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-rw-r--r--crypto/src/math/ec/ECFieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/djb/Curve25519.cs2
-rw-r--r--crypto/src/math/ec/custom/djb/Curve25519Field.cs2
-rw-r--r--crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/djb/Curve25519Point.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP192K1Field.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/sec/SecP192K1Point.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP192R1Field.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/sec/SecP192R1Point.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP224K1Field.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/sec/SecP224K1Point.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP224R1Field.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/sec/SecP224R1Point.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP256K1Field.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/sec/SecP256K1Point.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP256R1Field.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/sec/SecP256R1Point.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP384R1Field.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/sec/SecP384R1Point.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP521R1Field.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs1
-rw-r--r--crypto/src/math/ec/custom/sec/SecP521R1Point.cs2
-rw-r--r--crypto/src/math/raw/Interleave.cs70
-rw-r--r--crypto/src/math/raw/Mod.cs (renamed from crypto/src/math/ec/Mod.cs)2
-rw-r--r--crypto/src/math/raw/Nat.cs (renamed from crypto/src/math/ec/Nat.cs)42
-rw-r--r--crypto/src/math/raw/Nat128.cs856
-rw-r--r--crypto/src/math/raw/Nat160.cs874
-rw-r--r--crypto/src/math/raw/Nat192.cs (renamed from crypto/src/math/ec/custom/sec/Nat192.cs)88
-rw-r--r--crypto/src/math/raw/Nat224.cs (renamed from crypto/src/math/ec/custom/sec/Nat224.cs)2
-rw-r--r--crypto/src/math/raw/Nat256.cs (renamed from crypto/src/math/ec/custom/sec/Nat256.cs)89
-rw-r--r--crypto/src/math/raw/Nat320.cs98
-rw-r--r--crypto/src/math/raw/Nat384.cs (renamed from crypto/src/math/ec/custom/sec/Nat384.cs)2
-rw-r--r--crypto/src/math/raw/Nat448.cs100
-rw-r--r--crypto/src/math/raw/Nat512.cs (renamed from crypto/src/math/ec/custom/sec/Nat512.cs)2
-rw-r--r--crypto/src/math/raw/Nat576.cs102
42 files changed, 2365 insertions, 11 deletions
diff --git a/crypto/src/math/ec/ECFieldElement.cs b/crypto/src/math/ec/ECFieldElement.cs
index 27c4ba2d0..844bed649 100644
--- a/crypto/src/math/ec/ECFieldElement.cs
+++ b/crypto/src/math/ec/ECFieldElement.cs
@@ -1,6 +1,7 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC
diff --git a/crypto/src/math/ec/custom/djb/Curve25519.cs b/crypto/src/math/ec/custom/djb/Curve25519.cs
index 712b68f29..6ed7c0648 100644
--- a/crypto/src/math/ec/custom/djb/Curve25519.cs
+++ b/crypto/src/math/ec/custom/djb/Curve25519.cs
@@ -1,6 +1,6 @@
 using System;
 
-using Org.BouncyCastle.Math.EC.Custom.Sec;
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities.Encoders;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Djb
diff --git a/crypto/src/math/ec/custom/djb/Curve25519Field.cs b/crypto/src/math/ec/custom/djb/Curve25519Field.cs
index 809e51b80..837821e1a 100644
--- a/crypto/src/math/ec/custom/djb/Curve25519Field.cs
+++ b/crypto/src/math/ec/custom/djb/Curve25519Field.cs
@@ -1,7 +1,7 @@
 using System;
 using System.Diagnostics;
 
-using Org.BouncyCastle.Math.EC.Custom.Sec;
+using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Djb
 {
diff --git a/crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs b/crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs
index 8d5a80326..732e9e468 100644
--- a/crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs
+++ b/crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs
@@ -1,6 +1,6 @@
 using System;
 
-using Org.BouncyCastle.Math.EC.Custom.Sec;
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Djb
diff --git a/crypto/src/math/ec/custom/djb/Curve25519Point.cs b/crypto/src/math/ec/custom/djb/Curve25519Point.cs
index bfec1d11d..eb8fc12f2 100644
--- a/crypto/src/math/ec/custom/djb/Curve25519Point.cs
+++ b/crypto/src/math/ec/custom/djb/Curve25519Point.cs
@@ -1,6 +1,6 @@
 using System;
 
-using Org.BouncyCastle.Math.EC.Custom.Sec;
+using Org.BouncyCastle.Math.Raw;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Djb
 {
diff --git a/crypto/src/math/ec/custom/sec/SecP192K1Field.cs b/crypto/src/math/ec/custom/sec/SecP192K1Field.cs
index d5ca903d1..a00360360 100644
--- a/crypto/src/math/ec/custom/sec/SecP192K1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192K1Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP192K1Field
diff --git a/crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs
index 78886dd8c..dce377035 100644
--- a/crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs
@@ -1,6 +1,7 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
diff --git a/crypto/src/math/ec/custom/sec/SecP192K1Point.cs b/crypto/src/math/ec/custom/sec/SecP192K1Point.cs
index 648aca502..58eb09102 100644
--- a/crypto/src/math/ec/custom/sec/SecP192K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192K1Point.cs
@@ -1,5 +1,7 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP192K1Point
diff --git a/crypto/src/math/ec/custom/sec/SecP192R1Field.cs b/crypto/src/math/ec/custom/sec/SecP192R1Field.cs
index 85e3a0394..096c2b51f 100644
--- a/crypto/src/math/ec/custom/sec/SecP192R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192R1Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP192R1Field
diff --git a/crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs
index 020c5cdbb..45bcb00f0 100644
--- a/crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs
@@ -1,5 +1,6 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
diff --git a/crypto/src/math/ec/custom/sec/SecP192R1Point.cs b/crypto/src/math/ec/custom/sec/SecP192R1Point.cs
index 797a8de35..3b53e341e 100644
--- a/crypto/src/math/ec/custom/sec/SecP192R1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192R1Point.cs
@@ -1,5 +1,7 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP192R1Point
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1Field.cs b/crypto/src/math/ec/custom/sec/SecP224K1Field.cs
index a55810c6d..98cf777a5 100644
--- a/crypto/src/math/ec/custom/sec/SecP224K1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224K1Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP224K1Field
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs
index 72ff4b099..fec07436a 100644
--- a/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs
@@ -1,6 +1,7 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1Point.cs b/crypto/src/math/ec/custom/sec/SecP224K1Point.cs
index 8cbd29699..98cb29274 100644
--- a/crypto/src/math/ec/custom/sec/SecP224K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224K1Point.cs
@@ -1,5 +1,7 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP224K1Point
diff --git a/crypto/src/math/ec/custom/sec/SecP224R1Field.cs b/crypto/src/math/ec/custom/sec/SecP224R1Field.cs
index 559593c66..4f5c3bbda 100644
--- a/crypto/src/math/ec/custom/sec/SecP224R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224R1Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP224R1Field
diff --git a/crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs
index 06f47cded..2b9a06564 100644
--- a/crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs
@@ -1,5 +1,6 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
diff --git a/crypto/src/math/ec/custom/sec/SecP224R1Point.cs b/crypto/src/math/ec/custom/sec/SecP224R1Point.cs
index c3f4efb59..73c4f1948 100644
--- a/crypto/src/math/ec/custom/sec/SecP224R1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224R1Point.cs
@@ -1,5 +1,7 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP224R1Point
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1Field.cs b/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
index ba3a070a9..b0646e93f 100644
--- a/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP256K1Field
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
index d9a039a4f..473113d0f 100644
--- a/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
@@ -1,6 +1,7 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1Point.cs b/crypto/src/math/ec/custom/sec/SecP256K1Point.cs
index 3165682fa..072a0b969 100644
--- a/crypto/src/math/ec/custom/sec/SecP256K1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Point.cs
@@ -1,5 +1,7 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP256K1Point
diff --git a/crypto/src/math/ec/custom/sec/SecP256R1Field.cs b/crypto/src/math/ec/custom/sec/SecP256R1Field.cs
index 9ed9dcd41..11594b2ba 100644
--- a/crypto/src/math/ec/custom/sec/SecP256R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256R1Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP256R1Field
diff --git a/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs
index b22763cfa..d7838aead 100644
--- a/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs
@@ -1,5 +1,6 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
diff --git a/crypto/src/math/ec/custom/sec/SecP256R1Point.cs b/crypto/src/math/ec/custom/sec/SecP256R1Point.cs
index 1de4a0b4a..83320824d 100644
--- a/crypto/src/math/ec/custom/sec/SecP256R1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256R1Point.cs
@@ -1,5 +1,7 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP256R1Point
diff --git a/crypto/src/math/ec/custom/sec/SecP384R1Field.cs b/crypto/src/math/ec/custom/sec/SecP384R1Field.cs
index 508b01e3c..7820775ee 100644
--- a/crypto/src/math/ec/custom/sec/SecP384R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP384R1Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP384R1Field
diff --git a/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs
index 40086978d..18d48a57d 100644
--- a/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs
@@ -1,5 +1,6 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
diff --git a/crypto/src/math/ec/custom/sec/SecP384R1Point.cs b/crypto/src/math/ec/custom/sec/SecP384R1Point.cs
index 68c601611..83159ce61 100644
--- a/crypto/src/math/ec/custom/sec/SecP384R1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecP384R1Point.cs
@@ -1,5 +1,7 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP384R1Point
diff --git a/crypto/src/math/ec/custom/sec/SecP521R1Field.cs b/crypto/src/math/ec/custom/sec/SecP521R1Field.cs
index 3568156d8..b7f8eb146 100644
--- a/crypto/src/math/ec/custom/sec/SecP521R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP521R1Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP521R1Field
diff --git a/crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs
index 83a615928..6f02a7eb5 100644
--- a/crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs
@@ -1,5 +1,6 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
 using Org.BouncyCastle.Utilities;
 
