz[13..]);
+            ImplMulwAcc(u, x[6] ^ x[7], y[6] ^ y[7], zz[13..]);
+
+            ImplMulwAcc(u, x[6] ^ x[8], y[6] ^ y[8], zz[14..]);
+
+            ImplMulwAcc(u, x[7] ^ x[8], y[7] ^ y[8], zz[15..]);
+        }
+#else
+        private static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
         {
             //ulong[] precomp = PrecompMultiplicand(y);
 
@@ -363,8 +585,13 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             ImplMulwAcc(u, x[7] ^ x[8], y[7] ^ y[8], zz, 15);
         }
+#endif
 
-        protected static void ImplMultiplyPrecomp(ulong[] x, ulong[] precomp, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMultiplyPrecomp(ReadOnlySpan<ulong> x, ulong[] precomp, Span<ulong> zz)
+#else
+        private static void ImplMultiplyPrecomp(ulong[] x, ulong[] precomp, ulong[] zz)
+#endif
         {
 #if NETCOREAPP3_0_OR_GREATER
             ImplMultiply(x, precomp, zz);
@@ -382,9 +609,17 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                     uint aVal = (uint)(x[j] >> k);
                     uint u = aVal & MASK;
                     uint v = (aVal >> 4) & MASK;
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+                    AddBothTo(precomp.AsSpan((int)(9 * u)), precomp.AsSpan((int)(9 * (v + 16))), zz[(j - 1)..]);
+#else
                     AddBothTo(precomp, (int)(9 * u), precomp, (int)(9 * (v + 16)), zz, j - 1);
+#endif
                 }
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+                Nat.ShiftUpBits64(16, zz, 8, 0UL);
+#else
                 Nat.ShiftUpBits64(16, zz, 0, 8, 0UL);
+#endif
             }
 
             for (int k = 56; k >= 0; k -= 8)
@@ -394,17 +629,29 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                     uint aVal = (uint)(x[j] >> k);
                     uint u = aVal & MASK;
                     uint v = (aVal >> 4) & MASK;
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+                    AddBothTo(precomp.AsSpan((int)(9 * u)), precomp.AsSpan((int)(9 * (v + 16))), zz[j..]);
+#else
                     AddBothTo(precomp, (int)(9 * u), precomp, (int)(9 * (v + 16)), zz, j);
+#endif
                 }
                 if (k > 0)
                 {
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+                    Nat.ShiftUpBits64(18, zz, 8, 0UL);
+#else
                     Nat.ShiftUpBits64(18, zz, 0, 8, 0UL);
+#endif
                 }
             }
 #endif
-        }
+            }
 
-        protected static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplMulwAcc(Span<ulong> u, ulong x, ulong y, Span<ulong> z)
+#else
+        private static void ImplMulwAcc(ulong[] u, ulong x, ulong y, ulong[] z, int zOff)
+#endif
         {
 #if NETCOREAPP3_0_OR_GREATER
             if (Pclmulqdq.IsSupported)
@@ -412,8 +659,8 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                 var X = Vector128.CreateScalar(x);
                 var Y = Vector128.CreateScalar(y);
                 var Z = Pclmulqdq.CarrylessMultiply(X, Y, 0x00);
-                z[zOff    ] ^= Z.GetElement(0);
-                z[zOff + 1] ^= Z.GetElement(1);
+                z[0] ^= Z.GetElement(0);
+                z[1] ^= Z.GetElement(1);
                 return;
             }
 #endif
@@ -427,14 +674,14 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
 
             uint j = (uint)x;
-            ulong g, h = 0, l = u[j & 15]
-                              ^ u[(j >> 4) & 15] << 4;
+            ulong g, h = 0, l = u[(int)j & 15]
+                              ^ u[(int)(j >> 4) & 15] << 4;
             int k = 56;
             do
             {
                 j  = (uint)(x >> k);
-                g  = u[j & 15]
-                   ^ u[(j >> 4) & 15] << 4;
+                g  = u[(int)j & 15]
+                   ^ u[(int)(j >> 4) & 15] << 4;
                 l ^= (g << k);
                 h ^= (g >> -k);
             }
@@ -448,11 +695,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             Debug.Assert(h >> 63 == 0);
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            z[0] ^= l;
+            z[1] ^= h;
+#else
             z[zOff    ] ^= l;
             z[zOff + 1] ^= h;
+#endif
         }
 
