/* Creates an odd BigInt with the specified number of digits.
* Returns it by reference in the "number" parameter. */
void PrimeGenerator::makePrimeCandidate(BigInt &number,
unsigned long int digitCount)
{
PrimeGenerator::MakeRandom(number, digitCount);
//make the number odd
if (!number.IsOdd())
number.SetDigit(0, number.GetDigit(0) + 1);
//make sure the leading digit is not a zero
if (number.GetDigit(number.Length() - 1) == 0)
number.SetDigit(number.Length() - 1, (std::rand() % 9) + 1);
}
/* 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.Length()) + 1;
MakeRandom(number, newDigitCount);
//make sure number < top
while (number >= top)
MakeRandom(number, newDigitCount);
}
/* Transforms a BigInt cyphertext into a std::string cyphertext. */
string RSA::decode(const BigInt &message)
{
string decoded;
// The special symbol '1' we added to the beginning of the encoded message
// will now be positioned at message[message.Length() - 1], and
// message.Length() -1 must be divisible by 3 without remainder. Thus we
// can ignore the special symbol by only using digits in the range
// from message[0] to message[message.Length() - 2].
for (unsigned long int i(0); i < message.Length() / 3; i++)
{
// Decode the characters using the ASCII values in the BigInt digits.
char ASCII = 100 * char(message.GetDigit(i * 3));
ASCII += 10 * char(message.GetDigit(i * 3 + 1));
decoded.push_back(ASCII + char(message.GetDigit(i * 3 + 2)));
}
return decoded;
}
/* Returns a probable prime number "digitCount" digits long,
* with a probability of at least 1 - 4^(-k) that it is prime. */
BigInt PrimeGenerator::Generate(unsigned long int digitCount,
unsigned long int k)
{
if (digitCount < 3)
throw "Error PRIMEGENERATOR00: Primes less than 3 digits long "
"not supported.";
BigInt primeCandidate;
PrimeGenerator::makePrimeCandidate(primeCandidate, digitCount);
while (!isProbablePrime(primeCandidate, k))
{
//select the next odd number and try again
primeCandidate = primeCandidate + 2;
if (primeCandidate.Length() != digitCount)
PrimeGenerator::makePrimeCandidate(primeCandidate, digitCount);
}
return primeCandidate;
}
