From b0d41e8b106d9a36943e5473a8db78131b8c0b6a Mon Sep 17 00:00:00 2001 From: "Jason A. Donenfeld" Date: Mon, 22 Jan 2018 17:58:44 +0100 Subject: [PATCH] wg: share curve25519 implementations with kernel Signed-off-by: Jason A. Donenfeld --- src/curve25519.c | 1579 +--------------------------------------------- 1 file changed, 35 insertions(+), 1544 deletions(-) diff --git a/src/curve25519.c b/src/curve25519.c index 7f6c9bf..061b913 100644 --- a/src/curve25519.c +++ b/src/curve25519.c @@ -14,1559 +14,45 @@ #include #include +typedef uint64_t u64; +typedef uint32_t u32; +typedef uint8_t u8; +typedef int64_t s64; +typedef u64 __le64; +typedef u32 __le32; +#define le64_to_cpup(a) le64toh(*(a)); +#define le32_to_cpup(a) le32toh(*(a)); +#define cpu_to_le64(a) htole64(a); #ifndef __always_inline #define __always_inline __inline __attribute__((__always_inline__)) #endif - +#ifndef noinline +#define noinline __attribute__((noinline)) +#endif #ifndef __aligned #define __aligned(x) __attribute__((aligned(x))) #endif +#ifndef __force +#define __force +#endif + +static noinline void memzero_explicit(void *s, size_t count) +{ + memset(s, 0, count); + __asm__ __volatile__("": :"r"(s) :"memory"); +} + +static __always_inline void normalize_secret(u8 secret[CURVE25519_POINT_SIZE]) +{ + secret[0] &= 248; + secret[31] &= 127; + secret[31] |= 64; +} #ifdef __SIZEOF_INT128__ -typedef __uint128_t uint128_t; - -static __always_inline uint64_t uint64_t_eq_mask(uint64_t x, uint64_t y) -{ - x = ~(x ^ y); - x &= x << 32; - x &= x << 16; - x &= x << 8; - x &= x << 4; - x &= x << 2; - x &= x << 1; - return ((int64_t)x) >> 63; -} - -static __always_inline uint64_t uint64_t_gte_mask(uint64_t x, uint64_t y) -{ - uint64_t low63 = ~((uint64_t)((int64_t)((int64_t)(x & 0x7fffffffffffffffLLU) - (int64_t)(y & 0x7fffffffffffffffLLU)) >> 63)); - uint64_t high_bit = ~((uint64_t)((int64_t)((int64_t)(x & 0x8000000000000000LLU) - (int64_t)(y & 0x8000000000000000LLU)) >> 63)); - return low63 & high_bit; -} - -static __always_inline void modulo_carry_top(uint64_t *b) -{ - uint64_t b4 = b[4]; - uint64_t b0 = b[0]; - uint64_t b4_ = b4 & 0x7ffffffffffffLLU; - uint64_t b0_ = b0 + 19 * (b4 >> 51); - b[4] = b4_; - b[0] = b0_; -} - -static __always_inline void fproduct_copy_from_wide_(uint64_t *output, uint128_t *input) -{ - { - uint128_t xi = input[0]; - output[0] = ((uint64_t)(xi)); - } - { - uint128_t xi = input[1]; - output[1] = ((uint64_t)(xi)); - } - { - uint128_t xi = input[2]; - output[2] = ((uint64_t)(xi)); - } - { - uint128_t xi = input[3]; - output[3] = ((uint64_t)(xi)); - } - { - uint128_t xi = input[4]; - output[4] = ((uint64_t)(xi)); - } -} - -static __always_inline void fproduct_sum_scalar_multiplication_(uint128_t *output, uint64_t *input, uint64_t s) -{ - uint32_t i; - for (i = 0; i < 5; ++i) { - uint128_t xi = output[i]; - uint64_t yi = input[i]; - output[i] = ((xi) + (((uint128_t)(yi) * (s)))); - } -} - -static __always_inline void fproduct_carry_wide_(uint128_t *tmp) -{ - uint32_t i; - for (i = 0; i < 4; ++i) { - uint32_t ctr = i; - uint128_t tctr = tmp[ctr]; - uint128_t tctrp1 = tmp[ctr + 1]; - uint64_t r0 = ((uint64_t)(tctr)) & 0x7ffffffffffffLLU; - uint128_t c = ((tctr) >> (51)); - tmp[ctr] = ((uint128_t)(r0)); - tmp[ctr + 1] = ((tctrp1) + (c)); - } -} - -static __always_inline void fmul_shift_reduce(uint64_t *output) -{ - uint64_t tmp = output[4]; - uint64_t b0; - { - uint32_t ctr = 5 - 0 - 1; - uint64_t z = output[ctr - 1]; - output[ctr] = z; - } - { - uint32_t ctr = 5 - 1 - 1; - uint64_t z = output[ctr - 1]; - output[ctr] = z; - } - { - uint32_t ctr = 5 - 2 - 1; - uint64_t z = output[ctr - 1]; - output[ctr] = z; - } - { - uint32_t ctr = 5 - 3 - 1; - uint64_t z = output[ctr - 1]; - output[ctr] = z; - } - output[0] = tmp; - b0 = output[0]; - output[0] = 19 * b0; -} - -static __always_inline void fmul_mul_shift_reduce_(uint128_t *output, uint64_t *input, uint64_t *input21) -{ - uint32_t i; - uint64_t input2i; - { - uint64_t input2i = input21[0]; - fproduct_sum_scalar_multiplication_(output, input, input2i); - fmul_shift_reduce(input); - } - { - uint64_t input2i = input21[1]; - fproduct_sum_scalar_multiplication_(output, input, input2i); - fmul_shift_reduce(input); - } - { - uint64_t input2i = input21[2]; - fproduct_sum_scalar_multiplication_(output, input, input2i); - fmul_shift_reduce(input); - } - { - uint64_t input2i = input21[3]; - fproduct_sum_scalar_multiplication_(output, input, input2i); - fmul_shift_reduce(input); - } - i = 4; - input2i = input21[i]; - fproduct_sum_scalar_multiplication_(output, input, input2i); -} - -static __always_inline void fmul_fmul(uint64_t *output, uint64_t *input, uint64_t *input21) -{ - uint64_t tmp[5]; - memcpy(tmp, input, 5 * sizeof(*input)); - { - uint128_t b4; - uint128_t b0; - uint128_t b4_; - uint128_t b0_; - uint64_t i0; - uint64_t i1; - uint64_t i0_; - uint64_t i1_; - uint128_t t[5]; - { - uint32_t _i; - for (_i = 0; _i < 5; ++_i) - t[_i] = ((uint128_t)(0)); - } - fmul_mul_shift_reduce_(t, tmp, input21); - fproduct_carry_wide_(t); - b4 = t[4]; - b0 = t[0]; - b4_ = ((b4) & (((uint128_t)(0x7ffffffffffffLLU)))); - b0_ = ((b0) + (((uint128_t)(19) * (((uint64_t)(((b4) >> (51)))))))); - t[4] = b4_; - t[0] = b0_; - fproduct_copy_from_wide_(output, t); - i0 = output[0]; - i1 = output[1]; - i0_ = i0 & 0x7ffffffffffffLLU; - i1_ = i1 + (i0 >> 51); - output[0] = i0_; - output[1] = i1_; - } -} - -static __always_inline void fsquare_fsquare__(uint128_t *tmp, uint64_t *output) -{ - uint64_t r0 = output[0]; - uint64_t r1 = output[1]; - uint64_t r2 = output[2]; - uint64_t r3 = output[3]; - uint64_t r4 = output[4]; - uint64_t d0 = r0 * 2; - uint64_t d1 = r1 * 2; - uint64_t d2 = r2 * 2 * 19; - uint64_t d419 = r4 * 19; - uint64_t d4 = d419 * 2; - uint128_t s0 = ((((((uint128_t)(r0) * (r0))) + (((uint128_t)(d4) * (r1))))) + (((uint128_t)(d2) * (r3)))); - uint128_t s1 = ((((((uint128_t)(d0) * (r1))) + (((uint128_t)(d4) * (r2))))) + (((uint128_t)(r3 * 19) * (r3)))); - uint128_t s2 = ((((((uint128_t)(d0) * (r2))) + (((uint128_t)(r1) * (r1))))) + (((uint128_t)(d4) * (r3)))); - uint128_t s3 = ((((((uint128_t)(d0) * (r3))) + (((uint128_t)(d1) * (r2))))) + (((uint128_t)(r4) * (d419)))); - uint128_t s4 = ((((((uint128_t)(d0) * (r4))) + (((uint128_t)(d1) * (r3))))) + (((uint128_t)(r2) * (r2)))); - tmp[0] = s0; - tmp[1] = s1; - tmp[2] = s2; - tmp[3] = s3; - tmp[4] = s4; -} - -static __always_inline void fsquare_fsquare_(uint128_t *tmp, uint64_t *output) -{ - uint128_t b4; - uint128_t b0; - uint128_t b4_; - uint128_t b0_; - uint64_t i0; - uint64_t i1; - uint64_t i0_; - uint64_t i1_; - fsquare_fsquare__(tmp, output); - fproduct_carry_wide_(tmp); - b4 = tmp[4]; - b0 = tmp[0]; - b4_ = ((b4) & (((uint128_t)(0x7ffffffffffffLLU)))); - b0_ = ((b0) + (((uint128_t)(19) * (((uint64_t)(((b4) >> (51)))))))); - tmp[4] = b4_; - tmp[0] = b0_; - fproduct_copy_from_wide_(output, tmp); - i0 = output[0]; - i1 = output[1]; - i0_ = i0 & 0x7ffffffffffffLLU; - i1_ = i1 + (i0 >> 51); - output[0] = i0_; - output[1] = i1_; -} - -static __always_inline void fsquare_fsquare_times_(uint64_t *input, uint128_t *tmp, uint32_t count1) -{ - uint32_t i; - fsquare_fsquare_(tmp, input); - for (i = 1; i < count1; ++i) - fsquare_fsquare_(tmp, input); -} - -static __always_inline void fsquare_fsquare_times(uint64_t *output, uint64_t *input, uint32_t count1) -{ - uint128_t t[5]; - { - uint32_t _i; - for (_i = 0; _i < 5; ++_i) - t[_i] = ((uint128_t)(0)); - } - memcpy(output, input, 5 * sizeof(*input)); - fsquare_fsquare_times_(output, t, count1); -} - -static __always_inline void fsquare_fsquare_times_inplace(uint64_t *output, uint32_t count1) -{ - uint128_t t[5]; - { - uint32_t _i; - for (_i = 0; _i < 5; ++_i) - t[_i] = ((uint128_t)(0)); - } - fsquare_fsquare_times_(output, t, count1); -} - -static __always_inline void crecip_crecip(uint64_t *out, uint64_t *z) -{ - uint64_t buf[20] = { 0 }; - uint64_t *a0 = buf; - uint64_t *t00 = buf + 5; - uint64_t *b0 = buf + 10; - uint64_t *t01; - uint64_t *b1; - uint64_t *c0; - uint64_t *a; - uint64_t *t0; - uint64_t *b; - uint64_t *c; - fsquare_fsquare_times(a0, z, 1); - fsquare_fsquare_times(t00, a0, 2); - fmul_fmul(b0, t00, z); - fmul_fmul(a0, b0, a0); - fsquare_fsquare_times(t00, a0, 1); - fmul_fmul(b0, t00, b0); - fsquare_fsquare_times(t00, b0, 5); - t01 = buf + 5; - b1 = buf + 10; - c0 = buf + 15; - fmul_fmul(b1, t01, b1); - fsquare_fsquare_times(t01, b1, 10); - fmul_fmul(c0, t01, b1); - fsquare_fsquare_times(t01, c0, 20); - fmul_fmul(t01, t01, c0); - fsquare_fsquare_times_inplace(t01, 10); - fmul_fmul(b1, t01, b1); - fsquare_fsquare_times(t01, b1, 50); - a = buf; - t0 = buf + 5; - b = buf + 10; - c = buf + 15; - fmul_fmul(c, t0, b); - fsquare_fsquare_times(t0, c, 100); - fmul_fmul(t0, t0, c); - fsquare_fsquare_times_inplace(t0, 50); - fmul_fmul(t0, t0, b); - fsquare_fsquare_times_inplace(t0, 5); - fmul_fmul(out, t0, a); -} - -static __always_inline void fsum(uint64_t *a, uint64_t *b) -{ - uint32_t i; - for (i = 0; i < 5; ++i) { - uint64_t xi = a[i]; - uint64_t yi = b[i]; - a[i] = xi + yi; - } -} - -static __always_inline void fdifference(uint64_t *a, uint64_t *b) -{ - uint64_t tmp[5] = { 0 }; - uint64_t b0; - uint64_t b1; - uint64_t b2; - uint64_t b3; - uint64_t b4; - memcpy(tmp, b, 5 * sizeof(*b)); - b0 = tmp[0]; - b1 = tmp[1]; - b2 = tmp[2]; - b3 = tmp[3]; - b4 = tmp[4]; - tmp[0] = b0 + 0x3fffffffffff68LLU; - tmp[1] = b1 + 0x3ffffffffffff8LLU; - tmp[2] = b2 + 0x3ffffffffffff8LLU; - tmp[3] = b3 + 0x3ffffffffffff8LLU; - tmp[4] = b4 + 0x3ffffffffffff8LLU; - { - uint64_t xi = a[0]; - uint64_t yi = tmp[0]; - a[0] = yi - xi; - } - { - uint64_t xi = a[1]; - uint64_t yi = tmp[1]; - a[1] = yi - xi; - } - { - uint64_t xi = a[2]; - uint64_t yi = tmp[2]; - a[2] = yi - xi; - } - { - uint64_t xi = a[3]; - uint64_t yi = tmp[3]; - a[3] = yi - xi; - } - { - uint64_t xi = a[4]; - uint64_t yi = tmp[4]; - a[4] = yi - xi; - } -} - -static __always_inline void fscalar(uint64_t *output, uint64_t *b, uint64_t s) -{ - uint128_t tmp[5]; - uint128_t b4; - uint128_t b0; - uint128_t