/* Returns the greatest common divisor of the two arguments
* "a" and "b", using the Euclidean algorithm. */
BigInt RSA::GCD(const BigInt &a, const BigInt &b)
{
if (b.EqualsZero())
return a;
else
return RSA::GCD(b, a % b);
}
/* Generates a random "number" such as 1 <= "number" < "top".
* Returns it by reference in the "number" parameter. */
void PrimeGenerator::makeRandom(BigInt &number, const BigInt &top)
{
//randomly select the number of digits for the random number
unsigned long int newDigitCount = (rand() % top.digitCount) + 1;
makeRandom(number, newDigitCount);
//make sure the number is < top and not zero
while (number >= top || number.EqualsZero())
makeRandom(number, newDigitCount);
//make sure the leading digit is not zero
while (number.digits[number.digitCount - 1] == 0)
number.digitCount--;
}
/* Solves the equation
* d = ax + by
* given a and b, and returns d, x and y by reference.
* It uses the Extended Euclidean Algorithm */
void RSA::extendedEuclideanAlgorithm(const BigInt &a, const BigInt &b,
BigInt &d, BigInt &x, BigInt &y)
{
if (b.EqualsZero())
{
d = a;
x = BigIntOne;
y = BigIntZero;
return;
}
RSA::extendedEuclideanAlgorithm(b, a % b, d, x, y);
BigInt temp(x);
x = y;
y = temp - a / b * y;
}
