void PrivateCoin::mintCoin(const CoinDenomination denomination) { // 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++) { // 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 Pedersen commitment to the serial number "s" Commitment coin(¶ms->coinCommitmentGroup, s); // Now 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 (coin.getCommitmentValue().isPrime(ZEROCOIN_MINT_PRIME_PARAM) && coin.getCommitmentValue() >= params->accumulatorParams.minCoinValue && coin.getCommitmentValue() <= params->accumulatorParams.maxCoinValue) { // Found a valid coin. Store it. this->serialNumber = s; this->randomness = coin.getRandomness(); this->publicCoin = PublicCoin(params,coin.getCommitmentValue(), denomination); // Success! We're done. return; } } // 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)"); }
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. // And where the serial also doubles as a public key CKey key; CBigNum s; bool isValid = false; while (!isValid) { isValid = GenerateKeyPair(this->params->coinCommitmentGroup.groupOrder, uint256(0), key, s); } // Generate a random number "r" in the range 0...{q-1} CBigNum r = CBigNum::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 CBigNum 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); this->privkey = key.GetPrivKey(); this->version = 2; // Success! We're done. return; } // Generate a new random "r_delta" in 0...{q-1} CBigNum r_delta = CBigNum::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 std::runtime_error("Unable to mint a new Zerocoin (too many attempts)"); }