pcurves_secp256r1.cpp

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/*
* (C) 2024 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#include <botan/internal/pcurves_instance.h>
 
#include <botan/internal/pcurves_solinas.h>
#include <botan/internal/pcurves_wrap.h>
 
namespace Botan::PCurve {
 
namespace {
 
template <typename Params>
class Secp256r1Rep final {
   public:
      static constexpr auto P = Params::P;
      static constexpr size_t N = Params::N;
      typedef typename Params::W W;
 
      // Adds 4 * P-256 to prevent underflow
      static constexpr auto P256_4 =
         hex_to_words<uint32_t>("0x3fffffffc00000004000000000000000000000003fffffffffffffffffffffffc");
 
      constexpr static std::array<W, N> redc(const std::array<W, 2 * N>& z) {
         const int64_t X00 = get_uint32(z.data(), 0);
         const int64_t X01 = get_uint32(z.data(), 1);
         const int64_t X02 = get_uint32(z.data(), 2);
         const int64_t X03 = get_uint32(z.data(), 3);
         const int64_t X04 = get_uint32(z.data(), 4);
         const int64_t X05 = get_uint32(z.data(), 5);
         const int64_t X06 = get_uint32(z.data(), 6);
         const int64_t X07 = get_uint32(z.data(), 7);
         const int64_t X08 = get_uint32(z.data(), 8);
         const int64_t X09 = get_uint32(z.data(), 9);
         const int64_t X10 = get_uint32(z.data(), 10);
         const int64_t X11 = get_uint32(z.data(), 11);
         const int64_t X12 = get_uint32(z.data(), 12);
         const int64_t X13 = get_uint32(z.data(), 13);
         const int64_t X14 = get_uint32(z.data(), 14);
         const int64_t X15 = get_uint32(z.data(), 15);
 
         // See SP 800-186 section G.1.2
         const int64_t S0 = P256_4[0] + X00 + X08 + X09 - (X11 + X12 + X13 + X14);
         const int64_t S1 = P256_4[1] + X01 + X09 + X10 - (X12 + X13 + X14 + X15);
         const int64_t S2 = P256_4[2] + X02 + X10 + X11 - (X13 + X14 + X15);
         const int64_t S3 = P256_4[3] + X03 + 2 * (X11 + X12) + X13 - (X15 + X08 + X09);
         const int64_t S4 = P256_4[4] + X04 + 2 * (X12 + X13) + X14 - (X09 + X10);
         const int64_t S5 = P256_4[5] + X05 + 2 * (X13 + X14) + X15 - (X10 + X11);
         const int64_t S6 = P256_4[6] + X06 + X13 + X14 * 3 + X15 * 2 - (X08 + X09);
         const int64_t S7 = P256_4[7] + X07 + X15 * 3 + X08 - (X10 + X11 + X12 + X13);
         const int64_t S8 = P256_4[8];
 
         std::array<W, N> r = {};
 
         SolinasAccum sum(r);
 
         sum.accum(S0);
         sum.accum(S1);
         sum.accum(S2);
         sum.accum(S3);
         sum.accum(S4);
         sum.accum(S5);
         sum.accum(S6);
         sum.accum(S7);
         const auto S = sum.final_carry(S8);
 
         BOTAN_DEBUG_ASSERT(S <= 8);
 
         solinas_correct_redc<N>(r, P, p256_mul_mod_256(S));
 
         return r;
      }
 
      constexpr static std::array<W, N> one() { return std::array<W, N>{1}; }
 
      constexpr static std::array<W, N> to_rep(const std::array<W, N>& x) { return x; }
 
      constexpr static std::array<W, N> wide_to_rep(const std::array<W, 2 * N>& x) { return redc(x); }
 
      constexpr static std::array<W, N> from_rep(const std::array<W, N>& z) { return z; }
 
   private:
      // Return (i*P-256) % 2**256
      //
      // Assumes i is small
      constexpr static std::array<W, N> p256_mul_mod_256(W i) {
         static_assert(WordInfo<W>::bits == 32 || WordInfo<W>::bits == 64);
 
