#include #include #include #include typedef uint64_t fe4[4]; typedef uint8_t fiat_uint1; typedef int8_t fiat_int1; static __inline__ uint64_t fiat_value_barrier_u64(uint64_t a) { __asm__("" : "+r"(a) : /* no inputs */); return a; } __attribute__((target("adx,bmi2"))) static inline void fe4_mul(fe4 out, const fe4 x, const fe4 y) { fiat_curve25519_adx_mul(out, x, y); } __attribute__((target("adx,bmi2"))) static inline void fe4_sq(fe4 out, const fe4 x) { fiat_curve25519_adx_square(out, x); } /* * The function fiat_mulx_u64 is a multiplication, returning the full double-width result. * * Postconditions: * out1 = (arg1 * arg2) mod 2^64 * out2 = ⌊arg1 * arg2 / 2^64⌋ * * Input Bounds: * arg1: [0x0 ~> 0xffffffffffffffff] * arg2: [0x0 ~> 0xffffffffffffffff] * Output Bounds: * out1: [0x0 ~> 0xffffffffffffffff] * out2: [0x0 ~> 0xffffffffffffffff] */ __attribute__((target("adx,bmi2"))) static inline void fiat_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) { // NOTE: edited after generation #if defined(_M_X64) unsigned long long t; *out1 = _umul128(arg1, arg2, &t); *out2 = t; #elif defined(_M_ARM64) *out1 = arg1 * arg2; *out2 = __umulh(arg1, arg2); #else unsigned __int128 t = (unsigned __int128)arg1 * arg2; *out1 = t; *out2 = (t >> 64); #endif } /* * The function fiat_addcarryx_u64 is an addition with carry. * * Postconditions: * out1 = (arg1 + arg2 + arg3) mod 2^64 * out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋ * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [0x0 ~> 0xffffffffffffffff] * arg3: [0x0 ~> 0xffffffffffffffff] * Output Bounds: * out1: [0x0 ~> 0xffffffffffffffff] * out2: [0x0 ~> 0x1] */ __attribute__((target("adx,bmi2"))) static inline void fiat_addcarryx_u64(uint64_t* out1, fiat_uint1* out2, fiat_uint1 arg1, uint64_t arg2, uint64_t arg3) { // NOTE: edited after generation #if defined(__has_builtin) # if __has_builtin(__builtin_ia32_addcarryx_u64) # define addcarry64 __builtin_ia32_addcarryx_u64 # endif #endif #if defined(addcarry64) long long unsigned int t; *out2 = addcarry64(arg1, arg2, arg3, &t); *out1 = t; #elif defined(_M_X64) long long unsigned int t; *out2 = _addcarry_u64(arg1, arg2, arg3, out1); *out1 = t; #else arg2 += arg1; arg1 = arg2 < arg1; uint64_t ret = arg2 + arg3; arg1 += ret < arg2; *out1 = ret; *out2 = arg1; #endif #undef addcarry64 } /* * The function fiat_subborrowx_u64 is a subtraction with borrow. * * Postconditions: * out1 = (-arg1 + arg2 + -arg3) mod 2^64 * out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋ * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [0x0 ~> 0xffffffffffffffff] * arg3: [0x0 ~> 0xffffffffffffffff] * Output Bounds: * out1: [0x0 ~> 0xffffffffffffffff] * out2: [0x0 ~> 0x1] */ __attribute__((target("adx,bmi2"))) static inline void fiat_subborrowx_u64(uint64_t* out1, fiat_uint1* out2, fiat_uint1 arg1, uint64_t arg2, uint64_t arg3) { #if defined(__has_builtin) # if __has_builtin(__builtin_ia32_subborrow_u64) # define subborrow64 __builtin_ia32_subborrow_u64 # endif #endif #if defined(subborrow64) long long unsigned int t; *out2 = subborrow64(arg1, arg2, arg3, &t); *out1 = t; #elif defined(_M_X64) long long unsigned int t; *out2 = _subborrow_u64(arg1, arg2, arg3, &t); // NOTE: edited after generation *out1 = t; #else *out1 = arg2 - arg3 - arg1; *out2 = (arg2 < arg3) | ((arg2 == arg3) & arg1); #endif #undef subborrow64 } /* * The function fiat_cmovznz_u64 is a single-word conditional move. * * Postconditions: * out1 = (if arg1 = 0 then arg2 else arg3) * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [0x0 ~> 0xffffffffffffffff] * arg3: [0x0 ~> 0xffffffffffffffff] * Output Bounds: * out1: [0x0 ~> 0xffffffffffffffff] */ __attribute__((target("adx,bmi2"))) static inline void fiat_cmovznz_u64(uint64_t* out1, fiat_uint1 arg1, uint64_t arg2, uint64_t arg3) { fiat_uint1 x1; uint64_t x2; uint64_t x3; x1 = (!(!arg1)); x2 = ((fiat_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff)); x3 = ((fiat_value_barrier_u64(x2) & arg3) | (fiat_value_barrier_u64((~x2)) & arg2)); *out1 = x3; } /* * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ __attribute__((target("adx,bmi2"))) static void fe4_add(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) { uint64_t x1; fiat_uint1 x2; uint64_t x3; fiat_uint1 x4; uint64_t x5; fiat_uint1 x6; uint64_t x7; fiat_uint1 x8; uint64_t x9; uint64_t x10; fiat_uint1 x11; uint64_t x12; fiat_uint1 x13; uint64_t x14; fiat_uint1 x15; uint64_t x16; fiat_uint1 x17; uint64_t x18; uint64_t x19; fiat_uint1 x20; fiat_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); fiat_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1])); fiat_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2])); fiat_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3])); fiat_cmovznz_u64(&x9, x8, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and fiat_addcarryx_u64(&x10, &x11, 0x0, x1, x9); fiat_addcarryx_u64(&x12, &x13, x11, x3, 0x0); fiat_addcarryx_u64(&x14, &x15, x13, x5, 0x0); fiat_addcarryx_u64(&x16, &x17, x15, x7, 0x0); fiat_cmovznz_u64(&x18, x17, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and fiat_addcarryx_u64(&x19, &x20, 0x0, x10, x18); out1[0] = x19; out1[1] = x12; out1[2] = x14; out1[3] = x16; } /* * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ __attribute__((target("adx,bmi2"))) static void fe4_sub(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) { uint64_t x1; uint64_t x2; fiat_uint1 x3; uint64_t x4; uint64_t x5; fiat_uint1 x6; uint64_t x7; uint64_t x8; fiat_uint1 x9; uint64_t x10; uint64_t x11; fiat_uint1 x12; uint64_t x13; uint64_t x14; fiat_uint1 x15; uint64_t x16; fiat_uint1 x17; uint64_t x18; fiat_uint1 x19; uint64_t x20; fiat_uint1 x21; uint64_t x22; uint64_t x23; fiat_uint1 x24; x1 = (arg2[0]); fiat_subborrowx_u64(&x2, &x3, 0x0, (arg1[0]), x1); x4 = (arg2[1]); fiat_subborrowx_u64(&x5, &x6, x3, (arg1[1]), x4); x7 = (arg2[2]); fiat_subborrowx_u64(&x8, &x9, x6, (arg1[2]), x7); x10 = (arg2[3]); fiat_subborrowx_u64(&x11, &x12, x9, (arg1[3]), x10); fiat_cmovznz_u64(&x13, x12, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and fiat_subborrowx_u64(&x14, &x15, 0x0, x2, x13); fiat_subborrowx_u64(&x16, &x17, x15, x5, 