AccumulatorProofOfKnowledge::AccumulatorProofOfKnowledge(const AccumulatorAndProofParams* p,
const Commitment& commitmentToCoin, const AccumulatorWitness& witness,
Accumulator& a): params(p) {
Bignum sg = params->accumulatorPoKCommitmentGroup.g;
Bignum sh = params->accumulatorPoKCommitmentGroup.h;
Bignum g_n = params->accumulatorQRNCommitmentGroup.g;
Bignum h_n = params->accumulatorQRNCommitmentGroup.h;
Bignum e = commitmentToCoin.getContents();
Bignum r = commitmentToCoin.getRandomness();
Bignum r_1 = Bignum::randBignum(params->accumulatorModulus/4);
Bignum r_2 = Bignum::randBignum(params->accumulatorModulus/4);
Bignum r_3 = Bignum::randBignum(params->accumulatorModulus/4);
this->C_e = g_n.pow_mod(e, params->accumulatorModulus) * h_n.pow_mod(r_1, params->accumulatorModulus);
this->C_u = witness.getValue() * h_n.pow_mod(r_2, params->accumulatorModulus);
this->C_r = g_n.pow_mod(r_2, params->accumulatorModulus) * h_n.pow_mod(r_3, params->accumulatorModulus);
Bignum r_alpha = Bignum::randBignum(params->maxCoinValue * Bignum(2).pow(params->k_prime + params->k_dprime));
if(!(Bignum::randBignum(Bignum(3)) % 2)) {
r_alpha = 0-r_alpha;
}
Bignum r_gamma = Bignum::randBignum(params->accumulatorPoKCommitmentGroup.modulus);
Bignum r_phi = Bignum::randBignum(params->accumulatorPoKCommitmentGroup.modulus);
Bignum r_psi = Bignum::randBignum(params->accumulatorPoKCommitmentGroup.modulus);
Bignum r_sigma = Bignum::randBignum(params->accumulatorPoKCommitmentGroup.modulus);
Bignum r_xi = Bignum::randBignum(params->accumulatorPoKCommitmentGroup.modulus);
Bignum r_epsilon = Bignum::randBignum((params->accumulatorModulus/4) * Bignum(2).pow(params->k_prime + params->k_dprime));
if(!(Bignum::randBignum(Bignum(3)) % 2)) {
r_epsilon = 0-r_epsilon;
}
Bignum r_eta = Bignum::randBignum((params->accumulatorModulus/4) * Bignum(2).pow(params->k_prime + params->k_dprime));
if(!(Bignum::randBignum(Bignum(3)) % 2)) {
r_eta = 0-r_eta;
}
Bignum r_zeta = Bignum::randBignum((params->accumulatorModulus/4) * Bignum(2).pow(params->k_prime + params->k_dprime));
if(!(Bignum::randBignum(Bignum(3)) % 2)) {
r_zeta = 0-r_zeta;
}
Bignum r_beta = Bignum::randBignum((params->accumulatorModulus/4) * params->accumulatorPoKCommitmentGroup.modulus * Bignum(2).pow(params->k_prime + params->k_dprime));
if(!(Bignum::randBignum(Bignum(3)) % 2)) {
r_beta = 0-r_beta;
}
Bignum r_delta = Bignum::randBignum((params->accumulatorModulus/4) * params->accumulatorPoKCommitmentGroup.modulus * Bignum(2).pow(params->k_prime + params->k_dprime));
if(!(Bignum::randBignum(Bignum(3)) % 2)) {
r_delta = 0-r_delta;
}
this->st_1 = (sg.pow_mod(r_alpha, params->accumulatorPoKCommitmentGroup.modulus) * sh.pow_mod(r_phi, params->accumulatorPoKCommitmentGroup.modulus)) % params->accumulatorPoKCommitmentGroup.modulus;
this->st_2 = (((commitmentToCoin.getCommitmentValue() * sg.inverse(params->accumulatorPoKCommitmentGroup.modulus)).pow_mod(r_gamma, params->accumulatorPoKCommitmentGroup.modulus)) * sh.pow_mod(r_psi, params->accumulatorPoKCommitmentGroup.modulus)) % params->accumulatorPoKCommitmentGroup.modulus;
this->st_3 = ((sg * commitmentToCoin.getCommitmentValue()).pow_mod(r_sigma, params->accumulatorPoKCommitmentGroup.modulus) * sh.pow_mod(r_xi, params->accumulatorPoKCommitmentGroup.modulus)) % params->accumulatorPoKCommitmentGroup.modulus;
this->t_1 = (h_n.pow_mod(r_zeta, params->accumulatorModulus) * g_n.pow_mod(r_epsilon, params->accumulatorModulus)) % params->accumulatorModulus;
this->t_2 = (h_n.pow_mod(r_eta, params->accumulatorModulus) * g_n.pow_mod(r_alpha, params->accumulatorModulus)) % params->accumulatorModulus;
this->t_3 = (C_u.pow_mod(r_alpha, params->accumulatorModulus) * ((h_n.inverse(params->accumulatorModulus)).pow_mod(r_beta, params->accumulatorModulus))) % params->accumulatorModulus;
this->t_4 = (C_r.pow_mod(r_alpha, params->accumulatorModulus) * ((h_n.inverse(params->accumulatorModulus)).pow_mod(r_delta, params->accumulatorModulus)) * ((g_n.inverse(params->accumulatorModulus)).pow_mod(r_beta, params->accumulatorModulus))) % params->accumulatorModulus;
CHashWriter hasher(0,0);
hasher << *params << sg << sh << g_n << h_n << commitmentToCoin.getCommitmentValue() << C_e << C_u << C_r << st_1 << st_2 << st_3 << t_1 << t_2 << t_3 << t_4;
//According to the proof, this hash should be of length k_prime bits. It is currently greater than that, which should not be a problem, but we should check this.