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
diff --git a/crypto/src/math/ec/custom/sec/SecP521R1Point.cs b/crypto/src/math/ec/custom/sec/SecP521R1Point.cs
index fb1996cfd..7ad97f76f 100644
--- a/crypto/src/math/ec/custom/sec/SecP521R1Point.cs
+++ b/crypto/src/math/ec/custom/sec/SecP521R1Point.cs
@@ -1,5 +1,7 @@
 using System;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP521R1Point
diff --git a/crypto/src/math/raw/Interleave.cs b/crypto/src/math/raw/Interleave.cs
new file mode 100644
index 000000000..9755c9d6f
--- /dev/null
+++ b/crypto/src/math/raw/Interleave.cs
@@ -0,0 +1,70 @@
+using System;
+
+namespace Org.BouncyCastle.Math.Raw
+{
+    internal abstract class Interleave
+    {
+        /*
+         * This expands 8 bit indices into 16 bit contents (high bit 14), by inserting 0s between bits.
+         * In a binary field, this operation is the same as squaring an 8 bit number.
+         */
+        private static readonly ushort[] INTERLEAVE2_TABLE = new ushort[]
+        {
+            0x0000, 0x0001, 0x0004, 0x0005, 0x0010, 0x0011, 0x0014, 0x0015,
+            0x0040, 0x0041, 0x0044, 0x0045, 0x0050, 0x0051, 0x0054, 0x0055,
+            0x0100, 0x0101, 0x0104, 0x0105, 0x0110, 0x0111, 0x0114, 0x0115,
+            0x0140, 0x0141, 0x0144, 0x0145, 0x0150, 0x0151, 0x0154, 0x0155,
+            0x0400, 0x0401, 0x0404, 0x0405, 0x0410, 0x0411, 0x0414, 0x0415,
+            0x0440, 0x0441, 0x0444, 0x0445, 0x0450, 0x0451, 0x0454, 0x0455,
+            0x0500, 0x0501, 0x0504, 0x0505, 0x0510, 0x0511, 0x0514, 0x0515,
+            0x0540, 0x0541, 0x0544, 0x0545, 0x0550, 0x0551, 0x0554, 0x0555,
+            0x1000, 0x1001, 0x1004, 0x1005, 0x1010, 0x1011, 0x1014, 0x1015,
+            0x1040, 0x1041, 0x1044, 0x1045, 0x1050, 0x1051, 0x1054, 0x1055,
+            0x1100, 0x1101, 0x1104, 0x1105, 0x1110, 0x1111, 0x1114, 0x1115,
+            0x1140, 0x1141, 0x1144, 0x1145, 0x1150, 0x1151, 0x1154, 0x1155,
+            0x1400, 0x1401, 0x1404, 0x1405, 0x1410, 0x1411, 0x1414, 0x1415,
+            0x1440, 0x1441, 0x1444, 0x1445, 0x1450, 0x1451, 0x1454, 0x1455,
+            0x1500, 0x1501, 0x1504, 0x1505, 0x1510, 0x1511, 0x1514, 0x1515,
+            0x1540, 0x1541, 0x1544, 0x1545, 0x1550, 0x1551, 0x1554, 0x1555,
+            0x4000, 0x4001, 0x4004, 0x4005, 0x4010, 0x4011, 0x4014, 0x4015,
+            0x4040, 0x4041, 0x4044, 0x4045, 0x4050, 0x4051, 0x4054, 0x4055,
+            0x4100, 0x4101, 0x4104, 0x4105, 0x4110, 0x4111, 0x4114, 0x4115,
+            0x4140, 0x4141, 0x4144, 0x4145, 0x4150, 0x4151, 0x4154, 0x4155,
+            0x4400, 0x4401, 0x4404, 0x4405, 0x4410, 0x4411, 0x4414, 0x4415,
+            0x4440, 0x4441, 0x4444, 0x4445, 0x4450, 0x4451, 0x4454, 0x4455,
+            0x4500, 0x4501, 0x4504, 0x4505, 0x4510, 0x4511, 0x4514, 0x4515,
+            0x4540, 0x4541, 0x4544, 0x4545, 0x4550, 0x4551, 0x4554, 0x4555,
+            0x5000, 0x5001, 0x5004, 0x5005, 0x5010, 0x5011, 0x5014, 0x5015,
+            0x5040, 0x5041, 0x5044, 0x5045, 0x5050, 0x5051, 0x5054, 0x5055,
+            0x5100, 0x5101, 0x5104, 0x5105, 0x5110, 0x5111, 0x5114, 0x5115,
+            0x5140, 0x5141, 0x5144, 0x5145, 0x5150, 0x5151, 0x5154, 0x5155,
+            0x5400, 0x5401, 0x5404, 0x5405, 0x5410, 0x5411, 0x5414, 0x5415,
+            0x5440, 0x5441, 0x5444, 0x5445, 0x5450, 0x5451, 0x5454, 0x5455,
+            0x5500, 0x5501, 0x5504, 0x5505, 0x5510, 0x5511, 0x5514, 0x5515,
+            0x5540, 0x5541, 0x5544, 0x5545, 0x5550, 0x5551, 0x5554, 0x5555
+        };
+
+        internal static uint Expand8to16(uint x)
+        {
+            return INTERLEAVE2_TABLE[x & 0xFF];
+        }
+
+        internal static uint Expand16to32(uint x)
+        {
+            return (uint)(INTERLEAVE2_TABLE[x & 0xFF] | INTERLEAVE2_TABLE[(x >> 8) & 0xFF] << 16);
+        }
+
+        internal static ulong Expand32to64(uint x)
+        {
+            uint r00 = (uint)(INTERLEAVE2_TABLE[x & 0xFF] | INTERLEAVE2_TABLE[(x >> 8) & 0xFF] << 16);
+            uint r32 = (uint)(INTERLEAVE2_TABLE[(x >> 16) & 0xFF] | INTERLEAVE2_TABLE[x >> 24] << 16);
+            return (ulong)r32 << 32 | (ulong)r00;
+        }
+
+        internal static void Expand64To128(ulong x, ulong[] z, int zOff)
+        {
+            z[zOff    ] = Expand32to64((uint)x);
+            z[zOff + 1] = Expand32to64((uint)(x >> 32));
+        }
+    }
+}
diff --git a/crypto/src/math/ec/Mod.cs b/crypto/src/math/raw/Mod.cs
index 80534ca9f..63467e668 100644
--- a/crypto/src/math/ec/Mod.cs
+++ b/crypto/src/math/raw/Mod.cs
@@ -4,7 +4,7 @@ using System.Diagnostics;
 using Org.BouncyCastle.Crypto.Utilities;
 using Org.BouncyCastle.Utilities;
 
-namespace Org.BouncyCastle.Math.EC
+namespace Org.BouncyCastle.Math.Raw
 {
     internal abstract class Mod
     {
diff --git a/crypto/src/math/ec/Nat.cs b/crypto/src/math/raw/Nat.cs
index 17b632f26..1f9ab00ec 100644
--- a/crypto/src/math/ec/Nat.cs
+++ b/crypto/src/math/raw/Nat.cs
@@ -3,7 +3,7 @@ using System.Diagnostics;
 
 using Org.BouncyCastle.Crypto.Utilities;
 
-namespace Org.BouncyCastle.Math.EC
+namespace Org.BouncyCastle.Math.Raw
 {
     internal abstract class Nat
     {
@@ -212,6 +212,11 @@ namespace Org.BouncyCastle.Math.EC
             return new uint[len];
         }
 
+        public static ulong[] Create64(int len)
+        {
+            return new ulong[len];
+        }
+
         public static int Dec(int len, uint[] z)
         {
             for (int i = 0; i < len; ++i)
@@ -666,6 +671,17 @@ namespace Org.BouncyCastle.Math.EC
             return c >> 31;
         }
 
