本文整理汇总了C#中BigInteger.Gcd方法的典型用法代码示例。如果您正苦于以下问题：C# BigInteger.Gcd方法的具体用法？C# BigInteger.Gcd怎么用？C# BigInteger.Gcd使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类BigInteger的用法示例。
在下文中一共展示了BigInteger.Gcd方法的8个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的C#代码示例。
示例1: GenerateBlindingFactor
/**
* Generate a suitable blind factor for the public key the generator was initialised with.
*
* @return a random blind factor
*/
public BigInteger GenerateBlindingFactor()
{
if (key == null)
throw new InvalidOperationException("generator not initialised");
BigInteger m = key.Modulus;
int length = m.BitLength - 1; // must be less than m.BitLength
BigInteger factor;
BigInteger gcd;
do
{
factor = new BigInteger(length, random);
gcd = factor.Gcd(m);
}
while (factor.Sign == 0 || factor.Equals(BigInteger.One) || !gcd.Equals(BigInteger.One));
return factor;
}示例2: BIDivide
public static object BIDivide(BigInteger n, BigInteger d)
{
if (d.Equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero");
BigInteger gcd = n.Gcd(d);
if (gcd.Equals(BigInteger.ZERO))
return BigInt.ZERO;
n = n / gcd;
d = d / gcd;
if (d.Equals(BigInteger.ONE))
return BigInt.fromBigInteger(n);
else if (d.Equals(BigInteger.NEGATIVE_ONE))
return BigInt.fromBigInteger(n.Negate());
return new Ratio((d.Signum < 0 ? -n : n), d.Abs());
}示例3: BIDivide
public static object BIDivide(BigInteger n, BigInteger d)
{
if (d.Equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero");
//BigInteger gcd = n.gcd(d);
BigInteger gcd = n.Gcd(d);
if (gcd.Equals(BigInteger.ZERO))
return 0;
//n = n.divide(gcd);
//d = d.divide(gcd);
n = n / gcd;
d = d / gcd;
if (d.Equals(BigInteger.ONE))
return reduce(n);
//return new Ratio((d.signum() < 0 ? n.negate() : n),
// (d.signum() < 0 ? d.negate() : d));
return new Ratio((d.Signum < 0 ? -n : n), d.Abs());
}示例4: GenCoPrime
//***********************************************************************
// Generates a random number with the specified number of bits such
// that gcd(number, this) = 1
//***********************************************************************
public BigInteger GenCoPrime(int bits, Random rand)
{
bool done = false;
BigInteger result = new BigInteger();
while(!done)
{
result.GenRandomBits(bits, rand);
//Console.WriteLine(result.ToString(16));
// gcd test
BigInteger g = result.Gcd(this);
if(g.dataLength == 1 && g.data[0] == 1)
done = true;
}
return result;
}示例5: LucasStrongTestHelper
//.........这里部分代码省略.........
