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Implement Fast CIOS for Montgomery modular multiplication #1009

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Implement Fast CIOS for Montgomery modular multiplication #1009

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1d3aab1
improve CIOS implementation
clementjuventin Sep 16, 2024
2c9d6f6
improve CIOS implementation - second approach
clementjuventin Sep 19, 2024
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34 changes: 28 additions & 6 deletions include/evmmax/evmmax.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -83,7 +83,12 @@ class ModArith
// Based on 2.3.2 from
// High-Speed Algorithms & Architectures For Number-Theoretic Cryptosystems
// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
// and on 2.2 from
// EdMSM: Multi-Scalar-Multiplication for SNARKs and Faster Montgomery multiplication
// https://eprint.iacr.org/2022/1400.pdf

constexpr uint64_t most_significant_mod_word_limit{
std::numeric_limits<uint64_t>::max() >> 1};
constexpr auto S = UintT::num_words; // TODO(C++23): Make it static

intx::uint<UintT::num_bits + 64> t;
Expand All @@ -92,17 +97,34 @@ class ModArith
uint64_t c = 0;
for (size_t j = 0; j != S; ++j)
std::tie(c, t[j]) = addmul(t[j], x[j], y[i], c);
auto tmp = intx::addc(t[S], c);
t[S] = tmp.value;
const auto d = tmp.carry; // TODO: Carry is 0 for sparse modulus.

uint64_t carry = 0;
if (mod[S - 1] < most_significant_mod_word_limit)
{
carry = c;
}
else
{
auto tmp = intx::addc(t[S], c);
t[S] = tmp.value;
carry = tmp.carry;
}

const auto m = t[0] * m_mod_inv;
std::tie(c, std::ignore) = addmul(t[0], m, mod[0], 0);
for (size_t j = 1; j != S; ++j)
std::tie(c, t[j - 1]) = addmul(t[j], m, mod[j], c);
tmp = intx::addc(t[S], c);
t[S - 1] = tmp.value;
t[S] = d + tmp.carry; // TODO: Carry is 0 for sparse modulus.

if (mod[S - 1] < most_significant_mod_word_limit)
{
t[S - 1] = carry + c;
}
else
{
auto tmp = intx::addc(t[S], c);
t[S - 1] = tmp.value;
t[S] = carry + tmp.carry;
}
}

if (t >= mod)
Expand Down