diff options
Diffstat (limited to 'crypto/src/pqc/math/linearalgebra/GF2mField.cs')
| -rw-r--r-- | crypto/src/pqc/math/linearalgebra/GF2mField.cs | 370 |
1 files changed, 370 insertions, 0 deletions
diff --git a/crypto/src/pqc/math/linearalgebra/GF2mField.cs b/crypto/src/pqc/math/linearalgebra/GF2mField.cs new file mode 100644 index 000000000..e8182bf6f --- /dev/null +++ b/crypto/src/pqc/math/linearalgebra/GF2mField.cs @@ -0,0 +1,370 @@ +using Org.BouncyCastle.Security; +using System; + +namespace Org.BouncyCastle.Pqc.Math.LinearAlgebra +{ + public class GF2mField + { + + /* + * degree - degree of the field polynomial - the field polynomial ring - + * polynomial ring over the finite field GF(2) + */ + + private int degree = 0; + + private int polynomial; + + /** + * create a finite field GF(2^m) + * + * @param degree the degree of the field + */ + public GF2mField(int degree) + { + if (degree >= 32) + { + throw new ArgumentException( + " Error: the degree of field is too large "); + } + if (degree < 1) + { + throw new ArgumentException( + " Error: the degree of field is non-positive "); + } + this.degree = degree; + polynomial = PolynomialRingGF2.GetIrreduciblePolynomial(degree); + } + + /** + * create a finite field GF(2^m) with the fixed field polynomial + * + * @param degree the degree of the field + * @param poly the field polynomial + */ + public GF2mField(int degree, int poly) + { + if (degree != PolynomialRingGF2.Degree(poly)) + { + throw new ArgumentException( + " Error: the degree is not correct"); + } + if (!PolynomialRingGF2.IsIrreducible(poly)) + { + throw new ArgumentException( + " Error: given polynomial is reducible"); + } + this.degree = degree; + polynomial = poly; + + } + + public GF2mField(byte[] enc) + { + if (enc.Length != 4) + { + throw new ArgumentException( + "byte array is not an encoded finite field"); + } + polynomial = LittleEndianConversions.OS2IP(enc); + if (!PolynomialRingGF2.IsIrreducible(polynomial)) + { + throw new ArgumentException( + "byte array is not an encoded finite field"); + } + + degree = PolynomialRingGF2.Degree(polynomial); + } + + public GF2mField(GF2mField field) + { + degree = field.degree; + polynomial = field.polynomial; + } + + /** + * return degree of the field + * + * @return degree of the field + */ + public int GetDegree() + { + return degree; + } + + /** + * return the field polynomial + * + * @return the field polynomial + */ + public int GetPolynomial() + { + return polynomial; + } + + /** + * return the encoded form of this field + * + * @return the field in byte array form + */ + public byte[] GetEncoded() + { + return LittleEndianConversions.I2OSP(polynomial); + } + + /** + * Return sum of two elements + * + * @param a + * @param b + * @return a+b + */ + public int add(int a, int b) + { + return a ^ b; + } + + /** + * Return product of two elements + * + * @param a + * @param b + * @return a*b + */ + public int Mult(int a, int b) + { + return PolynomialRingGF2.modMultiply(a, b, polynomial); + } + + /** + * compute exponentiation a^k + * + * @param a a field element a + * @param k k degree + * @return a^k + */ + public int Exp(int a, int k) + { + if (k == 0) + { + return 1; + } + if (a == 0) + { + return 0; + } + if (a == 1) + { + return 1; + } + int result = 1; + if (k < 0) + { + a = Inverse(a); + k = -k; + } + while (k != 0) + { + if ((k & 1) == 1) + { + result = Mult(result, a); + } + a = Mult(a, a); + //k >>>= 1; + uint kTmp = (uint)k; + kTmp >>= 1; + k = (int) kTmp; + } + return result; + } + + /** + * compute the multiplicative inverse of a + * + * @param a a field element a + * @return a<sup>-1</sup> + */ + public int Inverse(int a) + { + int d = (1 << degree) - 2; + + return Exp(a, d); + } + + /** + * compute the square root of an integer + * + * @param a a field element a + * @return a<sup>1/2</sup> + */ + public int SqRoot(int a) + { + for (int i = 1; i < degree; i++) + { + a = Mult(a, a); + } + return a; + } + + /** + * create a random field element using PRNG sr + * + * @param sr SecureRandom + * @return a random element + */ + public int GetRandomElement(SecureRandom sr) + { + int result = RandUtils.NextInt(sr, 1 << degree); + return result; + } + + /** + * create a random non-zero field element + * + * @return a random element + */ + //public int getRandomNonZeroElement() + //{ + // return getRandomNonZeroElement(CryptoServicesRegistrar.getSecureRandom()); + //} + + /** + * create a random non-zero field element using PRNG sr + * + * @param sr SecureRandom + * @return a random non-zero element + */ + public int GetRandomNonZeroElement(SecureRandom sr) + { + int controltime = 1 << 20; + int count = 0; + int result = RandUtils.NextInt(sr, 1 << degree); + while ((result == 0) && (count < controltime)) + { + result = RandUtils.NextInt(sr, 1 << degree); + count++; + } + if (count == controltime) + { + result = 1; + } + return result; + } + + /** + * @return true if e is encoded element of this field and false otherwise + */ + public bool IsElementOfThisField(int e) + { + // e is encoded element of this field iff 0<= e < |2^m| + if (degree == 31) + { + return e >= 0; + } + return e >= 0 && e < (1 << degree); + } + + /* + * help method for visual control + */ + public String ElementToStr(int a) + { + String s = ""; + for (int i = 0; i < degree; i++) + { + if (((byte)a & 0x01) == 0) + { + s = "0" + s; + } + else + { + s = "1" + s; + } + //a >>>= 1; + uint aTmp = (uint)a; + aTmp >>= 1; + a = (int)aTmp; + } + return s; + } + + /** + * checks if given object is equal to this field. + * <p> + * The method returns false whenever the given object is not GF2m. + * + * @param other object + * @return true or false + */ + public bool Equals(Object other) + { + if ((other == null) || !(other is GF2mField)) + { + return false; + } + + GF2mField otherField = (GF2mField)other; + + if ((degree == otherField.degree) + && (polynomial == otherField.polynomial)) + { + return true; + } + + return false; + } + + public int HashCode() + { + return polynomial; + } + + /** + * Returns a human readable form of this field. + * + * @return a human readable form of this field. + */ + public String ToString() + { + String str = "Finite Field GF(2^" + degree + ") = " + "GF(2)[X]/<" + + PolyToString(polynomial) + "> "; + return str; + } + + private static String PolyToString(int p) + { + String str = ""; + if (p == 0) + { + str = "0"; + } + else + { + byte b = (byte)(p & 0x01); + if (b == 1) + { + str = "1"; + } + //p >>>= 1; + uint pTmp = (uint)p; + pTmp >>= 1; + p = (int)pTmp; + int i = 1; + while (p != 0) + { + b = (byte)(p & 0x01); + if (b == 1) + { + str = str + "+x^" + i; + } + //p >>>= 1; + pTmp = (uint) p; + pTmp >>= 1; + p = (int)pTmp; + i++; + } + } + return str; + } + } +} \ No newline at end of file |