}
//Console.WriteLine(D);
D = (Math.Abs(D) + 2) * sign;
sign = -sign;
}
dCount++;
}
long Q = (1 - D) >> 2;
/*
Console.WriteLine("D = " + D);
Console.WriteLine("Q = " + Q);
Console.WriteLine("(n,D) = " + thisVal.gcd(D));
Console.WriteLine("(n,Q) = " + thisVal.gcd(Q));
Console.WriteLine("J(D|n) = " + BigInteger.Jacobi(D, thisVal));
*/
BigInteger p_add1 = thisVal + 1;
int s = 0;
for(int index = 0; index < p_add1.dataLength; index++)
{
uint mask = 0x01;
for(int i = 0; i < 32; i++)
{
if((p_add1.data[index] & mask) != 0)
{
index = p_add1.dataLength; // to break the outer loop
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = p_add1 >> s;
// calculate constant = b^(2k) / m
// for Barrett Reduction
BigInteger constant = new BigInteger();
int nLen = thisVal.dataLength << 1;
constant.data[nLen] = 0x00000001;
constant.dataLength = nLen + 1;
constant = constant / thisVal;
BigInteger[] lucas = LucasSequenceHelper(1, Q, t, thisVal, constant, 0);
bool isPrime = false;
if((lucas[0].dataLength == 1 && lucas[0].data[0] == 0) ||
(lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
{
// u(t) = 0 or V(t) = 0
isPrime = true;
}
for(int i = 1; i < s; i++)
{
if(!isPrime)
{
// doubling of index
lucas[1] = thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal, constant);
lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal;
//lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal;
if((lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
isPrime = true;
}
lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant); //Q^k
}
if(isPrime) // additional checks for composite numbers
{
// If n is prime and gcd(n, Q) == 1, then
// Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n
BigInteger g = thisVal.Gcd(Q);
if(g.dataLength == 1 && g.data[0] == 1) // gcd(this, Q) == 1
{
if((lucas[2].data[MaxLength-1] & 0x80000000) != 0)
lucas[2] += thisVal;
BigInteger temp = (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal;
if((temp.data[MaxLength-1] & 0x80000000) != 0)
temp += thisVal;
if(lucas[2] != temp)
isPrime = false;
}
}
return isPrime;
}示例6: SolovayStrassenTest
//***********************************************************************
// Probabilistic prime test based on Solovay-Strassen (Euler Criterion)
//
// p is probably prime if for any a < p (a is not multiple of p),
// a^((p-1)/2) mod p = J(a, p)
//
// where J is the Jacobi symbol.
//
// Otherwise, p is composite.
//
// Returns
// -------
// True if "this" is a Euler pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
//***********************************************************************
public bool SolovayStrassenTest(int confidence)
{
BigInteger thisVal;
if((this.data[MaxLength-1] & 0x80000000) != 0) // negative
thisVal = -this;
else
thisVal = this;
if(thisVal.dataLength == 1)
{
// test small numbers
if(thisVal.data[0] == 0 || thisVal.data[0] == 1)
return false;
else if(thisVal.data[0] == 2 || thisVal.data[0] == 3)
return true;
}
if((thisVal.data[0] & 0x1) == 0) // even numbers
return false;
int bits = thisVal.bitCount();
BigInteger a = new BigInteger();
BigInteger p_sub1 = thisVal - 1;
BigInteger p_sub1_shift = p_sub1 >> 1;
Random rand = new Random();
for(int round = 0; round < confidence; round++)
{
bool done = false;
while(!done) // generate a < n
{
int testBits = 0;
// make sure "a" has at least 2 bits
while(testBits < 2)
testBits = (int)(rand.NextDouble() * bits);
a.GenRandomBits(testBits, rand);
int byteLen = a.dataLength;
// make sure "a" is not 0
if(byteLen > 1 || (byteLen == 1 && a.data[0] != 1))
done = true;
}
// check whether a factor exists (fix for version 1.03)
BigInteger gcdTest = a.Gcd(thisVal);
if(gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
// calculate a^((p-1)/2) mod p
BigInteger expResult = a.ModPow(p_sub1_shift, thisVal);
if(expResult == p_sub1)
expResult = -1;
// calculate Jacobi symbol
BigInteger jacob = Jacobi(a, thisVal);
//Console.WriteLine("a = " + a.ToString(10) + " b = " + thisVal.ToString(10));
//Console.WriteLine("expResult = " + expResult.ToString(10) + " Jacob = " + jacob.ToString(10));
// if they are different then it is not prime
if(expResult != jacob)
return false;
}
return true;
}示例7: RabinMillerTest
//***********************************************************************
// Probabilistic prime test based on Rabin-Miller's
//
// for any p > 0 with p - 1 = 2^s * t
//
// p is probably prime (strong pseudoprime) if for any a < p,
// 1) a^t mod p = 1 or
// 2) a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
//
// Otherwise, p is composite.
