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crypto: Fold the pairing line coefficients into one function #1639

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crypto: Fold the pairing line coefficients into one function #1639

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55 changes: 24 additions & 31 deletions lib/evmone_precompiles/pairing/bn254/utils.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -295,10 +295,17 @@ constexpr ecc::ProjPoint<E2> lin_func_and_dbl(
return ecc::ProjPoint<E2>{Xp, Yp, Zp};
}

/// Computes points P0 and P1 addition for twisted curve + line defined by untwisted P1 and P2
/// points on the curve (not twisted curve) evaluated at point P. Formula is simplified for P1.z
/// == 1. For more details see https://notes.ethereum.org/@ipsilon/Hkn2a2qk0
[[nodiscard]] constexpr ecc::ProjPoint<E2> lin_func_and_add(
/// The line terms that the point addition of lin_func_and_add() needs as well.
struct LineTerms
{
Fq2 H; ///< x1·z0² − x0
Fq2 R; ///< y1·z0³ − y0
};

/// Computes the line defined by the untwisted P0 and P1 points on the curve (not twisted curve),
/// evaluated at point P and returned in `t`. Formula is simplified for P1.z == 1.
/// For more details see https://notes.ethereum.org/@ipsilon/Hkn2a2qk0
[[gnu::always_inline]] constexpr LineTerms lin_func(
const ecc::ProjPoint<E2>& P0, const ecc::AffinePoint<E2>& P1, std::array<Fq2, 3>& t) noexcept
{
const auto& x0 = P0.x;
Expand All @@ -316,45 +323,31 @@ constexpr ecc::ProjPoint<E2> lin_func_and_dbl(
const auto H = U2 - x0; // x1 * z0^2 - x0 * z1^2
const auto R = S2 - y0; // y1 * z0^3 - y0 * z1^3

const auto H_squared = H * H;
const auto H_cubed = H * H_squared;
const auto R_squared = R * R;

const auto V = x0 * H_squared;

const auto X3 = R_squared - H_cubed - (V + V);
const auto Y3 = R * (V - X3) - y0 * H_cubed;
const auto Z3 = H * z0;

t[0] = -H * z0_cubed; // = x0·z0³ − U2·z0³
t[1] = R * z0_squared; // = S2·z0² − y0·z0²
t[2] = y0 * U2 - x0 * S2;

return ecc::ProjPoint<E2>{X3, Y3, Z3};
return {H, R};
}

/// Computes points P0 and P1 addition for twisted curve + line defined by untwisted P1 and P2
/// points on the curve (not twisted curve) evaluated at point P. Formula is simplified for P1.z
/// == 1. For more details see https://notes.ethereum.org/@ipsilon/Hkn2a2qk0
constexpr void lin_func(
/// Computes points P0 and P1 addition on the twisted curve, along with the line of lin_func().
/// For more details see https://notes.ethereum.org/@ipsilon/Hkn2a2qk0
[[nodiscard]] constexpr ecc::ProjPoint<E2> lin_func_and_add(
const ecc::ProjPoint<E2>& P0, const ecc::AffinePoint<E2>& P1, std::array<Fq2, 3>& t) noexcept
{
const auto& x0 = P0.x;
const auto& y0 = P0.y;
const auto& z0 = P0.z;
const auto [H, R] = lin_func(P0, P1, t);

const auto& x1 = P1.x;
const auto& y1 = P1.y;
const auto H_squared = H * H;
const auto H_cubed = H * H_squared;
const auto R_squared = R * R;

const auto z0_squared = z0 * z0;
const auto z0_cubed = z0 * z0_squared;
const auto V = P0.x * H_squared;

const auto U2 = x1 * z0_squared;
const auto S2 = y1 * z0_cubed;
const auto X3 = R_squared - H_cubed - (V + V);
const auto Y3 = R * (V - X3) - P0.y * H_cubed;
const auto Z3 = H * P0.z;

t[0] = (x0 - U2) * z0_cubed; // = x0·z0³ − U2·z0³
t[1] = (S2 - y0) * z0_squared; // = S2·z0² − y0·z0²
t[2] = y0 * U2 - x0 * S2;
return ecc::ProjPoint<E2>{X3, Y3, Z3};
}

/// Computes f^2 for f in Fq12. For more ref https://eprint.iacr.org/2010/354.pdf Algorithm 22
Expand Down