+        public static ulong ShiftUpBit64(int len, ulong[] x, int xOff, ulong c, ulong[] z, int zOff)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                ulong next = x[xOff + i];
+                z[zOff + i] = (next << 1) | (c >> 63);
+                c = next;
+            }
+            return c >> 63;
+        }
+
         public static uint ShiftUpBits(int len, uint[] z, int bits, uint c)
         {
             Debug.Assert(bits > 0 && bits < 32);
@@ -690,6 +706,18 @@ namespace Org.BouncyCastle.Math.EC
             return c >> -bits;
         }
 
+        public static ulong ShiftUpBits64(int len, ulong[] z, int zOff, int bits, ulong c)
+        {
+            Debug.Assert(bits > 0 && bits < 64);
+            for (int i = 0; i < len; ++i)
+            {
+                ulong next = z[zOff + i];
+                z[zOff + i] = (next << bits) | (c >> -bits);
+                c = next;
+            }
+            return c >> -bits;
+        }
+
         public static uint ShiftUpBits(int len, uint[] x, int bits, uint c, uint[] z)
         {
             Debug.Assert(bits > 0 && bits < 32);
@@ -714,6 +742,18 @@ namespace Org.BouncyCastle.Math.EC
             return c >> -bits;
         }
 
+        public static ulong ShiftUpBits64(int len, ulong[] x, int xOff, int bits, ulong c, ulong[] z, int zOff)
+        {
+            Debug.Assert(bits > 0 && bits < 64);
+            for (int i = 0; i < len; ++i)
+            {
+                ulong next = x[xOff + i];
+                z[zOff + i] = (next << bits) | (c >> -bits);
+                c = next;
+            }
+            return c >> -bits;
+        }
+
         public static void Square(int len, uint[] x, uint[] zz)
         {
             int extLen = len << 1;
diff --git a/crypto/src/math/raw/Nat128.cs b/crypto/src/math/raw/Nat128.cs
new file mode 100644
index 000000000..819c52062
--- /dev/null
+++ b/crypto/src/math/raw/Nat128.cs
@@ -0,0 +1,856 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Crypto.Utilities;
+
+namespace Org.BouncyCastle.Math.Raw
+{
+    internal abstract class Nat128
+    {
+        private const ulong M = 0xFFFFFFFFUL;
+
+        public static uint Add(uint[] x, uint[] y, uint[] z)
+        {
+            ulong c = 0;
+            c += (ulong)x[0] + y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[1] + y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[2] + y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[3] + y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddBothTo(uint[] x, uint[] y, uint[] z)
+        {
+            ulong c = 0;
+            c += (ulong)x[0] + y[0] + z[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[1] + y[1] + z[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[2] + y[2] + z[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[3] + y[3] + z[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddTo(uint[] x, uint[] z)
+        {
+            ulong c = 0;
+            c += (ulong)x[0] + z[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[1] + z[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[2] + z[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[3] + z[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddTo(uint[] x, int xOff, uint[] z, int zOff, uint cIn)
+        {
+            ulong c = cIn;
+            c += (ulong)x[xOff + 0] + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 1] + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 2] + z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 3] + z[zOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddToEachOther(uint[] u, int uOff, uint[] v, int vOff)
+        {
+            ulong c = 0;
+            c += (ulong)u[uOff + 0] + v[vOff + 0];
+            u[uOff + 0] = (uint)c;
+            v[vOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)u[uOff + 1] + v[vOff + 1];
+            u[uOff + 1] = (uint)c;
+            v[vOff + 1] = (uint)c;
+            c >>= 32;
+            c += (ulong)u[uOff + 2] + v[vOff + 2];
+            u[uOff + 2] = (uint)c;
+            v[vOff + 2] = (uint)c;
+            c >>= 32;
+            c += (ulong)u[uOff + 3] + v[vOff + 3];
+            u[uOff + 3] = (uint)c;
+            v[vOff + 3] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static void Copy(uint[] x, uint[] z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+        }
+
+        public static void Copy64(ulong[] x, ulong[] z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+        }
+
+        public static uint[] Create()
+        {
+            return new uint[4];
+        }
+
+        public static ulong[] Create64()
+        {
+            return new ulong[2];
+        }
+
+        public static uint[] CreateExt()
+        {
+            return new uint[8];
+        }
+
+        public static ulong[] CreateExt64()
+        {
+            return new ulong[4];
+        }
+
+        public static bool Diff(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            bool pos = Gte(x, xOff, y, yOff);
+            if (pos)
+            {
+                Sub(x, xOff, y, yOff, z, zOff);
+            }
+            else
+            {
+                Sub(y, yOff, x, xOff, z, zOff);
+            }
+            return pos;
+        }
+
+        public static bool Eq(uint[] x, uint[] y)
+        {
+            for (int i = 3; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                    return false;
+            }
+            return true;
+        }
+
+        public static bool Eq64(ulong[] x, ulong[] y)
+        {
+            for (int i = 1; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                    return false;
+            }
+            return true;
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 128)
+                throw new ArgumentException();
+
+            uint[] z = Create();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (uint)x.IntValue;
+                x = x.ShiftRight(32);
+            }
+            return z;
+        }
+
+        public static ulong[] FromBigInteger64(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 128)
+                throw new ArgumentException();
+
+            ulong[] z = Create64();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (ulong)x.LongValue;
+                x = x.ShiftRight(64);
+            }
+            return z;
+        }
+
+        public static uint GetBit(uint[] x, int bit)
+        {
+            if (bit == 0)
+            {
+                return x[0] & 1;
+            }
+            if ((bit & 127) != bit)
+            {
+                return 0;
+            }
+            int w = bit >> 5;
+            int b = bit & 31;
+            return (x[w] >> b) & 1;
+        }
+
+        public static bool Gte(uint[] x, uint[] y)
+        {
+            for (int i = 3; i >= 0; --i)
+            {
+                uint x_i = x[i], y_i = y[i];
+                if (x_i < y_i)
+                    return false;
+                if (x_i > y_i)
+                    return true;
+            }
+            return true;
+        }
+
+        public static bool Gte(uint[] x, int xOff, uint[] y, int yOff)
+        {
+            for (int i = 3; i >= 0; --i)
+            {
+                uint x_i = x[xOff + i], y_i = y[yOff + i];
+                if (x_i < y_i)
+                    return false;
+                if (x_i > y_i)
+                    return true;
+            }
+            return true;
+        }
+
+        public static bool IsOne(uint[] x)
+        {
+            if (x[0] != 1)
+            {
+                return false;
+            }
+            for (int i = 1; i < 4; ++i)
+            {
+                if (x[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsOne64(ulong[] x)
+        {
+            if (x[0] != 1UL)
+            {
+                return false;
+            }
+            for (int i = 1; i < 2; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZero(uint[] x)
+        {
+            for (int i = 0; i < 4; ++i)
+            {
+                if (x[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZero64(ulong[] x)
+        {
+            for (int i = 0; i < 2; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static void Mul(uint[] x, uint[] y, uint[] zz)
+        {
+            ulong y_0 = y[0];
+            ulong y_1 = y[1];
+            ulong y_2 = y[2];
+            ulong y_3 = y[3];
+
+            {
+                ulong c = 0, x_0 = x[0];
+                c += x_0 * y_0;
+                zz[0] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_1;
+                zz[1] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_2;
+                zz[2] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_3;
+                zz[3] = (uint)c;
+                c >>= 32;
+                zz[4] = (uint)c;
+            }
+
+            for (int i = 1; i < 4; ++i)
+            {
+                ulong c = 0, x_i = x[i];
+                c += x_i * y_0 + zz[i + 0];
+                zz[i + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[i + 1];
+                zz[i + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[i + 2];
+                zz[i + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[i + 3];
+                zz[i + 3] = (uint)c;
+                c >>= 32;
+                zz[i + 4] = (uint)c;
+            }
+        }
+
+        public static void Mul(uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff)
+        {
+            ulong y_0 = y[yOff + 0];
+            ulong y_1 = y[yOff + 1];
+            ulong y_2 = y[yOff + 2];
+            ulong y_3 = y[yOff + 3];
+
+            {
+                ulong c = 0, x_0 = x[xOff + 0];
+                c += x_0 * y_0;
+                zz[zzOff + 0] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_1;
+                zz[zzOff + 1] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_2;
+                zz[zzOff + 2] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_3;
+                zz[zzOff + 3] = (uint)c;
+                c >>= 32;
+                zz[zzOff + 4] = (uint)c;
+            }
+
+            for (int i = 1; i < 4; ++i)
+            {
+                ++zzOff;
+                ulong c = 0, x_i = x[xOff + i];
+                c += x_i * y_0 + zz[zzOff + 0];
+                zz[zzOff + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[zzOff + 1];
+                zz[zzOff + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[zzOff + 2];
+                zz[zzOff + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[zzOff + 3];
+                zz[zzOff + 3] = (uint)c;
+                c >>= 32;
+                zz[zzOff + 4] = (uint)c;
+            }
+        }
+
+        public static uint MulAddTo(uint[] x, uint[] y, uint[] zz)
+        {
+            ulong y_0 = y[0];
+            ulong y_1 = y[1];
+            ulong y_2 = y[2];
+            ulong y_3 = y[3];
+
+            ulong zc = 0;
+            for (int i = 0; i < 4; ++i)
+            {
+                ulong c = 0, x_i = x[i];
+                c += x_i * y_0 + zz[i + 0];
+                zz[i + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[i + 1];
+                zz[i + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[i + 2];
+                zz[i + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[i + 3];
+                zz[i + 3] = (uint)c;
+                c >>= 32;
+                c += zc + zz[i + 4];
+                zz[i + 4] = (uint)c;
+                zc = c >> 32;
+            }
+            return (uint)zc;