//
// Returns
// -------
// True if "this" is a strong pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
//***********************************************************************
public bool RabinMillerTest(int confidence)
{
BigInteger thisVal;
if((this.data[MaxLength-1] & 0x80000000) != 0) // negative
thisVal = -this;
else
thisVal = this;
if(thisVal.dataLength == 1)
{
// test small numbers
if(thisVal.data[0] == 0 || thisVal.data[0] == 1)
return false;
else if(thisVal.data[0] == 2 || thisVal.data[0] == 3)
return true;
}
if((thisVal.data[0] & 0x1) == 0) // even numbers
return false;
// calculate values of s and t
BigInteger p_sub1 = thisVal - (new BigInteger(1));
int s = 0;
for(int index = 0; index < p_sub1.dataLength; index++)
{
uint mask = 0x01;
for(int i = 0; i < 32; i++)
{
if((p_sub1.data[index] & mask) != 0)
{
index = p_sub1.dataLength; // to break the outer loop
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = p_sub1 >> s;
int bits = thisVal.bitCount();
BigInteger a = new BigInteger();
Random rand = new Random();
for(int round = 0; round < confidence; round++)
{
bool done = false;
while(!done) // generate a < n
{
int testBits = 0;
// make sure "a" has at least 2 bits
while(testBits < 2)
testBits = (int)(rand.NextDouble() * bits);
a.GenRandomBits(testBits, rand);
int byteLen = a.dataLength;
// make sure "a" is not 0
if(byteLen > 1 || (byteLen == 1 && a.data[0] != 1))
done = true;
}
// check whether a factor exists (fix for version 1.03)
BigInteger gcdTest = a.Gcd(thisVal);
if(gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
BigInteger b = a.ModPow(t, thisVal);
/*
Console.WriteLine("a = " + a.ToString(10));
Console.WriteLine("b = " + b.ToString(10));
Console.WriteLine("t = " + t.ToString(10));
//.........这里部分代码省略.........
示例8: FermatLittleTest
//***********************************************************************
// Probabilistic prime test based on Fermat's little theorem
//
// for any a < p (p does not divide a) if
// a^(p-1) mod p != 1 then p is not prime.
//
// Otherwise, p is probably prime (pseudoprime to the chosen base).
//
// Returns
// -------
// True if "this" is a pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
// Note - this method is fast but fails for Carmichael numbers except
// when the randomly chosen base is a factor of the number.
//
//***********************************************************************
public bool FermatLittleTest(int confidence)
{
BigInteger thisVal;
if((this.data[MaxLength-1] & 0x80000000) != 0) // negative
thisVal = -this;
else
thisVal = this;
if(thisVal.dataLength == 1)
{
// test small numbers
if(thisVal.data[0] == 0 || thisVal.data[0] == 1)
return false;
else if(thisVal.data[0] == 2 || thisVal.data[0] == 3)
return true;
}
if((thisVal.data[0] & 0x1) == 0) // even numbers
return false;
int bits = thisVal.bitCount();
BigInteger a = new BigInteger();
BigInteger p_sub1 = thisVal - (new BigInteger(1));
Random rand = new Random();
for(int round = 0; round < confidence; round++)
{
bool done = false;
while(!done) // generate a < n
{
int testBits = 0;
// make sure "a" has at least 2 bits
while(testBits < 2)
testBits = (int)(rand.NextDouble() * bits);
a.GenRandomBits(testBits, rand);
int byteLen = a.dataLength;
// make sure "a" is not 0
if(byteLen > 1 || (byteLen == 1 && a.data[0] != 1))
done = true;
}
// check whether a factor exists (fix for version 1.03)
BigInteger gcdTest = a.Gcd(thisVal);
if(gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
// calculate a^(p-1) mod p
BigInteger expResult = a.ModPow(p_sub1, thisVal);
int resultLen = expResult.dataLength;
// is NOT prime is a^(p-1) mod p != 1
if(resultLen > 1 || (resultLen == 1 && expResult.data[0] != 1))
{
//Console.WriteLine("a = " + a.ToString());
return false;
}
}
return true;
}