0x0); fiat_subborrowx_u64(&x18, &x19, x17, x8, 0x0); fiat_subborrowx_u64(&x20, &x21, x19, x11, 0x0); fiat_cmovznz_u64(&x22, x21, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and fiat_subborrowx_u64(&x23, &x24, 0x0, x14, x22); out1[0] = x23; out1[1] = x16; out1[2] = x18; out1[3] = x20; } /* * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [0x0 ~> 0x3ffffffffffffff] // NOTE: this is not any uint64! * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ __attribute__((target("adx,bmi2"))) static void fe4_scmul(uint64_t out1[4], const uint64_t arg1[4], uint64_t arg2) { uint64_t x1; uint64_t x2; uint64_t x3; uint64_t x4; uint64_t x5; fiat_uint1 x6; uint64_t x7; uint64_t x8; uint64_t x9; fiat_uint1 x10; uint64_t x11; uint64_t x12; uint64_t x13; fiat_uint1 x14; uint64_t x15; uint64_t x16; uint64_t x17; fiat_uint1 x18; uint64_t x19; fiat_uint1 x20; uint64_t x21; fiat_uint1 x22; uint64_t x23; fiat_uint1 x24; uint64_t x25; uint64_t x26; fiat_uint1 x27; fiat_mulx_u64(&x1, &x2, (arg1[0]), arg2); fiat_mulx_u64(&x3, &x4, (arg1[1]), arg2); fiat_addcarryx_u64(&x5, &x6, 0x0, x2, x3); fiat_mulx_u64(&x7, &x8, (arg1[2]), arg2); fiat_addcarryx_u64(&x9, &x10, x6, x4, x7); fiat_mulx_u64(&x11, &x12, (arg1[3]), arg2); fiat_addcarryx_u64(&x13, &x14, x10, x8, x11); fiat_mulx_u64(&x15, &x16, (x12 + (uint64_t)x14), UINT8_C(0x26)); fiat_addcarryx_u64(&x17, &x18, 0x0, x1, x15); fiat_addcarryx_u64(&x19, &x20, x18, x5, 0x0); fiat_addcarryx_u64(&x21, &x22, x20, x9, 0x0); fiat_addcarryx_u64(&x23, &x24, x22, x13, 0x0); fiat_cmovznz_u64(&x25, x24, 0x0, UINT8_C(0x26)); // NOTE: clang 14 for Zen 2 uses sbb, and fiat_addcarryx_u64(&x26, &x27, 0x0, x17, x25); out1[0] = x26; out1[1] = x19; out1[2] = x21; out1[3] = x23; } /* * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ __attribute__((target("adx,bmi2"))) static void fe4_canon(uint64_t out1[4], const uint64_t arg1[4]) { uint64_t x1; fiat_uint1 x2; uint64_t x3; fiat_uint1 x4; uint64_t x5; fiat_uint1 x6; uint64_t x7; fiat_uint1 x8; uint64_t x9; uint64_t x10; uint64_t x11; uint64_t x12; uint64_t x13; fiat_uint1 x14; uint64_t x15; fiat_uint1 x16; uint64_t x17; fiat_uint1 x18; uint64_t x19; fiat_uint1 x20; uint64_t x21; uint64_t x22; uint64_t x23; uint64_t x24; fiat_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), UINT64_C(0xffffffffffffffed)); fiat_subborrowx_u64(&x3, &x4, x2, (arg1[1]), UINT64_C(0xffffffffffffffff)); fiat_subborrowx_u64(&x5, &x6, x4, (arg1[2]), UINT64_C(0xffffffffffffffff)); fiat_subborrowx_u64(&x7, &x8, x6, (arg1[3]), UINT64_C(0x7fffffffffffffff)); fiat_cmovznz_u64(&x9, x8, x1, (arg1[0])); fiat_cmovznz_u64(&x10, x8, x3, (arg1[1])); fiat_cmovznz_u64(&x11, x8, x5, (arg1[2])); fiat_cmovznz_u64(&x12, x8, x7, (arg1[3])); fiat_subborrowx_u64(&x13, &x14, 0x0, x9, UINT64_C(0xffffffffffffffed)); fiat_subborrowx_u64(&x15, &x16, x14, x10, UINT64_C(0xffffffffffffffff)); fiat_subborrowx_u64(&x17, &x18, x16, x11, UINT64_C(0xffffffffffffffff)); fiat_subborrowx_u64(&x19, &x20, x18, x12, UINT64_C(0x7fffffffffffffff)); fiat_cmovznz_u64(&x21, x20, x13, x9); fiat_cmovznz_u64(&x22, x20, x15, x10); fiat_cmovznz_u64(&x23, x20, x17, x11); fiat_cmovznz_u64(&x24, x20, x19, x12); out1[0] = x21; out1[1] = x22; out1[2] = x23; out1[3] = x24; } /* * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */ __attribute__((target("adx,bmi2"))) static void fe4_cswap(uint64_t out1[4], uint64_t out2[4], fiat_uint1 arg1, const uint64_t arg2[4], const uint64_t arg3[4]) { uint64_t x1; uint64_t x2; uint64_t x3; uint64_t x4; uint64_t x5; uint64_t x6; uint64_t x7; uint64_t x8; // NOTE: clang 14 for Zen 2 uses YMM registers fiat_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0])); fiat_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1])); fiat_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2])); fiat_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3])); fiat_cmovznz_u64(&x5, arg1, (arg3[0]), (arg2[0])); fiat_cmovznz_u64(&x6, arg1, (arg3[1]), (arg2[1])); fiat_cmovznz_u64(&x7, arg1, (arg3[2]), (arg2[2])); fiat_cmovznz_u64(&x8, arg1, (arg3[3]), (arg2[3])); out1[0] = x1; out1[1] = x2; out1[2] = x3; out1[3] = x4; out2[0] = x5; out2[1] = x6; out2[2] = x7; out2[3] = x8; } // The following functions are adaped from crypto/curve25519/curve25519.c // It would be desirable to share the code, but with the current field // implementations both 4-limb and 5-limb versions of the curve-level code need // to be included in builds targetting an unknown variant of x86_64. __attribute__((target("adx,bmi2"))) static void fe4_invert(fe4 out, const fe4 z) { fe4 t0; fe4 t1; fe4 t2; fe4 t3; int i; fe4_sq(t0, z); fe4_sq(t1, t0); for (i = 1; i < 2; ++i) { fe4_sq(t1, t1); } fe4_mul(t1, z, t1); fe4_mul(t0, t0, t1); fe4_sq(t2, t0); fe4_mul(t1, t1, t2); fe4_sq(t2, t1); for (i = 1; i < 5; ++i) { fe4_sq(t2, t2); } fe4_mul(t1, t2, t1); fe4_sq(t2, t1); for (i = 1; i < 10; ++i) { fe4_sq(t2, t2); } fe4_mul(t2, t2, t1); fe4_sq(t3, t2); for (i = 1; i < 20; ++i) { fe4_sq(t3, t3); } fe4_mul(t2, t3, t2); fe4_sq(t2, t2); for (i = 1; i < 10; ++i) { fe4_sq(t2, t2); } fe4_mul(t1, t2, t1); fe4_sq(t2, t1); for (i = 1; i < 50; ++i) { fe4_sq(t2, t2); } fe4_mul(t2, t2, t1); fe4_sq(t3, t2); for (i = 1; i < 100; ++i) { fe4_sq(t3, t3); } fe4_mul(t2, t3, t2); fe4_sq(t2, t2); for (i = 1; i < 50; ++i) { fe4_sq(t2, t2); } fe4_mul(t1, t2, t1); fe4_sq(t1, t1); for (i = 1; i < 5; ++i) { fe4_sq(t1, t1); } fe4_mul(out, t1, t0); } __attribute__((target("adx,bmi2"))) void x25519_scalar_mult_adx(uint8_t out[32], const uint8_t scalar[32], const uint8_t point[32]) { uint8_t e[32]; memcpy(e, scalar, 32); e[0] &= 248; e[31] &= 127; e[31] |= 64; // The following implementation was transcribed to Coq and proven to // correspond to unary scalar multiplication in affine coordinates given that // x1 != 0 is the x coordinate of some point on the curve. It was also checked // in Coq that doing a ladderstep with x1 = x3 = 0 gives z2' = z3' = 0, and z2 // = z3 = 0 gives z2' = z3' = 0. The statement was quantified over the // underlying field, so it applies to Curve25519 itself and the quadratic // twist of Curve25519. It was not proven in Coq that prime-field