+        }
+
+        public static uint MulAddTo(uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff)
+        {
+            ulong y_0 = y[yOff + 0];
+            ulong y_1 = y[yOff + 1];
+            ulong y_2 = y[yOff + 2];
+            ulong y_3 = y[yOff + 3];
+
+            ulong zc = 0;
+            for (int i = 0; i < 4; ++i)
+            {
+                ulong c = 0, x_i = x[xOff + i];
+                c += x_i * y_0 + zz[zzOff + 0];
+                zz[zzOff + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[zzOff + 1];
+                zz[zzOff + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[zzOff + 2];
+                zz[zzOff + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[zzOff + 3];
+                zz[zzOff + 3] = (uint)c;
+                c >>= 32;
+                c += zc + zz[zzOff + 4];
+                zz[zzOff + 4] = (uint)c;
+                zc = c >> 32;
+                ++zzOff;
+            }
+            return (uint)zc;
+        }
+
+        public static ulong Mul33Add(uint w, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            Debug.Assert(w >> 31 == 0);
+
+            ulong c = 0, wVal = w;
+            ulong x0 = x[xOff + 0];
+            c += wVal * x0 + y[yOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            ulong x1 = x[xOff + 1];
+            c += wVal * x1 + x0 + y[yOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            ulong x2 = x[xOff + 2];
+            c += wVal * x2 + x1 + y[yOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            ulong x3 = x[xOff + 3];
+            c += wVal * x3 + x2 + y[yOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            c += x3;
+            return c;
+        }
+
+        public static uint MulWordAddExt(uint x, uint[] yy, int yyOff, uint[] zz, int zzOff)
+        {
+            Debug.Assert(yyOff <= 4);
+            Debug.Assert(zzOff <= 4);
+
+            ulong c = 0, xVal = x;
+            c += xVal * yy[yyOff + 0] + zz[zzOff + 0];
+            zz[zzOff + 0] = (uint)c;
+            c >>= 32;
+            c += xVal * yy[yyOff + 1] + zz[zzOff + 1];
+            zz[zzOff + 1] = (uint)c;
+            c >>= 32;
+            c += xVal * yy[yyOff + 2] + zz[zzOff + 2];
+            zz[zzOff + 2] = (uint)c;
+            c >>= 32;
+            c += xVal * yy[yyOff + 3] + zz[zzOff + 3];
+            zz[zzOff + 3] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint Mul33DWordAdd(uint x, ulong y, uint[] z, int zOff)
+        {
+            Debug.Assert(x >> 31 == 0);
+            Debug.Assert(zOff <= 0);
+            ulong c = 0, xVal = x;
+            ulong y00 = y & M;
+            c += xVal * y00 + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            ulong y01 = y >> 32;
+            c += xVal * y01 + y00 + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += y01 + z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff)
+        {
+            Debug.Assert(x >> 31 == 0);
+            Debug.Assert(zOff <= 1);
+            ulong c = 0, yVal = y;
+            c += yVal * x + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += yVal + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Nat.IncAt(4, z, zOff, 3);
+        }
+
+        public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff)
+        {
+            Debug.Assert(zOff <= 1);
+            ulong c = 0, xVal = x;
+            c += xVal * y + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += xVal * (y >> 32) + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Nat.IncAt(4, z, zOff, 3);
+        }
+
+        public static uint MulWordsAdd(uint x, uint y, uint[] z, int zOff)
+        {
+            Debug.Assert(zOff <= 2);
+
+            ulong c = 0, xVal = x, yVal = y;
+            c += yVal * xVal + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Nat.IncAt(4, z, zOff, 2);
+        }
+
+        public static uint MulWord(uint x, uint[] y, uint[] z, int zOff)
+        {
+            ulong c = 0, xVal = x;
+            int i = 0;
+            do
+            {
+                c += xVal * y[i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < 4);
+            return (uint)c;
+        }
+
+        public static void Square(uint[] x, uint[] zz)
+        {
+            ulong x_0 = x[0];
+            ulong zz_1;
+
+            uint c = 0, w;
+            {
+                int i = 3, j = 8;
+                do
+                {
+                    ulong xVal = x[i--];
+                    ulong p = xVal * xVal;
+                    zz[--j] = (c << 31) | (uint)(p >> 33);
+                    zz[--j] = (uint)(p >> 1);
+                    c = (uint)p;
+                }
+                while (i > 0);
+
+                {
+                    ulong p = x_0 * x_0;
+                    zz_1 = (ulong)(c << 31) | (p >> 33);
+                    zz[0] = (uint)p;
+                    c = (uint)(p >> 32) & 1;
+                }
+            }
+
+            ulong x_1 = x[1];
+            ulong zz_2 = zz[2];
+
+            {
+                zz_1 += x_1 * x_0;
+                w = (uint)zz_1;
+                zz[1] = (w << 1) | c;
+                c = w >> 31;
+                zz_2 += zz_1 >> 32;
+            }
+
+            ulong x_2 = x[2];
+            ulong zz_3 = zz[3];
+            ulong zz_4 = zz[4];
+            {
+                zz_2 += x_2 * x_0;
+                w = (uint)zz_2;
+                zz[2] = (w << 1) | c;
+                c = w >> 31;
+                zz_3 += (zz_2 >> 32) + x_2 * x_1;
+                zz_4 += zz_3 >> 32;
+                zz_3 &= M;
+            }
+
+            ulong x_3 = x[3];
+            ulong zz_5 = zz[5];
+            ulong zz_6 = zz[6];
+            {
+                zz_3 += x_3 * x_0;
+                w = (uint)zz_3;
+                zz[3] = (w << 1) | c;
+                c = w >> 31;
+                zz_4 += (zz_3 >> 32) + x_3 * x_1;
+                zz_5 += (zz_4 >> 32) + x_3 * x_2;
+                zz_6 += zz_5 >> 32;
+            }
+
+            w = (uint)zz_4;
+            zz[4] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_5;
+            zz[5] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_6;
+            zz[6] = (w << 1) | c;
+            c = w >> 31;
+            w = zz[7] + (uint)(zz_6 >> 32);
+            zz[7] = (w << 1) | c;
+        }
+
+        public static void Square(uint[] x, int xOff, uint[] zz, int zzOff)
+        {
+            ulong x_0 = x[xOff + 0];
+            ulong zz_1;
+
+            uint c = 0, w;
+            {
+                int i = 3, j = 8;
+                do
+                {
+                    ulong xVal = x[xOff + i--];
+                    ulong p = xVal * xVal;
+                    zz[zzOff + --j] = (c << 31) | (uint)(p >> 33);
+                    zz[zzOff + --j] = (uint)(p >> 1);
+                    c = (uint)p;
+                }
+                while (i > 0);
+
+                {
+                    ulong p = x_0 * x_0;
+                    zz_1 = (ulong)(c << 31) | (p >> 33);
+                    zz[zzOff + 0] = (uint)p;
+                    c = (uint)(p >> 32) & 1;
+                }
+            }
+
+            ulong x_1 = x[xOff + 1];
+            ulong zz_2 = zz[zzOff + 2];
+
+            {
+                zz_1 += x_1 * x_0;
+                w = (uint)zz_1;
+                zz[zzOff + 1] = (w << 1) | c;
+                c = w >> 31;
+                zz_2 += zz_1 >> 32;
+            }
+
+            ulong x_2 = x[xOff + 2];
+            ulong zz_3 = zz[zzOff + 3];
+            ulong zz_4 = zz[zzOff + 4];
+            {
+                zz_2 += x_2 * x_0;
+                w = (uint)zz_2;
+                zz[zzOff + 2] = (w << 1) | c;
+                c = w >> 31;
+                zz_3 += (zz_2 >> 32) + x_2 * x_1;
+                zz_4 += zz_3 >> 32;
+                zz_3 &= M;
+            }
+
+            ulong x_3 = x[xOff + 3];
+            ulong zz_5 = zz[zzOff + 5];
+            ulong zz_6 = zz[zzOff + 6];
+            {
+                zz_3 += x_3 * x_0;
+                w = (uint)zz_3;
+                zz[zzOff + 3] = (w << 1) | c;
+                c = w >> 31;
+                zz_4 += (zz_3 >> 32) + x_3 * x_1;
+                zz_5 += (zz_4 >> 32) + x_3 * x_2;
+                zz_6 += zz_5 >> 32;
+            }
+
+            w = (uint)zz_4;
+            zz[zzOff + 4] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_5;
+            zz[zzOff + 5] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_6;
+            zz[zzOff + 6] = (w << 1) | c;
+            c = w >> 31;
+            w = zz[zzOff + 7] + (uint)(zz_6 >> 32);
+            zz[zzOff + 7] = (w << 1) | c;
+        }
+
+        public static int Sub(uint[] x, uint[] y, uint[] z)
+        {
+            long c = 0;
+            c += (long)x[0] - y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)x[1] - y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (long)x[2] - y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)x[3] - y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int Sub(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            long c = 0;
+            c += (long)x[xOff + 0] - y[yOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)x[xOff + 1] - y[yOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += (long)x[xOff + 2] - y[yOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += (long)x[xOff + 3] - y[yOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int SubBothFrom(uint[] x, uint[] y, uint[] z)
+        {
+            long c = 0;
+            c += (long)z[0] - x[0] - y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - x[1] - y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (long)z[2] - x[2] - y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)z[3] - x[3] - y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int SubFrom(uint[] x, uint[] z)
+        {
+            long c = 0;
+            c += (long)z[0] - x[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - x[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (long)z[2] - x[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)z[3] - x[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int SubFrom(uint[] x, int xOff, uint[] z, int zOff)
+        {
+            long c = 0;
+            c += (long)z[zOff + 0] - x[xOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 1] - x[xOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 2] - x[xOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 3] - x[xOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static BigInteger ToBigInteger(uint[] x)
+        {
+            byte[] bs = new byte[16];
+            for (int i = 0; i < 4; ++i)
+            {
+                uint x_i = x[i];
+                if (x_i != 0)
+                {
+                    Pack.UInt32_To_BE(x_i, bs, (3 - i) << 2);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+
+        public static BigInteger ToBigInteger64(ulong[] x)
+        {
+            byte[] bs = new byte[16];
+            for (int i = 0; i < 2; ++i)
+            {
+                ulong x_i = x[i];
+                if (x_i != 0UL)
+                {
+                    Pack.UInt64_To_BE(x_i, bs, (1 - i) << 3);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+
+        public static void Zero(uint[] z)
+        {
+            z[0] = 0;
+            z[1] = 0;
+            z[2] = 0;
+            z[3] = 0;
+        }
+    }
+}
diff --git a/crypto/src/math/raw/Nat160.cs b/crypto/src/math/raw/Nat160.cs
new file mode 100644
index 000000000..153ac0a43