Bignum c = Bignum(hasher.GetHash());
this->s_alpha = r_alpha - c*e;
this->s_beta = r_beta - c*r_2*e;
this->s_zeta = r_zeta - c*r_3;
this->s_sigma = r_sigma - c*((e+1).inverse(params->accumulatorPoKCommitmentGroup.groupOrder));
this->s_eta = r_eta - c*r_1;
this->s_epsilon = r_epsilon - c*r_2;
this->s_delta = r_delta - c*r_3*e;
this->s_xi = r_xi + c*r*((e+1).inverse(params->accumulatorPoKCommitmentGroup.groupOrder));
this->s_phi = (r_phi - c*r) % params->accumulatorPoKCommitmentGroup.groupOrder;
this->s_gamma = r_gamma - c*((e-1).inverse(params->accumulatorPoKCommitmentGroup.groupOrder));
this->s_psi = r_psi + c*r*((e-1).inverse(params->accumulatorPoKCommitmentGroup.groupOrder));
}
bool CalculateAccumulatorWitnessFor(
const ZerocoinParams* params,
int startHeight,
int maxCalulationRange,
CoinDenomination den,
const CBloomFilter& filter,
Accumulator& accumulator,
AccumulatorWitness& witness,
int& nMintsAdded,
string& strError,
list<CBigNum>& ret,
int &heightStop
){
// Lock
if (!LockMethod()) return false;
try {
// Dummy coin init
PublicCoin temp(params, 0, den);
// Dummy Acc init
Accumulator testingAcc(params, den);
//get the checkpoint added at the next multiple of 10
int nHeightCheckpoint = startHeight + (10 - (startHeight % 10));
// Get the base accumulator
// TODO: This needs to be changed to the partial witness calculation on the next version.
CBigNum bnAccValue = 0;
if (GetAccumulatorValue(nHeightCheckpoint, den, bnAccValue)) {
accumulator.setValue(bnAccValue);
witness.resetValue(accumulator, temp);
}
// Add the pubcoins from the blockchain up to the next checksum starting from the block
CBlockIndex *pindex = chainActive[nHeightCheckpoint -10];
int nChainHeight = chainActive.Height();
int nHeightStop = nChainHeight % 10;
nHeightStop = nChainHeight - nHeightStop - 20; // at least two checkpoints deep
if (nHeightStop - startHeight > maxCalulationRange) {
int stop = (startHeight + maxCalulationRange);
int nHeightStop = stop % 10;
nHeightStop = stop - nHeightStop - 20;
}
heightStop = nHeightStop;
nMintsAdded = 0;
// Starts on top of the witness that the node sent
libzerocoin::Accumulator witnessAccumulator(params, den, witness.getValue());
if(!calculateAccumulatedBlocksFor(
startHeight,
nHeightStop,
pindex,
bnAccValue,
accumulator,
den,
filter,
witnessAccumulator,
ret,
strError
))
return error("CalculateAccumulatorWitnessFor(): Calculate accumulated coins failed");
// reset the value
witness.resetValue(witnessAccumulator, temp);
// calculate how many mints of this denomination existed in the accumulator we initialized
nMintsAdded += ComputeAccumulatedCoins(startHeight, den);
LogPrint("zero", "%s : %d mints added to witness\n", __func__, nMintsAdded);
return true;
} catch (ChecksumInDbNotFoundException e) {
return error("%s: ChecksumInDbNotFoundException: %s", __func__, e.message);
} catch (GetPubcoinException e) {
return error("%s: GetPubcoinException: %s", __func__, e.message);
}
}