void PrivateCoin::mintCoinFast(const CoinDenomination denomination) {
// Generate a random serial number in the range 0...{q-1} where
// "q" is the order of the commitment group.
Bignum s = Bignum::randBignum(this->params->coinCommitmentGroup.groupOrder);
// Generate a random number "r" in the range 0...{q-1}
Bignum r = Bignum::randBignum(this->params->coinCommitmentGroup.groupOrder);
// Manually compute a Pedersen commitment to the serial number "s" under randomness "r"
// C = g^s * h^r mod p
Bignum commitmentValue = this->params->coinCommitmentGroup.g.pow_mod(s, this->params->coinCommitmentGroup.modulus).mul_mod(this->params->coinCommitmentGroup.h.pow_mod(r, this->params->coinCommitmentGroup.modulus), this->params->coinCommitmentGroup.modulus);
// Repeat this process up to MAX_COINMINT_ATTEMPTS times until
// we obtain a prime number
for (uint32_t attempt = 0; attempt < MAX_COINMINT_ATTEMPTS; attempt++) {
// First verify that the commitment is a prime number
// in the appropriate range. If not, we'll throw this coin
// away and generate a new one.
if (commitmentValue.isPrime(ZEROCOIN_MINT_PRIME_PARAM) &&
commitmentValue >= params->accumulatorParams.minCoinValue &&
commitmentValue <= params->accumulatorParams.maxCoinValue) {
// Found a valid coin. Store it.
this->serialNumber = s;
this->randomness = r;
this->publicCoin = PublicCoin(params, commitmentValue, denomination);
// Success! We're done.
return;
}
// Generate a new random "r_delta" in 0...{q-1}
Bignum r_delta = Bignum::randBignum(this->params->coinCommitmentGroup.groupOrder);
// The commitment was not prime. Increment "r" and recalculate "C":
// r = r + r_delta mod q
// C = C * h mod p
r = (r + r_delta) % this->params->coinCommitmentGroup.groupOrder;
commitmentValue = commitmentValue.mul_mod(this->params->coinCommitmentGroup.h.pow_mod(r_delta, this->params->coinCommitmentGroup.modulus), this->params->coinCommitmentGroup.modulus);
}
// We only get here if we did not find a coin within
// MAX_COINMINT_ATTEMPTS. Throw an exception.
throw ZerocoinException("Unable to mint a new Zerocoin (too many attempts)");
}