--- /dev/null
+++ b/crypto/src/math/raw/Nat160.cs
@@ -0,0 +1,874 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Crypto.Utilities;
+
+namespace Org.BouncyCastle.Math.Raw
+{
+    internal abstract class Nat160
+    {
+        private const ulong M = 0xFFFFFFFFUL;
+
+        public static uint Add(uint[] x, uint[] y, uint[] z)
+        {
+            ulong c = 0;
+            c += (ulong)x[0] + y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[1] + y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[2] + y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[3] + y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[4] + y[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddBothTo(uint[] x, uint[] y, uint[] z)
+        {
+            ulong c = 0;
+            c += (ulong)x[0] + y[0] + z[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[1] + y[1] + z[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[2] + y[2] + z[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[3] + y[3] + z[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[4] + y[4] + z[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddTo(uint[] x, uint[] z)
+        {
+            ulong c = 0;
+            c += (ulong)x[0] + z[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[1] + z[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[2] + z[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[3] + z[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[4] + z[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddTo(uint[] x, int xOff, uint[] z, int zOff, uint cIn)
+        {
+            ulong c = cIn;
+            c += (ulong)x[xOff + 0] + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 1] + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 2] + z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 3] + z[zOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 4] + z[zOff + 4];
+            z[zOff + 4] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 5] + z[zOff + 5];
+            return (uint)c;
+        }
+
+        public static uint AddToEachOther(uint[] u, int uOff, uint[] v, int vOff)
+        {
+            ulong c = 0;
+            c += (ulong)u[uOff + 0] + v[vOff + 0];
+            u[uOff + 0] = (uint)c;
+            v[vOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)u[uOff + 1] + v[vOff + 1];
+            u[uOff + 1] = (uint)c;
+            v[vOff + 1] = (uint)c;
+            c >>= 32;
+            c += (ulong)u[uOff + 2] + v[vOff + 2];
+            u[uOff + 2] = (uint)c;
+            v[vOff + 2] = (uint)c;
+            c >>= 32;
+            c += (ulong)u[uOff + 3] + v[vOff + 3];
+            u[uOff + 3] = (uint)c;
+            v[vOff + 3] = (uint)c;
+            c >>= 32;
+            c += (ulong)u[uOff + 4] + v[vOff + 4];
+            u[uOff + 4] = (uint)c;
+            v[vOff + 4] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static void Copy(uint[] x, uint[] z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+            z[4] = x[4];
+        }
+
+        public static uint[] Create()
+        {
+            return new uint[5];
+        }
+
+        public static uint[] CreateExt()
+        {
+            return new uint[10];
+        }
+
+        public static bool Diff(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            bool pos = Gte(x, xOff, y, yOff);
+            if (pos)
+            {
+                Sub(x, xOff, y, yOff, z, zOff);
+            }
+            else
+            {
+                Sub(y, yOff, x, xOff, z, zOff);
+            }
+            return pos;
+        }
+
+        public static bool Eq(uint[] x, uint[] y)
+        {
+            for (int i = 4; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                    return false;
+            }
+            return true;
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 160)
+                throw new ArgumentException();
+
+            uint[] z = Create();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (uint)x.IntValue;
+                x = x.ShiftRight(32);
+            }
+            return z;
+        }
+
+        public static uint GetBit(uint[] x, int bit)
+        {
+            if (bit == 0)
+            {
+                return x[0] & 1;
+            }
+            int w = bit >> 5;
+            if (w < 0 || w >= 5)
+            {
+                return 0;
+            }
+            int b = bit & 31;
+            return (x[w] >> b) & 1;
+        }
+
+        public static bool Gte(uint[] x, uint[] y)
+        {
+            for (int i = 4; i >= 0; --i)
+            {
+                uint x_i = x[i], y_i = y[i];
+                if (x_i < y_i)
+                    return false;
+                if (x_i > y_i)
+                    return true;
+            }
+            return true;
+        }
+
+        public static bool Gte(uint[] x, int xOff, uint[] y, int yOff)
+        {
+            for (int i = 4; i >= 0; --i)
+            {
+                uint x_i = x[xOff + i], y_i = y[yOff + i];
+                if (x_i < y_i)
+                    return false;
+                if (x_i > y_i)
+                    return true;
+            }
+            return true;
+        }
+
+        public static bool IsOne(uint[] x)
+        {
+            if (x[0] != 1)
+            {
+                return false;
+            }
+            for (int i = 1; i < 5; ++i)
+            {
+                if (x[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZero(uint[] x)
+        {
+            for (int i = 0; i < 5; ++i)
+            {
+                if (x[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static void Mul(uint[] x, uint[] y, uint[] zz)
+        {
+            ulong y_0 = y[0];
+            ulong y_1 = y[1];
+            ulong y_2 = y[2];
+            ulong y_3 = y[3];
+            ulong y_4 = y[4];
+
+            {
+                ulong c = 0, x_0 = x[0];
+                c += x_0 * y_0;
+                zz[0] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_1;
+                zz[1] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_2;
+                zz[2] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_3;
+                zz[3] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_4;
+                zz[4] = (uint)c;
+                c >>= 32;
+                zz[5] = (uint)c;
+            }
+
+            for (int i = 1; i < 5; ++i)
+            {
+                ulong c = 0, x_i = x[i];
+                c += x_i * y_0 + zz[i + 0];
+                zz[i + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[i + 1];
+                zz[i + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[i + 2];
+                zz[i + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[i + 3];
+                zz[i + 3] = (uint)c;
+                c >>= 32;
+                c += x_i * y_4 + zz[i + 4];
+                zz[i + 4] = (uint)c;
+                c >>= 32;
+                zz[i + 5] = (uint)c;
+            }
+        }
+
+        public static void Mul(uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff)
+        {
+            ulong y_0 = y[yOff + 0];
+            ulong y_1 = y[yOff + 1];
+            ulong y_2 = y[yOff + 2];
+            ulong y_3 = y[yOff + 3];
+            ulong y_4 = y[yOff + 4];
+
+            {
+                ulong c = 0, x_0 = x[xOff + 0];
+                c += x_0 * y_0;
+                zz[zzOff + 0] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_1;
+                zz[zzOff + 1] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_2;
+                zz[zzOff + 2] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_3;
+                zz[zzOff + 3] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_4;
+                zz[zzOff + 4] = (uint)c;
+                c >>= 32;
+                zz[zzOff + 5] = (uint)c;
+            }
+
+            for (int i = 1; i < 5; ++i)
+            {
+                ++zzOff;
+                ulong c = 0, x_i = x[xOff + i];
+                c += x_i * y_0 + zz[zzOff + 0];
+                zz[zzOff + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[zzOff + 1];
+                zz[zzOff + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[zzOff + 2];
+                zz[zzOff + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[zzOff + 3];
+                zz[zzOff + 3] = (uint)c;
+                c >>= 32;
+                c += x_i * y_4 + zz[zzOff + 4];
+                zz[zzOff + 4] = (uint)c;
+                c >>= 32;
+                zz[zzOff + 5] = (uint)c;
+            }
+        }
+
+        public static uint MulAddTo(uint[] x, uint[] y, uint[] zz)
+        {
+            ulong y_0 = y[0];
+            ulong y_1 = y[1];
+            ulong y_2 = y[2];
+            ulong y_3 = y[3];
+            ulong y_4 = y[4];
+
+            ulong zc = 0;
+            for (int i = 0; i < 5; ++i)
+            {
+                ulong c = 0, x_i = x[i];
+                c += x_i * y_0 + zz[i + 0];
+                zz[i + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[i + 1];
+                zz[i + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[i + 2];
+                zz[i + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[i + 3];
+                zz[i + 3] = (uint)c;
+                c >>= 32;
+                c += x_i * y_4 + zz[i + 4];
+                zz[i + 4] = (uint)c;
+                c >>= 32;
+                c += zc + zz[i + 5];
+                zz[i + 5] = (uint)c;
+                zc = c >> 32;
+            }
+            return (uint)zc;
+        }
+
+        public static uint MulAddTo(uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff)
+        {
+            ulong y_0 = y[yOff + 0];
+            ulong y_1 = y[yOff + 1];
+            ulong y_2 = y[yOff + 2];
+            ulong y_3 = y[yOff + 3];
+            ulong y_4 = y[yOff + 4];
+
+            ulong zc = 0;
+            for (int i = 0; i < 5; ++i)
+            {
+                ulong c = 0, x_i = x[xOff + i];
+                c += x_i * y_0 + zz[zzOff + 0];
+                zz[zzOff + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[zzOff + 1];
+                zz[zzOff + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[zzOff + 2];
+                zz[zzOff + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[zzOff + 3];
+                zz[zzOff + 3] = (uint)c;
+                c >>= 32;
+                c += x_i * y_4 + zz[zzOff + 4];
+                zz[zzOff + 4] = (uint)c;
+                c >>= 32;
+                c += zc + zz[zzOff + 5];
+                zz[zzOff + 5] = (uint)c;
+                zc = c >> 32;
+                ++zzOff;
+            }
+            return (uint)zc;
+        }
+
+        public static ulong Mul33Add(uint w, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            Debug.Assert(w >> 31 == 0);
+
+            ulong c = 0, wVal = w;
+            ulong x0 = x[xOff + 0];
+            c += wVal * x0 + y[yOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            ulong x1 = x[xOff + 1];
+            c += wVal * x1 + x0 + y[yOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            ulong x2 = x[xOff + 2];
+            c += wVal * x2 + x1 + y[yOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            ulong x3 = x[xOff + 3];
+            c += wVal * x3 + x2 + y[yOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            ulong x4 = x[xOff + 4];
+            c += wVal * x4 + x3 + y[yOff + 4];
+            z[zOff + 4] = (uint)c;
