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crypto: Multiply Fq2 with the Karatsuba method #1644

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chfast merged 1 commit into from
Aug 10, 2026
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crypto: Multiply Fq2 with the Karatsuba method #1644

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8 changes: 7 additions & 1 deletion lib/evmone_precompiles/pairing/bn254/fields.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -42,7 +42,13 @@ constexpr Fq2 multiply(const Fq2& a, const Fq2& b) noexcept
{
const auto& [a0, a1] = a.coeffs;
const auto& [b0, b1] = b.coeffs;
return Fq2({a0 * b0 - a1 * b1, a1 * b0 + a0 * b1});

// Karatsuba: for u^2 == -1 the product is (t0 - t1) + ((a0+a1)(b0+b1) - t0 - t1)*u,
// trading one of the schoolbook's 4 base field multiplications for 3 additions.
// TODO: Lazy reduction (https://eprint.iacr.org/2010/526) needs wide mul and redc in ModArith.
const auto t0 = a0 * b0;
const auto t1 = a1 * b1;
return Fq2({t0 - t1, (a0 + a1) * (b0 + b1) - t0 - t1});
}

/// Squares an Fq^2 field element.
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