Integer ModularRoot(const Integer &a, const Integer &e,
const Integer &p, const Integer &q)
{
Integer dp = EuclideanMultiplicativeInverse(e, p-1);
Integer dq = EuclideanMultiplicativeInverse(e, q-1);
Integer u = EuclideanMultiplicativeInverse(p, q);
assert(!!dp && !!dq && !!u);
return ModularRoot(a, dp, dq, p, q, u);
}
Integer InvertibleRSAFunction::CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const
{
DoQuickSanityCheck();
ModularArithmetic modn(m_n);
Integer r(rng, Integer::One(), m_n - Integer::One());
Integer re = modn.Exponentiate(r, m_e);
re = modn.Multiply(re, x); // blind
// here we follow the notation of PKCS #1 and let u=q inverse mod p
// but in ModRoot, u=p inverse mod q, so we reverse the order of p and q
Integer y = ModularRoot(re, m_dq, m_dp, m_q, m_p, m_u);
y = modn.Divide(y, r); // unblind
ASSERT( modn.Exponentiate(y, m_e) == x ); // check
return y;
}
Integer InvertibleRSAFunction::CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const
{
DoQuickSanityCheck();
ModularArithmetic modn(m_n);
Integer r(rng, Integer::One(), m_n - Integer::One());
Integer re = modn.Exponentiate(r, m_e);
re = modn.Multiply(re, x); // blind
// here we follow the notation of PKCS #1 and let u=q inverse mod p
// but in ModRoot, u=p inverse mod q, so we reverse the order of p and q
Integer y = ModularRoot(re, m_dq, m_dp, m_q, m_p, m_u);
y = modn.Divide(y, r); // unblind
if (modn.Exponentiate(y, m_e) != x) // check
throw Exception(Exception::OTHER_ERROR, "InvertibleRSAFunction: computational error during private key operation");
return y;
}
Integer RSA_PrivateKey::CalculateInverse(RandomNumberGenerator& rng,
const Integer& x) const
{
ModularArithmetic modn(n_);
Integer r(rng, Integer::One(), n_ - Integer::One());
Integer re = modn.Exponentiate(r, e_);
re = modn.Multiply(re, x); // blind
// here we follow the notation of PKCS #1 and let u=q inverse mod p
// but in ModRoot, u=p inverse mod q, so we reverse the order of p and q
Integer y = ModularRoot(re, dq_, dp_, q_, p_, u_);
y = modn.Divide(y, r); // unblind
return y;
}
Integer InvertableRSAFunction::CalculateInverse(const Integer &x) const
{
// here we follow the notation of PKCS #1 and let u=q inverse mod p
// but in ModRoot, u=p inverse mod q, so we reverse the order of p and q
return ModularRoot(x, dq, dp, q, p, u);
}