+            c >>= 32;
+            c += x4;
+            return c;
+        }
+
+        public static uint MulWordAddExt(uint x, uint[] yy, int yyOff, uint[] zz, int zzOff)
+        {
+            Debug.Assert(yyOff <= 5);
+            Debug.Assert(zzOff <= 5);
+
+            ulong c = 0, xVal = x;
+            c += xVal * yy[yyOff + 0] + zz[zzOff + 0];
+            zz[zzOff + 0] = (uint)c;
+            c >>= 32;
+            c += xVal * yy[yyOff + 1] + zz[zzOff + 1];
+            zz[zzOff + 1] = (uint)c;
+            c >>= 32;
+            c += xVal * yy[yyOff + 2] + zz[zzOff + 2];
+            zz[zzOff + 2] = (uint)c;
+            c >>= 32;
+            c += xVal * yy[yyOff + 3] + zz[zzOff + 3];
+            zz[zzOff + 3] = (uint)c;
+            c >>= 32;
+            c += xVal * yy[yyOff + 4] + zz[zzOff + 4];
+            zz[zzOff + 4] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint Mul33DWordAdd(uint x, ulong y, uint[] z, int zOff)
+        {
+            Debug.Assert(x >> 31 == 0);
+            Debug.Assert(zOff <= 1);
+            ulong c = 0, xVal = x;
+            ulong y00 = y & M;
+            c += xVal * y00 + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            ulong y01 = y >> 32;
+            c += xVal * y01 + y00 + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += y01 + z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Nat.IncAt(5, z, zOff, 4);
+        }
+
+        public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff)
+        {
+            Debug.Assert(x >> 31 == 0);
+            Debug.Assert(zOff <= 2);
+            ulong c = 0, yVal = y;
+            c += yVal * x + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += yVal + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Nat.IncAt(5, z, zOff, 3);
+        }
+
+        public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff)
+        {
+            Debug.Assert(zOff <= 2);
+            ulong c = 0, xVal = x;
+            c += xVal * y + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += xVal * (y >> 32) + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Nat.IncAt(5, z, zOff, 3);
+        }
+
+        public static uint MulWordsAdd(uint x, uint y, uint[] z, int zOff)
+        {
+            Debug.Assert(zOff <= 3);
+
+            ulong c = 0, xVal = x, yVal = y;
+            c += yVal * xVal + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Nat.IncAt(5, z, zOff, 2);
+        }
+
+        public static uint MulWord(uint x, uint[] y, uint[] z, int zOff)
+        {
+            ulong c = 0, xVal = x;
+            int i = 0;
+            do
+            {
+                c += xVal * y[i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < 5);
+            return (uint)c;
+        }
+
+        public static void Square(uint[] x, uint[] zz)
+        {
+            ulong x_0 = x[0];
+            ulong zz_1;
+
+            uint c = 0, w;
+            {
+                int i = 4, j = 10;
+                do
+                {
+                    ulong xVal = x[i--];
+                    ulong p = xVal * xVal;
+                    zz[--j] = (c << 31) | (uint)(p >> 33);
+                    zz[--j] = (uint)(p >> 1);
+                    c = (uint)p;
+                }
+                while (i > 0);
+
+                {
+                    ulong p = x_0 * x_0;
+                    zz_1 = (ulong)(c << 31) | (p >> 33);
+                    zz[0] = (uint)p;
+                    c = (uint)(p >> 32) & 1;
+                }
+            }
+
+            ulong x_1 = x[1];
+            ulong zz_2 = zz[2];
+
+            {
+                zz_1 += x_1 * x_0;
+                w = (uint)zz_1;
+                zz[1] = (w << 1) | c;
+                c = w >> 31;
+                zz_2 += zz_1 >> 32;
+            }
+
+            ulong x_2 = x[2];
+            ulong zz_3 = zz[3];
+            ulong zz_4 = zz[4];
+            {
+                zz_2 += x_2 * x_0;
+                w = (uint)zz_2;
+                zz[2] = (w << 1) | c;
+                c = w >> 31;
+                zz_3 += (zz_2 >> 32) + x_2 * x_1;
+                zz_4 += zz_3 >> 32;
+                zz_3 &= M;
+            }
+
+            ulong x_3 = x[3];
+            ulong zz_5 = zz[5];
+            ulong zz_6 = zz[6];
+            {
+                zz_3 += x_3 * x_0;
+                w = (uint)zz_3;
+                zz[3] = (w << 1) | c;
+                c = w >> 31;
+                zz_4 += (zz_3 >> 32) + x_3 * x_1;
+                zz_5 += (zz_4 >> 32) + x_3 * x_2;
+                zz_4 &= M;
+                zz_6 += zz_5 >> 32;
+                zz_5 &= M;
+            }
+
+            ulong x_4 = x[4];
+            ulong zz_7 = zz[7];
+            ulong zz_8 = zz[8];
+            {
+                zz_4 += x_4 * x_0;
+                w = (uint)zz_4;
+                zz[4] = (w << 1) | c;
+                c = w >> 31;
+                zz_5 += (zz_4 >> 32) + x_4 * x_1;
+                zz_6 += (zz_5 >> 32) + x_4 * x_2;
+                zz_7 += (zz_6 >> 32) + x_4 * x_3;
+                zz_8 += zz_7 >> 32;
+            }
+
+            w = (uint)zz_5;
+            zz[5] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_6;
+            zz[6] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_7;
+            zz[7] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_8;
+            zz[8] = (w << 1) | c;
+            c = w >> 31;
+            w = zz[9] + (uint)(zz_8 >> 32);
+            zz[9] = (w << 1) | c;
+        }
+
+        public static void Square(uint[] x, int xOff, uint[] zz, int zzOff)
+        {
+            ulong x_0 = x[xOff + 0];
+            ulong zz_1;
+
+            uint c = 0, w;
+            {
+                int i = 4, j = 10;
+                do
+                {
+                    ulong xVal = x[xOff + i--];
+                    ulong p = xVal * xVal;
+                    zz[zzOff + --j] = (c << 31) | (uint)(p >> 33);
+                    zz[zzOff + --j] = (uint)(p >> 1);
+                    c = (uint)p;
+                }
+                while (i > 0);
+
+                {
+                    ulong p = x_0 * x_0;
+                    zz_1 = (ulong)(c << 31) | (p >> 33);
+                    zz[zzOff + 0] = (uint)p;
+                    c = (uint)(p >> 32) & 1;
+                }
+            }
+
+            ulong x_1 = x[xOff + 1];
+            ulong zz_2 = zz[zzOff + 2];
+
+            {
+                zz_1 += x_1 * x_0;
+                w = (uint)zz_1;
+                zz[zzOff + 1] = (w << 1) | c;
+                c = w >> 31;
+                zz_2 += zz_1 >> 32;
+            }
+
+            ulong x_2 = x[xOff + 2];
+            ulong zz_3 = zz[zzOff + 3];
+            ulong zz_4 = zz[zzOff + 4];
+            {
+                zz_2 += x_2 * x_0;
+                w = (uint)zz_2;
+                zz[zzOff + 2] = (w << 1) | c;
+                c = w >> 31;
+                zz_3 += (zz_2 >> 32) + x_2 * x_1;
+                zz_4 += zz_3 >> 32;
+                zz_3 &= M;
+            }
+
+            ulong x_3 = x[xOff + 3];
+            ulong zz_5 = zz[zzOff + 5];
+            ulong zz_6 = zz[zzOff + 6];
+            {
+                zz_3 += x_3 * x_0;
+                w = (uint)zz_3;
+                zz[zzOff + 3] = (w << 1) | c;
+                c = w >> 31;
+                zz_4 += (zz_3 >> 32) + x_3 * x_1;
+                zz_5 += (zz_4 >> 32) + x_3 * x_2;
+                zz_4 &= M;
+                zz_6 += zz_5 >> 32;
+                zz_5 &= M;
+            }
+
+            ulong x_4 = x[xOff + 4];
+            ulong zz_7 = zz[zzOff + 7];
+            ulong zz_8 = zz[zzOff + 8];
+            {
+                zz_4 += x_4 * x_0;
+                w = (uint)zz_4;
+                zz[zzOff + 4] = (w << 1) | c;
+                c = w >> 31;
+                zz_5 += (zz_4 >> 32) + x_4 * x_1;
+                zz_6 += (zz_5 >> 32) + x_4 * x_2;
+                zz_7 += (zz_6 >> 32) + x_4 * x_3;
+                zz_8 += zz_7 >> 32;
+            }
+
+            w = (uint)zz_5;
+            zz[zzOff + 5] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_6;
+            zz[zzOff + 6] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_7;
+            zz[zzOff + 7] = (w << 1) | c;
+            c = w >> 31;
+            w = (uint)zz_8;
+            zz[zzOff + 8] = (w << 1) | c;
+            c = w >> 31;
+            w = zz[zzOff + 9] + (uint)(zz_8 >> 32);
+            zz[zzOff + 9] = (w << 1) | c;
+        }
+
+        public static int Sub(uint[] x, uint[] y, uint[] z)
+        {
+            long c = 0;
+            c += (long)x[0] - y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)x[1] - y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (long)x[2] - y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)x[3] - y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (long)x[4] - y[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int Sub(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            long c = 0;
+            c += (long)x[xOff + 0] - y[yOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)x[xOff + 1] - y[yOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += (long)x[xOff + 2] - y[yOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += (long)x[xOff + 3] - y[yOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            c += (long)x[xOff + 4] - y[yOff + 4];
+            z[zOff + 4] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int SubBothFrom(uint[] x, uint[] y, uint[] z)
+        {
+            long c = 0;
+            c += (long)z[0] - x[0] - y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - x[1] - y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (long)z[2] - x[2] - y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)z[3] - x[3] - y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (long)z[4] - x[4] - y[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int SubFrom(uint[] x, uint[] z)
+        {
+            long c = 0;
+            c += (long)z[0] - x[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - x[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (long)z[2] - x[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)z[3] - x[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (long)z[4] - x[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int SubFrom(uint[] x, int xOff, uint[] z, int zOff)
+        {
+            long c = 0;
+            c += (long)z[zOff + 0] - x[xOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 1] - x[xOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 2] - x[xOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 3] - x[xOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 4] - x[xOff + 4];
+            z[zOff + 4] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static BigInteger ToBigInteger(uint[] x)
+        {
+            byte[] bs = new byte[20];
+            for (int i = 0; i < 5; ++i)
+            {
+                uint x_i = x[i];
+                if (x_i != 0)
+                {
+                    Pack.UInt32_To_BE(x_i, bs, (4 - i) << 2);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+
+        public static void Zero(uint[] z)
+        {
+            z[0] = 0;
+            z[1] = 0;
+            z[2] = 0;
+            z[3] = 0;
+            z[4] = 0;
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/Nat192.cs b/crypto/src/math/raw/Nat192.cs
index 94d7ed17c..4797609ee 100644
--- a/crypto/src/math/ec/custom/sec/Nat192.cs
+++ b/crypto/src/math/raw/Nat192.cs
@@ -3,7 +3,7 @@ using System.Diagnostics;
 