arithmetic // correctly simulates extension-field arithmetic on prime-field values. // The decoding of the byte array representation of e was not considered. // Specification of Montgomery curves in affine coordinates: // // Proof that these form a group that is isomorphic to a Weierstrass curve: // // Coq transcription and correctness proof of the loop (where scalarbits=255): // // // preconditions: 0 <= e < 2^255 (not necessarily e < order), fe_invert(0) = 0 fe4 x1, x2 = {1}, z2 = {0}, x3, z3 = {1}, tmp0, tmp1; OPENSSL_memcpy(x1, point, sizeof(fe4)); x1[3] &= (uint64_t)(-1)>>1; OPENSSL_memcpy(x3, x1, sizeof(fe4)); unsigned swap = 0; int pos; for (pos = 254; pos >= 0; --pos) { // loop invariant as of right before the test, for the case where x1 != 0: // pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 is nonzero // let r := e >> (pos+1) in the following equalities of projective points: // to_xz (r*P) === if swap then (x3, z3) else (x2, z2) // to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3) // x1 is the nonzero x coordinate of the nonzero point (r*P-(r+1)*P) unsigned b = 1 & (e[pos / 8] >> (pos & 7)); swap ^= b; fe4_cswap(x2, x3, swap, x2, x3); fe4_cswap(z2, z3, swap, z2, z3); swap = b; // Coq transcription of ladderstep formula (called from transcribed loop): // // // x1 != 0 // x1 = 0 fe4_sub(tmp0, x3, z3); fe4_sub(tmp1, x2, z2); fe4_add(x2, x2, z2); fe4_add(z2, x3, z3); fe4_mul(z3, tmp0, x2); fe4_mul(z2, z2, tmp1); fe4_sq(tmp0, tmp1); fe4_sq(tmp1, x2); fe4_add(x3, z3, z2); fe4_sub(z2, z3, z2); fe4_mul(x2, tmp1, tmp0); fe4_sub(tmp1, tmp1, tmp0); fe4_sq(z2, z2); fe4_scmul(z3, tmp1, 121666); fe4_sq(x3, x3); fe4_add(tmp0, tmp0, z3); fe4_mul(z3, x1, z2); fe4_mul(z2, tmp1, tmp0); } // here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) else (x2, z2) fe4_cswap(x2, x3, swap, x2, x3); fe4_cswap(z2, z3, swap, z2, z3); fe4_invert(z2, z2); fe4_mul(x2, x2, z2); fe4_canon(x2, x2); OPENSSL_memcpy(out, x2, sizeof(fe4)); } typedef struct { fe4 X; fe4 Y; fe4 Z; fe4 T; } ge_p3_4; typedef struct { fe4 yplusx; fe4 yminusx; fe4 xy2d; } ge_precomp_4; __attribute__((target("adx,bmi2"))) static void inline_x25519_ge_dbl_4(ge_p3_4 *r, const ge_p3_4 *p, bool skip_t) { // Transcribed from a Coq function proven against affine coordinates. // https://github.com/mit-plv/fiat-crypto/blob/9943ba9e7d8f3e1c0054b2c94a5edca46ea73ef8/src/Curves/Edwards/XYZT/Basic.v#L136-L165 fe4 trX, trZ, trT, t0, cX, cY, cZ, cT; fe4_sq(trX, p->X); fe4_sq(trZ, p->Y); fe4_sq(trT, p->Z); fe4_add(trT, trT, trT); fe4_add(cY, p->X, p->Y); fe4_sq(t0, cY); fe4_add(cY, trZ, trX); fe4_sub(cZ, trZ, trX); fe4_sub(cX, t0, cY); fe4_sub(cT, trT, cZ); fe4_mul(r->X, cX, cT); fe4_mul(r->Y, cY, cZ); fe4_mul(r->Z, cZ, cT); if (!skip_t) { fe4_mul(r->T, cX, cY); } } __attribute__((target("adx,bmi2"))) __attribute__((always_inline)) // 4% speedup with clang14 and zen2 static inline void ge_p3_add_p3_precomp_4(ge_p3_4 *r, const ge_p3_4 *p, const ge_precomp_4 *q) { fe4 A, B, C, YplusX, YminusX, D, X3, Y3, Z3, T3; // Transcribed from a Coq function proven against affine