void PaillierParty::secretShare() {
ZZ beta = getRandomInNStar(m_n);
std::vector<ZZ> coefficients;
coefficients.push_back(MulMod(beta,m_m,m_n*m_m));
for (uint32_t i=1; i < m_numOfParties; i++) {
coefficients.push_back(getRandomInNStar(m_n*m_m));
}
ZZ_p::init(m_n*m_m);
ZZ_pX polynomial;
for (uint32_t i=0; i < m_numOfParties; i++) {
SetCoeff(polynomial, i, conv<ZZ_p>(coefficients[i]));
}
for (auto &party : m_parties) {
ZZ result = rep(eval(polynomial,ZZ_p(party.first)));
sendZZTo(result,party.second);
}
ZZ_p s_i = eval(polynomial,ZZ_p(m_partyId));
for (auto &party : m_parties) {
ZZ value;
receiveZZFrom(value,party.second);
ZZ_p coefficient = conv<ZZ_p>(value);
s_i = s_i + coefficient;
}
m_share = rep(s_i);
m_pubKey = MulMod(MulMod(m_a,beta,m_n),m_m,m_n);
}
// Sets the prime defining the field for the curve and stores certain values
void Icart::setPrime(ZZ* p)
{
//ZZ_p::init(*p);
// Icart hash function uses 1/3 root, which is equivalent to (2p-1)/3
exp = MulMod( SubMod( MulMod(ZZ(2), *p, *p), ZZ(1), *p), InvMod(ZZ(3),*p), *p);
// Store inverse values to be used later
ts = inv(ZZ_p(27));
th = inv(ZZ_p(3));
}
// Icart's hash function
EPoint Icart::hash(ZZ_p u)
{
// 0 maps to the point at infinity
if (IsZero(u))
{
return EPoint(ZZ_p(0), ZZ_p(0), true);
}
// v = (3a - u^4) / 6u
ZZ_p v = ((ZZ_p(3) * a) - power(u, 4)) * inv(ZZ_p(6) * u);
// x = (v^2 - b - u^6/27)^(1/3) + u^2/3
ZZ_p x = power( sqr(v) - b - (power(u, ZZ(6)) * ts), exp) + (sqr(u) * th);
// y = ux + v
ZZ_p y = (u * x) + v;
return EPoint(x, y, false);
}
