Add Solinas reduction for P-224 pcurves

The speedup we get from Solinas for P-224 (around 25%) is much higher
than seen for P-192 or P-256. This may be due to the fact that unlike
P-192 and P-256, P-224 is not "Montgomery friendly", ie p' is not
equal to 1, so the Montgomery reduction is significantly more
expensive.

src/lib/math/pcurves/pcurves_impl/pcurves_solinas.h

@@ -66,7 +66,6 @@ class SolinasAccum {
       }
 
       constexpr W final_carry(int64_t C) {
-         BOTAN_DEBUG_ASSERT(m_idx == N32);
          m_S += C;
          BOTAN_DEBUG_ASSERT(m_S >= 0);
          return static_cast<W>(m_S);

src/lib/math/pcurves/pcurves_secp224r1/pcurves_secp224r1.cpp

@@ -6,6 +6,7 @@
 
 #include <botan/internal/pcurves_instance.h>
 
+#include <botan/internal/pcurves_solinas.h>
 #include <botan/internal/pcurves_wrap.h>
 
 namespace Botan::PCurve {
@@ -14,7 +15,91 @@ namespace {
 
 namespace secp224r1 {
 
-// TODO Secp224r1Rep
+template <typename Params>
+class Secp224r1Rep final {
+   public:
+      static constexpr auto P = Params::P;
+      static constexpr size_t N = Params::N;
+      typedef typename Params::W W;
+
+      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 S0 = 0x00000001 + X00 - X07 - X11;
+         const int64_t S1 = 0x00000000 + X01 - X08 - X12;
+         const int64_t S2 = 0x00000000 + X02 - X09 - X13;
+         const int64_t S3 = 0xFFFFFFFF + X03 + X07 + X11 - X10;
+         const int64_t S4 = 0xFFFFFFFF + X04 + X08 + X12 - X11;
+         const int64_t S5 = 0xFFFFFFFF + X05 + X09 + X13 - X12;
+         const int64_t S6 = 0xFFFFFFFF + X06 + X10 - X13;
+
+         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);
+         const auto S = sum.final_carry(0);
+
+         BOTAN_DEBUG_ASSERT(S <= 2);
+
+         const auto correction = p224_mul_mod_224(S);
+         W borrow = bigint_sub2(r.data(), N, correction.data(), N);
+
+         bigint_cnd_add(borrow, r.data(), N, P.data(), N);
+
+         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-224) % 2**224
+      //
+      // Assumes i is small
+      constexpr static std::array<W, N> p224_mul_mod_224(W i) {
+         static_assert(WordInfo<W>::bits == 32 || WordInfo<W>::bits == 64);
+
+         // For small i, multiples of P-224 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[3] -= i;
+            r[0] += i;
+         } else {
+            const W i32 = i << 32;
+            r[1] -= i32;
+            r[0] += i;
+         }
+         return r;
+      }
+};
 
 // clang-format off
 class Params final : public EllipticCurveParameters<
@@ -28,7 +113,7 @@ class Params final : public EllipticCurveParameters<
 
 // clang-format on
 
-class Curve final : public EllipticCurve<Params> {};
+class Curve final : public EllipticCurve<Params, Secp224r1Rep> {};
 
 }  // namespace secp224r1