coordinates. // https://github.com/mit-plv/fiat-crypto/blob/a36568d1d73aff5d7accc79fd28be672882f9c17/src/Curves/Edwards/XYZT/Precomputed.v#L38-L56 fe4_add(YplusX, p->Y, p->X); fe4_sub(YminusX, p->Y, p->X); fe4_mul(A, YplusX, q->yplusx); fe4_mul(B, YminusX, q->yminusx); fe4_mul(C, q->xy2d, p->T); fe4_add(D, p->Z, p->Z); fe4_sub(X3, A, B); fe4_add(Y3, A, B); fe4_add(Z3, D, C); fe4_sub(T3, D, C); fe4_mul(r->X, X3, T3); fe4_mul(r->Y, Y3, Z3); fe4_mul(r->Z, Z3, T3); fe4_mul(r->T, X3, Y3); } __attribute__((always_inline)) // 25% speedup with clang14 and zen2 static inline void table_select_4(ge_precomp_4 *t, const int pos, const signed char b) { uint8_t bnegative = constant_time_msb_w(b); uint8_t babs = b - ((bnegative & b) << 1); uint8_t t_bytes[3][32] = { {constant_time_is_zero_w(b) & 1}, {constant_time_is_zero_w(b) & 1}, {0}}; #if defined(__clang__) __asm__("" : "+m" (t_bytes) : /*no inputs*/); #endif static_assert(sizeof(t_bytes) == sizeof(k25519Precomp[pos][0]), ""); for (int i = 0; i < 8; i++) { constant_time_conditional_memxor(t_bytes, k25519Precomp[pos][i], sizeof(t_bytes), constant_time_eq_w(babs, 1 + i)); } static_assert(sizeof(t_bytes) == sizeof(ge_precomp_4), ""); // fe4 uses saturated 64-bit limbs, so converting from bytes is just a copy. OPENSSL_memcpy(t, t_bytes, sizeof(ge_precomp_4)); fe4 xy2d_neg = {0}; fe4_sub(xy2d_neg, xy2d_neg, t->xy2d); constant_time_conditional_memcpy(t->yplusx, t_bytes[1], sizeof(fe4), bnegative); constant_time_conditional_memcpy(t->yminusx, t_bytes[0], sizeof(fe4), bnegative); constant_time_conditional_memcpy(t->xy2d, xy2d_neg, sizeof(fe4), bnegative); } // h = a * B // where a = a[0]+256*a[1]+...+256^31 a[31] // B is the Ed25519 base point (x,4/5) with x positive. // // Preconditions: // a[31] <= 127 __attribute__((target("adx,bmi2"))) void x25519_ge_scalarmult_base_adx(uint8_t h[4][32], const uint8_t a[32]) { signed char e[64]; signed char carry; for (unsigned i = 0; i < 32; ++i) { e[2 * i + 0] = (a[i] >> 0) & 15; e[2 * i + 1] = (a[i] >> 4) & 15; } // each e[i] is between 0 and 15 // e[63] is between 0 and 7 carry = 0; for (unsigned i = 0; i < 63; ++i) { e[i] += carry; carry = e[i] + 8; carry >>= 4; e[i] -= carry << 4; } e[63] += carry; // each e[i] is between -8 and 8 ge_p3_4 r = {{0}, {1}, {1}, {0}}; for (unsigned i = 1; i < 64; i += 2) { ge_precomp_4 t; table_select_4(&t, i / 2, e[i]); ge_p3_add_p3_precomp_4(&r, &r, &t); } inline_x25519_ge_dbl_4(&r, &r, /*skip_t=*/true); inline_x25519_ge_dbl_4(&r, &r, /*skip_t=*/true); inline_x25519_ge_dbl_4(&r, &r, /*skip_t=*/true); inline_x25519_ge_dbl_4(&r, &r, /*skip_t=*/false); for (unsigned i = 0; i < 64; i += 2) { ge_precomp_4 t; table_select_4(&t, i / 2, e[i]); ge_p3_add_p3_precomp_4(&r, &r, &t); } // fe4 uses saturated 64-bit limbs, so converting to bytes is just a copy. // Satisfy stated precondition of fiat_25519_from_bytes; tests pass either way fe4_canon(r.X, r.X); fe4_canon(r.Y, r.Y); fe4_canon(r.Z, r.Z); fe4_canon(r.T, r.T); static_assert(sizeof(ge_p3_4) == sizeof(uint8_t[4][32]), ""); OPENSSL_memcpy(h, &r, sizeof(ge_p3_4)); }