C# Class MpcLib.Common.FiniteField.NumTheoryUtils

Implements some number-theoretic utility functions.
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Public Properties

Property Type Description
DHPrime1536 System.Numerics.BigInteger
DHPrime2048 System.Numerics.BigInteger
DHPrime768 System.Numerics.BigInteger

Public Methods

Method Description
CalcInverse ( System.Numerics.BigInteger n, System.Numerics.BigInteger prime ) : System.Numerics.BigInteger

Returns the inverse of n modulo p.
DLEncrypt ( BigZp x, System.Numerics.BigInteger p ) : System.Numerics.BigInteger

Discrete logarithm encryption.
ExtendedEuclidean ( System.Numerics.BigInteger a, System.Numerics.BigInteger b, System.Numerics.BigInteger &x, System.Numerics.BigInteger &y ) : System.Numerics.BigInteger

Performs the Extended Euclidean algorithm and returns gcd(a,b). The function also returns integers x and y such that ax + by = gcd(a,b). If gcd(a,b) = 1, then x is a multiplicative inverse of "a mod b" and y is a multiplicative inverse of "b mod a".
ExtendedEuclidean ( int a, int b, int &x, int &y ) : int

Performs the Extended Euclidean algorithm and returns gcd(a,b). The function also returns integers x and y such that ax + by = gcd(a,b). If gcd(a,b) = 1, then x is a multiplicative inverse of "a mod b" and y is a multiplicative inverse of "b mod a".
ExtendedEuclidean ( long a, long b, long &x, long &y ) : long

Performs the Extended Euclidean algorithm and returns gcd(a,b). The function also returns integers x and y such that ax + by = gcd(a,b). If gcd(a,b) = 1, then x is a multiplicative inverse of "a mod b" and y is a multiplicative inverse of "b mod a".
GetBitDecomposition ( System.Numerics.BigInteger a, System.Numerics.BigInteger prime ) : List
GetBitDecomposition ( System.Numerics.BigInteger a, System.Numerics.BigInteger prime, int length ) : List
GetBitLength ( System.Numerics.BigInteger a ) : int

Returns the actual number of bits of a byte array by ignoring trailing zeros in the binary representation.
GetBitLength ( byte a ) : int

Returns the actual number of bits of a byte array by ignoring trailing zeros in the binary representation.
GetBitLength2 ( System.Numerics.BigInteger a ) : int
GetFieldInverse ( int prime ) : int[]

Returns an array containing inverses of all field elements.
GetFieldMinimumPrimitive ( int prime ) : int
IsPrime ( int n ) : bool

Performs a O(sqrt(|n|)) primality test, where |n| is the bit-length of the input.
MillerRabin ( System.Numerics.BigInteger n, int k ) : bool

Implements the Miller-Rabin algorithm for fast compositeness test. Returns true if n is a composite number. If n is prime, returns false with high probability (this probability increases with k).
ModPow ( int powerBase, int exp, int prime ) : int

Performs modular exponentiation.
ModSqrRoot ( System.Numerics.BigInteger val, System.Numerics.BigInteger prime ) : System.Numerics.BigInteger
MultiplicativeInverse ( System.Numerics.BigInteger a, System.Numerics.BigInteger m ) : System.Numerics.BigInteger

Returns the multiplicative inverse of a modulo m.
MultiplicativeInverse ( int a, int m ) : int

Returns the multiplicative inverse of a modulo m.
MultiplicativeInverse ( long a, long m ) : long

Returns the multiplicative inverse of a modulo m.
NextRandomBigInt ( RNGCryptoServiceProvider rng, System.Numerics.BigInteger minValue, System.Numerics.BigInteger maxValue ) : System.Numerics.BigInteger

Returns a random big integer in the specified range. This is based on a simple probabilistic algorithm.

Method Details

CalcInverse() public static method

Returns the inverse of n modulo p.
public static CalcInverse ( System.Numerics.BigInteger n, System.Numerics.BigInteger prime ) : System.Numerics.BigInteger
n System.Numerics.BigInteger
prime System.Numerics.BigInteger
return System.Numerics.BigInteger

DLEncrypt() public static method

Discrete logarithm encryption.
public static DLEncrypt ( BigZp x, System.Numerics.BigInteger p ) : System.Numerics.BigInteger
x BigZp Value to be encrypted.
p System.Numerics.BigInteger Prime modulus. Should be large enough (> 1024 bits) to ensure security.
return System.Numerics.BigInteger

ExtendedEuclidean() public static method

Performs the Extended Euclidean algorithm and returns gcd(a,b). The function also returns integers x and y such that ax + by = gcd(a,b). If gcd(a,b) = 1, then x is a multiplicative inverse of "a mod b" and y is a multiplicative inverse of "b mod a".
public static ExtendedEuclidean ( System.Numerics.BigInteger a, System.Numerics.BigInteger b, System.Numerics.BigInteger &x, System.Numerics.BigInteger &y ) : System.Numerics.BigInteger
a System.Numerics.BigInteger
b System.Numerics.BigInteger
x System.Numerics.BigInteger
y System.Numerics.BigInteger
return System.Numerics.BigInteger