         // For small i, multiples of P-256 have a simple structure so it's faster to
         // compute the value directly vs a (constant time) table lookup
 
         auto r = P;
         if constexpr(WordInfo<W>::bits == 32) {
            r[7] -= i;
            r[6] += i;
            r[3] += i;
            r[0] -= i;
         } else {
            const uint64_t i32 = static_cast<uint64_t>(i) << 32;
            r[3] -= i32;
            r[3] += i;
            r[1] += i32;
            r[0] -= i;
         }
         return r;
      }
};
 
namespace secp256r1 {
 
// clang-format off
 
class Params final : public EllipticCurveParameters<
   "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
   "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
   "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
   "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
   "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",
   "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5",
   -10> {
};
 
// clang-format on
 
class Curve final : public EllipticCurve<Params, Secp256r1Rep> {
   public:
      // Return the square of the inverse of x
      static constexpr FieldElement fe_invert2(const FieldElement& x) {
         // Generated using https://github.com/mmcloughlin/addchain
 
         auto z = x.square();
         z *= x;
         z = z.square();
         z *= x;
         auto t0 = z;
         t0.square_n(3);
         t0 *= z;
         auto t1 = t0;
         t1.square_n(6);
         t0 *= t1;
         t0.square_n(3);
         z *= t0;
         t0 = z.square();
         t0 *= x;
         t1 = t0;
         t1.square_n(16);
         t0 *= t1;
         t0.square_n(15);
         z *= t0;
         t0.square_n(17);
         t0 *= x;
         t0.square_n(143);
         t0 *= z;
         t0.square_n(47);
         z *= t0;
         z.square_n(2);
 
         return z;
      }
 
      // Return the square root of x
      static constexpr FieldElement fe_sqrt(const FieldElement& x) {
         // Generated using addchain
         auto z = x.square();
         z *= x;
         auto t0 = z;
         t0.square_n(2);
         z *= t0;
         t0 = z;
         t0.square_n(4);
         z *= t0;
         t0 = z;
         t0.square_n(8);
         z *= t0;
         t0 = z;
         t0.square_n(16);
         z *= t0;
         z.square_n(32);
         z *= x;
         z.square_n(96);
         z *= x;
         z.square_n(94);
         return z;
      }
 
      static constexpr Scalar scalar_invert(const Scalar& x) {
         auto t1 = x.square();
         auto t5 = t1.square();
         auto t2 = t5 * x;
         auto t10 = t2 * x;
         auto t3 = t2 * t5;
         auto z = t10 * t3;
         auto t9 = t3.square();
         auto t4 = t10 * z;
         auto t0 = t10 * t9;
         auto t13 = t0 * t1;
         auto t8 = t13 * t4;
         t4 = t3 * t8;
         auto t7 = t2 * t4;
         t2 = t1 * t7;
         auto t6 = t7 * t9;
         t3 = t6 * t9;
         t1 *= t3;
         auto t12 = t3 * t9;
         t5 *= t12;
         auto t11 = t10 * t5;
         t0 *= t11;
         t9 *= t0;
         t10 *= t9;
         t4 *= t10;
         t13 *= t4;
         auto t14 = t13;
         t14.square_n(8);
         t13 *= t14;
         t14 = t13;
         t14.square_n(16);
         t14 *= t13;
         t14.square_n(48);
         t14 *= t13;
         t14.square_n(16);
         t14 *= t13;
         t14.square_n(16);
         t14 *= t13;
         t14.square_n(16);
         t13 *= t14;
         t13.square_n(6);
         t13 *= t8;
         t13.square_n(9);
         t12 *= t13;
         t12.square_n(8);
         t11 *= t12;
         t11.square_n(9);
         t10 *= t11;
         t10.square_n(8);
         t9 *= t10;
         t9.square_n(9);
         t8 *= t9;
         t8.square_n(8);
         t7 *= t8;
         t7.square_n(11);
         t6 *= t7;
         t6.square_n(9);
         t5 *= t6;
         t5.square_n(10);
         t4 *= t5;
         t4.square_n(8);
         t3 *= t4;
         t3.square_n(7);
         t2 *= t3;
         t2.square_n(10);
         t1 *= t2;
         t1.square_n(10);
         t0 *= t1;
         t0.square_n(6);
         z *= t0;
 
         return z;
      }
};
 
}  // namespace secp256r1
 
}  // namespace
 
std::shared_ptr<const PrimeOrderCurve> PCurveInstance::secp256r1() {
   return PrimeOrderCurveImpl<secp256r1::Curve>::instance();
}
 
}  // namespace Botan::PCurve