 using Org.BouncyCastle.Crypto.Utilities;
 
-namespace Org.BouncyCastle.Math.EC.Custom.Sec
+namespace Org.BouncyCastle.Math.Raw
 {
     internal abstract class Nat192
     {
@@ -145,16 +145,33 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[5] = x[5];
         }
 
+        public static void Copy64(ulong[] x, ulong[] z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+        }
+
         public static uint[] Create()
         {
             return new uint[6];
         }
 
+        public static ulong[] Create64()
+        {
+            return new ulong[3];
+        }
+
         public static uint[] CreateExt()
         {
             return new uint[12];
         }
 
+        public static ulong[] CreateExt64()
+        {
+            return new ulong[6];
+        }
+
         public static bool Diff(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
         {
             bool pos = Gte(x, xOff, y, yOff);
@@ -179,6 +196,18 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
+        public static bool Eq64(ulong[] x, ulong[] y)
+        {
+            for (int i = 2; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
         public static uint[] FromBigInteger(BigInteger x)
         {
             if (x.SignValue < 0 || x.BitLength > 192)
@@ -194,6 +223,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return z;
         }
 
+        public static ulong[] FromBigInteger64(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 192)
+                throw new ArgumentException();
+
+            ulong[] z = Create64();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (ulong)x.LongValue;
+                x = x.ShiftRight(64);
+            }
+            return z;
+        }
+
         public static uint GetBit(uint[] x, int bit)
         {
             if (bit == 0)
@@ -251,6 +295,22 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
+        public static bool IsOne64(ulong[] x)
+        {
+            if (x[0] != 1UL)
+            {
+                return false;
+            }
+            for (int i = 1; i < 3; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
         public static bool IsZero(uint[] x)
         {
             for (int i = 0; i < 6; ++i)
@@ -263,6 +323,18 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
+        public static bool IsZero64(ulong[] x)
+        {
+            for (int i = 0; i < 3; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
         public static void Mul(uint[] x, uint[] y, uint[] zz)
         {
             ulong y_0 = y[0];
@@ -949,6 +1021,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new BigInteger(1, bs);
         }
 
+        public static BigInteger ToBigInteger64(ulong[] x)
+        {
+            byte[] bs = new byte[24];
+            for (int i = 0; i < 3; ++i)
+            {
+                ulong x_i = x[i];
+                if (x_i != 0L)
+                {
+                    Pack.UInt64_To_BE(x_i, bs, (2 - i) << 3);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+
         public static void Zero(uint[] z)
         {
             z[0] = 0;
diff --git a/crypto/src/math/ec/custom/sec/Nat224.cs b/crypto/src/math/raw/Nat224.cs
index d5b916a54..940e930ac 100644
--- a/crypto/src/math/ec/custom/sec/Nat224.cs
+++ b/crypto/src/math/raw/Nat224.cs
@@ -3,7 +3,7 @@ using System.Diagnostics;
 
 using Org.BouncyCastle.Crypto.Utilities;
 