b4_; - uint128_t b0_; - { - uint64_t xi = b[0]; - tmp[0] = ((uint128_t)(xi) * (s)); - } - { - uint64_t xi = b[1]; - tmp[1] = ((uint128_t)(xi) * (s)); - } - { - uint64_t xi = b[2]; - tmp[2] = ((uint128_t)(xi) * (s)); - } - { - uint64_t xi = b[3]; - tmp[3] = ((uint128_t)(xi) * (s)); - } - { - uint64_t xi = b[4]; - tmp[4] = ((uint128_t)(xi) * (s)); - } - fproduct_carry_wide_(tmp); - b4 = tmp[4]; - b0 = tmp[0]; - b4_ = ((b4) & (((uint128_t)(0x7ffffffffffffLLU)))); - b0_ = ((b0) + (((uint128_t)(19) * (((uint64_t)(((b4) >> (51)))))))); - tmp[4] = b4_; - tmp[0] = b0_; - fproduct_copy_from_wide_(output, tmp); -} - -static __always_inline void fmul(uint64_t *output, uint64_t *a, uint64_t *b) -{ - fmul_fmul(output, a, b); -} - -static __always_inline void crecip(uint64_t *output, uint64_t *input) -{ - crecip_crecip(output, input); -} - -static __always_inline void point_swap_conditional_step(uint64_t *a, uint64_t *b, uint64_t swap1, uint32_t ctr) -{ - uint32_t i = ctr - 1; - uint64_t ai = a[i]; - uint64_t bi = b[i]; - uint64_t x = swap1 & (ai ^ bi); - uint64_t ai1 = ai ^ x; - uint64_t bi1 = bi ^ x; - a[i] = ai1; - b[i] = bi1; -} - -static __always_inline void point_swap_conditional_(uint64_t *a, uint64_t *b, uint64_t swap1, uint32_t ctr) -{ - uint32_t i; - for (i = ctr; i > 0; --i) - point_swap_conditional_step(a, b, swap1, i); -} - -static __always_inline void point_swap_conditional(uint64_t *a, uint64_t *b, uint64_t iswap) -{ - uint64_t swap1 = 0 - iswap; - point_swap_conditional_(a, b, swap1, 5); - point_swap_conditional_(a + 5, b + 5, swap1, 5); -} - -static __always_inline void point_copy(uint64_t *output, uint64_t *input) -{ - memcpy(output, input, 5 * sizeof(*input)); - memcpy(output + 5, input + 5, 5 * sizeof(*input)); -} - -static __always_inline void addanddouble_fmonty(uint64_t *pp, uint64_t *ppq, uint64_t *p, uint64_t *pq, uint64_t *qmqp) -{ - uint64_t *qx = qmqp; - uint64_t *x2 = pp; - uint64_t *z2 = pp + 5; - uint64_t *x3 = ppq; - uint64_t *z3 = ppq + 5; - uint64_t *x = p; - uint64_t *z = p + 5; - uint64_t *xprime = pq; - uint64_t *zprime = pq + 5; - uint64_t buf[40] = { 0 }; - uint64_t *origx = buf; - uint64_t *origxprime0 = buf + 5; - uint64_t *xxprime0; - uint64_t *zzprime0; - uint64_t *origxprime; - xxprime0 = buf + 25; - zzprime0 = buf + 30; - memcpy(origx, x, 5 * sizeof(*x)); - fsum(x, z); - fdifference(z, origx); - memcpy(origxprime0, xprime, 5 * sizeof(*xprime)); - fsum(xprime, zprime); - fdifference(zprime, origxprime0); - fmul(xxprime0, xprime, z); - fmul(zzprime0, x, zprime); - origxprime = buf + 5; - { - uint64_t *xx0; - uint64_t *zz0; - uint64_t *xxprime; - uint64_t *zzprime; - uint64_t *zzzprime; - xx0 = buf + 15; - zz0 = buf + 20; - xxprime = buf + 25; - zzprime = buf + 30; - zzzprime = buf + 35; - memcpy(origxprime, xxprime, 5 * sizeof(*xxprime)); - fsum(xxprime, zzprime); - fdifference(zzprime, origxprime); - fsquare_fsquare_times(x3, xxprime, 1); - fsquare_fsquare_times(zzzprime, zzprime, 1); - fmul(z3, zzzprime, qx); - fsquare_fsquare_times(xx0, x, 1); - fsquare_fsquare_times(zz0, z, 1); - { - uint64_t *zzz; - uint64_t *xx; - uint64_t *zz; - uint64_t scalar; - zzz = buf + 10; - xx = buf + 15; - zz = buf + 20; - fmul(x2, xx, zz); - fdifference(zz, xx); - scalar = 121665; - fscalar(zzz, zz, scalar); - fsum(zzz, xx); - fmul(z2, zzz, zz); - } - } -} - -static __always_inline