-        protected static void ImplSquare(ulong[] x, ulong[] zz)
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        private static void ImplSquare(ReadOnlySpan<ulong> x, Span<ulong> zz)
+#else
+        private static void ImplSquare(ulong[] x, ulong[] zz)
+#endif
         {
 #if NETCOREAPP3_0_OR_GREATER
             if (Bmi2.X64.IsSupported)
@@ -479,7 +735,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
 #endif
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Interleave.Expand64To128(x[..9], zz[..18]);
+#else
             Interleave.Expand64To128(x, 0, 9, zz, 0);
+#endif
         }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/SecT571K1Point.cs b/crypto/src/math/ec/custom/sec/SecT571K1Point.cs
index 95af0629f..0156c6283 100644
--- a/crypto/src/math/ec/custom/sec/SecT571K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecT571K1Point.cs
@@ -176,7 +176,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                     SecT571Field.MultiplyPrecomp(Z3.x, Z2Precomp, Z3.x);
                 }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+                Span<ulong> tt = stackalloc ulong[18];
+#else
                 ulong[] tt = Nat576.CreateExt64();
+#endif
 
                 SecT571Field.Add(AU2, B, t4);
                 SecT571Field.SquareExt(t4, tt);
diff --git a/crypto/src/math/ec/custom/sec/SecT571R1Point.cs b/crypto/src/math/ec/custom/sec/SecT571R1Point.cs
index 986885db6..1b519d819 100644
--- a/crypto/src/math/ec/custom/sec/SecT571R1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecT571R1Point.cs
@@ -176,7 +176,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                     SecT571Field.MultiplyPrecomp(Z3.x, Z2Precomp, Z3.x);
                 }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+                Span<ulong> tt = stackalloc ulong[18];
+#else
                 ulong[] tt = Nat576.CreateExt64();
+#endif
 
                 SecT571Field.Add(AU2, B, t4);
                 SecT571Field.SquareExt(t4, tt);
@@ -237,7 +241,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
                 return new SecT571R1Point(curve, new SecT571FieldElement(T), SecT571R1Curve.SecT571R1_B_SQRT);
             }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+            Span<ulong> tt = stackalloc ulong[18];
+#else
             ulong[] tt = Nat576.CreateExt64();
+#endif
             SecT571Field.MultiplyAddToExt(T, L1Z1, tt);
 