ExtendedEuclidean() public static method

Performs the Extended Euclidean algorithm and returns gcd(a,b). The function also returns integers x and y such that ax + by = gcd(a,b). If gcd(a,b) = 1, then x is a multiplicative inverse of "a mod b" and y is a multiplicative inverse of "b mod a".
public static ExtendedEuclidean ( int a, int b, int &x, int &y ) : int
a int
b int
x int
y int
return int

ExtendedEuclidean() public static method

Performs the Extended Euclidean algorithm and returns gcd(a,b). The function also returns integers x and y such that ax + by = gcd(a,b). If gcd(a,b) = 1, then x is a multiplicative inverse of "a mod b" and y is a multiplicative inverse of "b mod a".
public static ExtendedEuclidean ( long a, long b, long &x, long &y ) : long
a long
b long
x long
y long
return long

GetBitDecomposition() public static method

public static GetBitDecomposition ( System.Numerics.BigInteger a, System.Numerics.BigInteger prime ) : List
a System.Numerics.BigInteger
prime System.Numerics.BigInteger
return List

GetBitDecomposition() public static method

public static GetBitDecomposition ( System.Numerics.BigInteger a, System.Numerics.BigInteger prime, int length ) : List
a System.Numerics.BigInteger
prime System.Numerics.BigInteger
length int
return List

GetBitLength() public static method

Returns the actual number of bits of a byte array by ignoring trailing zeros in the binary representation.
public static GetBitLength ( System.Numerics.BigInteger a ) : int
a System.Numerics.BigInteger
return int

GetBitLength() public static method

Returns the actual number of bits of a byte array by ignoring trailing zeros in the binary representation.
public static GetBitLength ( byte a ) : int
a byte
return int

GetBitLength2() public static method

public static GetBitLength2 ( System.Numerics.BigInteger a ) : int
a System.Numerics.BigInteger
return int

GetFieldInverse() public static method

Returns an array containing inverses of all field elements.
public static GetFieldInverse ( int prime ) : int[]
prime int
return int[]

GetFieldMinimumPrimitive() public static method

public static GetFieldMinimumPrimitive ( int prime ) : int
prime int
return int

IsPrime() public static method

Performs a O(sqrt(|n|)) primality test, where |n| is the bit-length of the input.
public static IsPrime ( int n ) : bool
n int
return bool

MillerRabin() public static method

Implements the Miller-Rabin algorithm for fast compositeness test. Returns true if n is a composite number. If n is prime, returns false with high probability (this probability increases with k).
public static MillerRabin ( System.Numerics.BigInteger n, int k ) : bool
n System.Numerics.BigInteger
k int
return bool

ModPow() public static method

Performs modular exponentiation.
public static ModPow ( int powerBase, int exp, int prime ) : int
powerBase int
exp int
prime int
return int

ModSqrRoot() public static method

public static ModSqrRoot ( System.Numerics.BigInteger val, System.Numerics.BigInteger prime ) : System.Numerics.BigInteger
val System.Numerics.BigInteger
prime System.Numerics.BigInteger
return System.Numerics.BigInteger

MultiplicativeInverse() public static method

Returns the multiplicative inverse of a modulo m.
public static MultiplicativeInverse ( System.Numerics.BigInteger a, System.Numerics.BigInteger m ) : System.Numerics.BigInteger
a System.Numerics.BigInteger
m System.Numerics.BigInteger
return System.Numerics.BigInteger

MultiplicativeInverse() public static method

Returns the multiplicative inverse of a modulo m.
public static MultiplicativeInverse ( int a, int m ) : int
a int
m int
return int

MultiplicativeInverse() public static method

Returns the multiplicative inverse of a modulo m.
public static MultiplicativeInverse ( long a, long m ) : long
a long
m long
return long

NextRandomBigInt() public static method

Returns a random big integer in the specified range. This is based on a simple probabilistic algorithm.
public static NextRandomBigInt ( RNGCryptoServiceProvider rng, System.Numerics.BigInteger minValue, System.Numerics.BigInteger maxValue ) : System.Numerics.BigInteger
rng System.Security.Cryptography.RNGCryptoServiceProvider
minValue System.Numerics.BigInteger Inclusive lower bound.
maxValue System.Numerics.BigInteger Exclusive upper bound.
return System.Numerics.BigInteger

Property Details

DHPrime1536 public_oe static_oe property

public static BigInteger,System.Numerics DHPrime1536
return System.Numerics.BigInteger

DHPrime2048 public_oe static_oe property

public static BigInteger,System.Numerics DHPrime2048
return System.Numerics.BigInteger

DHPrime768 public_oe static_oe property

public static BigInteger,System.Numerics DHPrime768
return System.Numerics.BigInteger