void ladder_smallloop_cmult_small_loop_step(uint64_t *nq, uint64_t *nqpq, uint64_t *nq2, uint64_t *nqpq2, uint64_t *q, uint8_t byt) -{ - uint64_t bit0 = (uint64_t)(byt >> 7); - uint64_t bit; - point_swap_conditional(nq, nqpq, bit0); - addanddouble_fmonty(nq2, nqpq2, nq, nqpq, q); - bit = (uint64_t)(byt >> 7); - point_swap_conditional(nq2, nqpq2, bit); -} - -static __always_inline void ladder_smallloop_cmult_small_loop_double_step(uint64_t *nq, uint64_t *nqpq, uint64_t *nq2, uint64_t *nqpq2, uint64_t *q, uint8_t byt) -{ - uint8_t byt1; - ladder_smallloop_cmult_small_loop_step(nq, nqpq, nq2, nqpq2, q, byt); - byt1 = byt << 1; - ladder_smallloop_cmult_small_loop_step(nq2, nqpq2, nq, nqpq, q, byt1); -} - -static __always_inline void ladder_smallloop_cmult_small_loop(uint64_t *nq, uint64_t *nqpq, uint64_t *nq2, uint64_t *nqpq2, uint64_t *q, uint8_t byt, uint32_t i) -{ - while (i--) { - ladder_smallloop_cmult_small_loop_double_step(nq, nqpq, nq2, nqpq2, q, byt); - byt <<= 2; - } -} - -static __always_inline void ladder_bigloop_cmult_big_loop(uint8_t *n1, uint64_t *nq, uint64_t *nqpq, uint64_t *nq2, uint64_t *nqpq2, uint64_t *q, uint32_t i) -{ - while (i--) { - uint8_t byte = n1[i]; - ladder_smallloop_cmult_small_loop(nq, nqpq, nq2, nqpq2, q, byte, 4); - } -} - -static __always_inline void ladder_cmult(uint64_t *result, uint8_t *n1, uint64_t *q) -{ - uint64_t point_buf[40] = { 0 }; - uint64_t *nq = point_buf; - uint64_t *nqpq = point_buf + 10; - uint64_t *nq2 = point_buf + 20; - uint64_t *nqpq2 = point_buf + 30; - point_copy(nqpq, q); - nq[0] = 1; - ladder_bigloop_cmult_big_loop(n1, nq, nqpq, nq2, nqpq2, q, 32); - point_copy(result, nq); -} - -static __always_inline void format_fexpand(uint64_t *output, const uint8_t *input) -{ - const uint8_t *x00 = input + 6; - const uint8_t *x01 = input + 12; - const uint8_t *x02 = input + 19; - const uint8_t *x0 = input + 24; - uint64_t i0, i1, i2, i3, i4, output0, output1, output2, output3, output4; - i0 = le64toh(*(uint64_t *)input); - i1 = le64toh(*(uint64_t *)x00); - i2 = le64toh(*(uint64_t *)x01); - i3 = le64toh(*(uint64_t *)x02); - i4 = le64toh(*(uint64_t *)x0); - output0 = i0 & 0x7ffffffffffffLLU; - output1 = i1 >> 3 & 0x7ffffffffffffLLU; - output2 = i2 >> 6 & 0x7ffffffffffffLLU; - output3 = i3 >> 1 & 0x7ffffffffffffLLU; - output4 = i4 >> 12 & 0x7ffffffffffffLLU; - output[0] = output0; - output[1] = output1; - output[2] = output2; - output[3] = output3; - output[4] = output4; -} - -static __always_inline void format_fcontract_first_carry_pass(uint64_t *input) -{ - uint64_t t0 = input[0]; - uint64_t t1 = input[1]; - uint64_t t2 = input[2]; - uint64_t t3 = input[3]; - uint64_t t4 = input[4]; - uint64_t t1_ = t1 + (t0 >> 51); - uint64_t t0_ = t0 & 0x7ffffffffffffLLU; - uint64_t t2_ = t2 + (t1_ >> 51); - uint64_t t1__ = t1_ & 0x7ffffffffffffLLU; - uint64_t t3_ = t3 + (t2_ >> 51); - uint64_t t2__ = t2_ & 0x7ffffffffffffLLU; - uint64_t t4_ = t4 + (t3_ >> 51); - uint64_t t3__ = t3_ & 0x7ffffffffffffLLU; - input[0] = t0_; - input[1] = t1__; - input[2] = t2__; - input[3] = t3__; - input[4] = t4_; -} - -static __always_inline void format_fcontract_first_carry_full(uint64_t *input) -{ - format_fcontract_first_carry_pass(input); - modulo_carry_top(input); -} - -static __always_inline void format_fcontract_second_carry_pass(uint64_t *input) -{ - uint64_t t0 = input[0]; - uint64_t t1 = input[1]; - uint64_t t2 = input[2]; - uint64_t t3 = input[3]; - uint64_t t4 = input[4]; - uint64_t t1_ = t1 + (t0 >> 51); - uint64_t t0_ = t0 & 0x7ffffffffffffLLU; - uint64_t t2_ = t2 + (t1_ >> 51); - uint64_t t1__ = t1_ & 0x7ffffffffffffLLU; - uint64_t t3_ = t3 + (t2_ >> 51); - uint64_t t2__ = t2_ & 0x7ffffffffffffLLU; - uint64_t t4_ = t4 + (t3_ >> 51); - uint64_t t3__ = t3_ & 0x7ffffffffffffLLU; - input[0] = t0_; - input[1] = t1__; - input[2] = t2__; - input[3] = t3__; - input[4] = t4_; -} - -static __always_inline void format_fcontract_second_carry_full(uint64_t *input) -{ - uint64_t i0; - uint64_t i1; - uint64_t i0_; - uint64_t i1_; - format_fcontract_second_carry_pass(input); - modulo_carry_top(input); - i0 = input[0]; - i1 = input[1]; - i0_ = i0 & 0x7ffffffffffffLLU; - i1_ = i1 + (i0 >> 51); - input[0] = i0_; - input[1] = i1_; -} - -static __always_inline void format_fcontract_trim(uint64_t *input) -{ - uint64_t a0 = input[0]; - uint64_t a1 = input[1]; - uint64_t a2 = input[2]; - uint64_t a3 = input[3]; - uint64_t a4 = input[4]; - uint64_t mask0 = uint64_t_gte_mask(a0, 0x7ffffffffffedLLU); - uint64_t mask1 = uint64_t_eq_mask(a1, 0x7ffffffffffffLLU); - uint64_t mask2 = uint64_t_eq_mask(a2, 0x7ffffffffffffLLU); - uint64_t mask3 = uint64_t_eq_mask(a3, 0x7ffffffffffffLLU); - uint64_t mask4 = uint64_t_eq_mask(a4, 0x7ffffffffffffLLU); - uint64_t mask = (((mask0 & mask1) & mask2) & mask3) & mask4; - uint64_t a0_ = a0 - (0x7ffffffffffedLLU & mask); - uint64_t a1_ = a1 - (0x7ffffffffffffLLU & mask); - uint64_t a2_ = a2 - (0x7ffffffffffffLLU & mask); - uint64_t a3_ = a3 - (0x7ffffffffffffLLU & mask); - uint64_t a4_ = a4 - (0x7ffffffffffffLLU & mask); - input[0] = a0_; - input[1] = a1_; - input[2] = a2_; - input[3] = a3_; - input[4] = a4_; -} - -static __always_inline void format_fcontract_store(uint8_t *output, uint64_t *input) -{ - uint64_t t0 = input[0]; - uint64_t t1 = input[1]; - uint64_t t2 = input[2]; - uint64_t t3 = input[3]; - uint64_t t4 = input[4]; - uint64_t o0 = t1 << 51 | t0; - uint64_t o1 = t2 << 38 | t1 >> 13; - uint64_t o2 = t3 << 25 | t2 >> 26; - uint64_t o3 = t4 << 12 | t3 >> 39; - uint8_t *b0 = output; - uint8_t *b1 = output + 8; - uint8_t *b2 = output + 16; - uint8_t *b3 = output + 24; - *(uint64_t *)b0 = htole64(o0); - *(uint64_t *)b1 = htole64(o1); - *(uint64_t *)b2 = htole64(o2); - *(uint64_t *)b3 = htole64(o3); -} - -static __always_inline void format_fcontract(uint8_t *output, uint64_t *input) -{ - format_fcontract_first_carry_full(input); - format_fcontract_second_carry_full(input); - format_fcontract_trim(input); - format_fcontract_store(output, input); -} - -static __always_inline void format_scalar_of_point(uint8_t *scalar, uint64_t *point) -{ - uint64_t *x = point; - uint64_t *z = point + 5; - uint64_t buf[10] __aligned(32) = { 0 }; - uint64_t *zmone = buf; - uint64_t *sc = buf + 5; - crecip(zmone, z); - fmul(sc, x, zmone); - format_fcontract(scalar, sc); -} - -void curve25519(uint8_t mypublic[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE], const uint8_t basepoint[static CURVE25519_POINT_SIZE]) -{ - uint64_t buf0[10] __aligned(32) = { 0 }; - uint64_t *x0 = buf0; - uint64_t *z = buf0 + 5; - uint64_t *q; - format_fexpand(x0, basepoint); - z[0] = 1; - q = buf0; - { - uint8_t e[32] __aligned(32) = { 0 }; - uint8_t *scalar; - memcpy(e, secret, 32); - curve25519_normalize_secret(e); - scalar = e; - { - uint64_t buf[15] = { 0 }; - uint64_t *nq = buf; - uint64_t *x = nq; - x[0] = 1; - ladder_cmult(nq, scalar, q); - format_scalar_of_point(mypublic, nq); - } - } -} +#include "../crypto/curve25519-hacl64.h" #else -/* fe means field element. Here the field is \Z/(2^255-19). An element t, - * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 - * t[3]+2^102 t[4]+...