             SecT571FieldElement X3 = new SecT571FieldElement(t1);
diff --git a/crypto/src/math/raw/Nat128.cs b/crypto/src/math/raw/Nat128.cs
index d336b320a..0705844e7 100644
--- a/crypto/src/math/raw/Nat128.cs
+++ b/crypto/src/math/raw/Nat128.cs
@@ -131,6 +131,14 @@ namespace Org.BouncyCastle.Math.Raw
             z[zOff + 1] = x[xOff + 1];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Copy64(ReadOnlySpan<ulong> x, Span<ulong> z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+        }
+#endif
+
         public static uint[] Create()
         {
             return new uint[4];
@@ -270,7 +278,11 @@ namespace Org.BouncyCastle.Math.Raw
             return true;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static bool IsZero64(ReadOnlySpan<ulong> x)
+#else
         public static bool IsZero64(ulong[] x)
+#endif
         {
             for (int i = 0; i < 2; ++i)
             {
diff --git a/crypto/src/math/raw/Nat192.cs b/crypto/src/math/raw/Nat192.cs
index 752290747..7c36b21cf 100644
--- a/crypto/src/math/raw/Nat192.cs
+++ b/crypto/src/math/raw/Nat192.cs
@@ -169,6 +169,15 @@ namespace Org.BouncyCastle.Math.Raw
             z[zOff + 2] = x[xOff + 2];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Copy64(ReadOnlySpan<ulong> x, Span<ulong> z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+        }
+#endif
+
         public static uint[] Create()
         {
             return new uint[6];
@@ -310,7 +319,11 @@ namespace Org.BouncyCastle.Math.Raw
             return true;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static bool IsZero64(ReadOnlySpan<ulong> x)
+#else
         public static bool IsZero64(ulong[] x)
+#endif
         {
             for (int i = 0; i < 3; ++i)
             {
diff --git a/crypto/src/math/raw/Nat320.cs b/crypto/src/math/raw/Nat320.cs
index 0b250aa77..06f7b58cc 100644
--- a/crypto/src/math/raw/Nat320.cs
+++ b/crypto/src/math/raw/Nat320.cs
@@ -25,6 +25,17 @@ namespace Org.BouncyCastle.Math.Raw
             z[zOff + 4] = x[xOff + 4];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Copy64(ReadOnlySpan<ulong> x, Span<ulong> z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+            z[4] = x[4];
+        }
+#endif
+
         public static ulong[] Create64()
         {
             return new ulong[5];
@@ -63,7 +74,11 @@ namespace Org.BouncyCastle.Math.Raw
             return true;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static bool IsZero64(ReadOnlySpan<ulong> x)
+#else
         public static bool IsZero64(ulong[] x)
+#endif
         {
             for (int i = 0; i < 5; ++i)
             {
diff --git a/crypto/src/math/raw/Nat448.cs b/crypto/src/math/raw/Nat448.cs
index 688f327a4..2da03bf0f 100644
--- a/crypto/src/math/raw/Nat448.cs
+++ b/crypto/src/math/raw/Nat448.cs
@@ -29,6 +29,19 @@ namespace Org.BouncyCastle.Math.Raw
             z[zOff + 6] = x[xOff + 6];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Copy64(ReadOnlySpan<ulong> x, Span<ulong> z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+            z[4] = x[4];
+            z[5] = x[5];
+            z[6] = x[6];
+        }
+#endif
+
         public static ulong[] Create64()
         {
             return new ulong[7];
@@ -67,7 +80,11 @@ namespace Org.BouncyCastle.Math.Raw
             return true;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static bool IsZero64(ReadOnlySpan<ulong> x)
+#else
         public static bool IsZero64(ulong[] x)
+#endif
         {
             for (int i = 0; i < 7; ++i)
             {
diff --git a/crypto/src/math/raw/Nat576.cs b/crypto/src/math/raw/Nat576.cs
index 174d52bcf..3525a0f05 100644
--- a/crypto/src/math/raw/Nat576.cs
+++ b/crypto/src/math/raw/Nat576.cs
@@ -33,6 +33,21 @@ namespace Org.BouncyCastle.Math.Raw
             z[zOff + 8] = x[xOff + 8];
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static void Copy64(ReadOnlySpan<ulong> x, Span<ulong> z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+            z[4] = x[4];
+            z[5] = x[5];
+            z[6] = x[6];
+            z[7] = x[7];
+            z[8] = x[8];
+        }
+#endif
+
         public static ulong[] Create64()
         {
             return new ulong[9];
@@ -71,7 +86,11 @@ namespace Org.BouncyCastle.Math.Raw
             return true;
         }
 
+#if NETCOREAPP2_1_OR_GREATER || NETSTANDARD2_1_OR_GREATER
+        public static bool IsZero64(ReadOnlySpan<ulong> x)
+#else
         public static bool IsZero64(ulong[] x)
+#endif
         {
             for (int i = 0; i < 9; ++i)
             {