-namespace Org.BouncyCastle.Math.EC.Custom.Sec
+namespace Org.BouncyCastle.Math.Raw
 {
     internal abstract class Nat224
     {
diff --git a/crypto/src/math/ec/custom/sec/Nat256.cs b/crypto/src/math/raw/Nat256.cs
index bd2d6da47..19455031a 100644
--- a/crypto/src/math/ec/custom/sec/Nat256.cs
+++ b/crypto/src/math/raw/Nat256.cs
@@ -3,7 +3,7 @@ using System.Diagnostics;
 
 using Org.BouncyCastle.Crypto.Utilities;
 
-namespace Org.BouncyCastle.Math.EC.Custom.Sec
+namespace Org.BouncyCastle.Math.Raw
 {
     internal abstract class Nat256
     {
@@ -239,16 +239,34 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             z[7] = x[7];
         }
 
+        public static void Copy64(ulong[] x, ulong[] z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+        }
+
         public static uint[] Create()
         {
             return new uint[8];
         }
 
+        public static ulong[] Create64()
+        {
+            return new ulong[4];
+        }
+
         public static uint[] CreateExt()
         {
             return new uint[16];
         }
 
+        public static ulong[] CreateExt64()
+        {
+            return new ulong[8];
+        }
+
         public static bool Diff(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
         {
             bool pos = Gte(x, xOff, y, yOff);
@@ -273,6 +291,18 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
+        public static bool Eq64(ulong[] x, ulong[] y)
+        {
+            for (int i = 3; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
         public static uint[] FromBigInteger(BigInteger x)
         {
             if (x.SignValue < 0 || x.BitLength > 256)
@@ -288,6 +318,21 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return z;
         }
 
+        public static ulong[] FromBigInteger64(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 256)
+                throw new ArgumentException();
+
+            ulong[] z = Create64();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (ulong)x.LongValue;
+                x = x.ShiftRight(64);
+            }
+            return z;
+        }
+
         public static uint GetBit(uint[] x, int bit)
         {
             if (bit == 0)
@@ -345,6 +390,22 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
+        public static bool IsOne64(ulong[] x)
+        {
+            if (x[0] != 1UL)
+            {
+                return false;
+            }
+            for (int i = 1; i < 4; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
         public static bool IsZero(uint[] x)
         {
             for (int i = 0; i < 8; ++i)
@@ -357,6 +418,18 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
+        public static bool IsZero64(ulong[] x)
+        {
+            for (int i = 0; i < 4; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
         public static void Mul(uint[] x, uint[] y, uint[] zz)
         {
             ulong y_0 = y[0];
@@ -1285,6 +1358,20 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new BigInteger(1, bs);
         }
 
+        public static BigInteger ToBigInteger64(ulong[] x)
+        {
+            byte[] bs = new byte[32];
+            for (int i = 0; i < 4; ++i)
+            {
+                ulong x_i = x[i];
+                if (x_i != 0L)
+                {
+                    Pack.UInt64_To_BE(x_i, bs, (3 - i) << 3);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+
         public static void Zero(uint[] z)
         {
             z[0] = 0;
diff --git a/crypto/src/math/raw/Nat320.cs b/crypto/src/math/raw/Nat320.cs
new file mode 100644
index 000000000..c7daa71e2
--- /dev/null
+++ b/crypto/src/math/raw/Nat320.cs
@@ -0,0 +1,98 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Crypto.Utilities;
+
+namespace Org.BouncyCastle.Math.Raw
+{
+    internal abstract class Nat320
+    {
+        public static void Copy64(ulong[] x, ulong[] z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+            z[4] = x[4];
+        }
+
+        public static ulong[] Create64()
+        {
+            return new ulong[5];
+        }
+
+        public static ulong[] CreateExt64()
+        {
+            return new ulong[10];
+        }
+
+        public static bool Eq64(ulong[] x, ulong[] y)
+        {
+            for (int i = 4; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static ulong[] FromBigInteger64(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 320)
+                throw new ArgumentException();
+
+            ulong[] z = Create64();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (ulong)x.LongValue;
+                x = x.ShiftRight(64);
+            }
+            return z;
+        }
+
+        public static bool IsOne64(ulong[] x)
+        {
+            if (x[0] != 1UL)
+            {
+                return false;
+            }
+            for (int i = 1; i < 5; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZero64(ulong[] x)
+        {
+            for (int i = 0; i < 5; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static BigInteger ToBigInteger64(ulong[] x)
+        {
+            byte[] bs = new byte[40];
+            for (int i = 0; i < 5; ++i)
+            {
+                ulong x_i = x[i];
+                if (x_i != 0L)
+                {
+                    Pack.UInt64_To_BE(x_i, bs, (4 - i) << 3);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/Nat384.cs b/crypto/src/math/raw/Nat384.cs
index dd93e68b6..ed1c47e8c 100644
--- a/crypto/src/math/ec/custom/sec/Nat384.cs
+++ b/crypto/src/math/raw/Nat384.cs
@@ -1,7 +1,7 @@
 using System;
 using System.Diagnostics;
 
-namespace Org.BouncyCastle.Math.EC.Custom.Sec
+namespace Org.BouncyCastle.Math.Raw
 {
     internal abstract class Nat384
     {
diff --git a/crypto/src/math/raw/Nat448.cs b/crypto/src/math/raw/Nat448.cs
new file mode 100644
index 000000000..52a253f1b
--- /dev/null
+++ b/crypto/src/math/raw/Nat448.cs
@@ -0,0 +1,100 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Crypto.Utilities;
+
+namespace Org.BouncyCastle.Math.Raw
+{
+    internal abstract class Nat448
+    {
+        public static void Copy64(ulong[] x, 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];
+        }
+
+        public static ulong[] Create64()
+        {
+            return new ulong[7];
+        }
+
+        public static ulong[] CreateExt64()
+        {
+            return new ulong[14];
+        }
+
+        public static bool Eq64(ulong[] x, ulong[] y)
+        {
+            for (int i = 6; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static ulong[] FromBigInteger64(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 448)
+                throw new ArgumentException();
+
+            ulong[] z = Create64();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (ulong)x.LongValue;
+                x = x.ShiftRight(64);
+            }
+            return z;
+        }
+
+        public static bool IsOne64(ulong[] x)
+        {
+            if (x[0] != 1UL)
+            {
+                return false;
+            }
+            for (int i = 1; i < 7; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZero64(ulong[] x)
+        {
+            for (int i = 0; i < 7; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static BigInteger ToBigInteger64(ulong[] x)
+        {
+            byte[] bs = new byte[56];
+            for (int i = 0; i < 7; ++i)
+            {
+                ulong x_i = x[i];
+                if (x_i != 0L)
+                {
+                    Pack.UInt64_To_BE(x_i, bs, (6 - i) << 3);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/Nat512.cs b/crypto/src/math/raw/Nat512.cs
index 46e10f995..a9ef2b3b6 100644
--- a/crypto/src/math/ec/custom/sec/Nat512.cs
+++ b/crypto/src/math/raw/Nat512.cs
@@ -1,7 +1,7 @@
 using System;
 using System.Diagnostics;
 
-namespace Org.BouncyCastle.Math.EC.Custom.Sec
+namespace Org.BouncyCastle.Math.Raw
 {
     internal abstract class Nat512
     {
diff --git a/crypto/src/math/raw/Nat576.cs b/crypto/src/math/raw/Nat576.cs
new file mode 100644
index 000000000..813fb86be
--- /dev/null
+++ b/crypto/src/math/raw/Nat576.cs
@@ -0,0 +1,102 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Crypto.Utilities;
+
+namespace Org.BouncyCastle.Math.Raw
+{
+    internal abstract class Nat576
+    {
+        public static void Copy64(ulong[] x, 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];
+        }
+
+        public static ulong[] Create64()
+        {
+            return new ulong[9];
+        }
+
+        public static ulong[] CreateExt64()
+        {
+            return new ulong[18];
+        }
+
+        public static bool Eq64(ulong[] x, ulong[] y)
+        {
+            for (int i = 8; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static ulong[] FromBigInteger64(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 576)
+                throw new ArgumentException();
+
+            ulong[] z = Create64();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (ulong)x.LongValue;
+                x = x.ShiftRight(64);
+            }
+            return z;
+        }
+
+        public static bool IsOne64(ulong[] x)
+        {
+            if (x[0] != 1UL)
+            {
+                return false;
+            }
+            for (int i = 1; i < 9; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZero64(ulong[] x)
+        {
+            for (int i = 0; i < 9; ++i)
+            {
+                if (x[i] != 0UL)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static BigInteger ToBigInteger64(ulong[] x)
+        {
+            byte[] bs = new byte[72];
+            for (int i = 0; i < 9; ++i)
+            {
+                ulong x_i = x[i];
+                if (x_i != 0L)
+                {
+                    Pack.UInt64_To_BE(x_i, bs, (8 - i) << 3);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+    }
+}