+2^230 t[9]. - * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc. - * Multiplication and carrying produce fe from fe_loose. - */ -typedef struct fe { uint32_t v[10]; } fe; - -/* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc. - * Addition and subtraction produce fe_loose from (fe, fe). - */ -typedef struct fe_loose { uint32_t v[10]; } fe_loose; - -static __always_inline void fe_frombytes_impl(uint32_t h[10], const uint8_t *s) -{ - /* Ignores top bit of s. */ - uint32_t a0 = le32toh(*(uint32_t *)(s)); - uint32_t a1 = le32toh(*(uint32_t *)(s+4)); - uint32_t a2 = le32toh(*(uint32_t *)(s+8)); - uint32_t a3 = le32toh(*(uint32_t *)(s+12)); - uint32_t a4 = le32toh(*(uint32_t *)(s+16)); - uint32_t a5 = le32toh(*(uint32_t *)(s+20)); - uint32_t a6 = le32toh(*(uint32_t *)(s+24)); - uint32_t a7 = le32toh(*(uint32_t *)(s+28)); - h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */ - h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */ - h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */ - h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */ - h[4] = (a3>> 6); /* (32- 6) = 26 */ - h[5] = a4&((1<<25)-1); /* 25 */ - h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */ - h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */ - h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */ - h[9] = (a7>> 6)&((1<<25)-1); /* 25 */ -} - -static __always_inline void fe_frombytes(fe *h, const uint8_t *s) -{ - fe_frombytes_impl(h->v, s); -} - -static __always_inline uint8_t /*bool*/ addcarryx_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low) -{ - /* This function extracts 25 bits of result and 1 bit of carry (26 total), so - * a 32-bit intermediate is sufficient. - */ - uint32_t x = a + b + c; - *low = x & ((1 << 25) - 1); - return (x >> 25) & 1; -} - -static __always_inline uint8_t /*bool*/ addcarryx_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low) -{ - /* This function extracts 26 bits of result and 1 bit of carry (27 total), so - * a 32-bit intermediate is sufficient. - */ - uint32_t x = a + b + c; - *low = x & ((1 << 26) - 1); - return (x >> 26) & 1; -} - -static __always_inline uint8_t /*bool*/ subborrow_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low) -{ - /* This function extracts 25 bits of result and 1 bit of borrow (26 total), so - * a 32-bit intermediate is sufficient. - */ - uint32_t x = a - b - c; - *low = x & ((1 << 25) - 1); - return x >> 31; -} - -static __always_inline uint8_t /*bool*/ subborrow_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low) -{ - /* This function extracts 26 bits of result and 1 bit of borrow (27 total), so - * a 32-bit intermediate is sufficient. - */ - uint32_t x = a - b - c; - *low = x & ((1 << 26) - 1); - return x >> 31; -} - -static __always_inline uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz) -{ - t = -!!t; /* all set if nonzero, 0 if 0 */ - return (t&nz) | ((~t)&z); -} - -static __always_inline void fe_freeze(uint32_t out[10], const uint32_t in1[10]) -{ - { const uint32_t x17 = in1[9]; - { const uint32_t x18 = in1[8]; - { const uint32_t x16 = in1[7]; - { const uint32_t x14 = in1[6]; - { const uint32_t x12 = in1[5]; - { const uint32_t x10 = in1[4]; - { const uint32_t x8 = in1[3]; - { const uint32_t x6 = in1[2]; - { const uint32_t x4 = in1[1]; - { const uint32_t x2 = in1[0]; - { uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20); - { uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23); - { uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26); - { uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29); - { uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32); - { uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35); - { uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38); - { uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41); - { uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44); - { uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47); - { uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff); - { uint32_t x50 = (x49 & 0x3ffffed); - { uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52); - { uint32_t x54 = (x49 & 0x1ffffff); - { uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56); - { uint32_t x58 = (x49 & 0x3ffffff); - { uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60); - { uint32_t x62 = (x49 & 0x1ffffff); - { uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64); - { uint32_t x66 = (x49 & 0x3ffffff); - { uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68); - { uint32_t x70 = (x49 & 0x1ffffff); - { uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72); - { uint32_t x74 = (x49 & 0x3ffffff); - { uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76); - { uint32_t x78 = (x49 & 0x1ffffff); - { uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80); - { uint32_t x82 = (x49 & 0x3ffffff); - { uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84); - { uint32_t x86 = (x49 & 0x1ffffff); - { uint32_t x88; addcarryx_u25(x85, x47, x86, &x88); - out[0] = x52; - out[1] = x56; - out[2] = x60; - out[3] = x64; - out[4] = x68; - out[5] = x72; - out[6] = x76; - out[7] = x80; - out[8] = x84; - out[9] = x88; - }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} -} - -static __always_inline void fe_tobytes(uint8_t s[32], const fe *f) -{ - uint32_t h[10]; - fe_freeze(h, f->v); - s[0] = h[0] >> 0; - s[1] = h[0] >> 8; - s[2] = h[0] >> 16; - s[3] = (h[0] >> 24) | (h[1] << 2); - s[4] = h[1] >> 6; - s[5] = h[1] >> 14; - s[6] = (h[1] >> 22) | (h[2] << 3); - s[7] = h[2] >> 5; - s[8] = h[2] >> 13; - s[9] = (h[2] >> 21) | (h[3] << 5); - s[10] = h[3] >> 3; - s[11] = h[3] >> 11; - s[12] = (h[3] >> 19) | (h[4] << 6); - s[13] = h[4] >> 2; - s[14] = h[4] >> 10; - s[15] = h[4] >> 18; - s[16] = h[5] >> 0; - s[17] = h[5] >> 8; - s[18] = h[5] >> 16; - s[19] = (h[5] >> 24) | (h[6] << 1); - s[20] = h[6] >> 7; - s[21] = h[6] >> 15; - s[22] = (h[6] >> 23) | (h[7] << 3); - s[23] = h[7] >> 5; - s[24] = h[7] >> 13; - s[25] = (h[7] >> 21) | (h[8] << 4); - s[26] = h[8] >> 4; - s[27] = h[8] >> 12; - s[28] = (h[8] >> 20) | (h[9] << 6); - s[29] = h[9] >> 2; - s[30] = h[9] >> 10; - s[31] = h[9] >> 18; -} - -/* h = f */ -static __always_inline void fe_copy(fe *h, const fe *f) -{ - memmove(h, f, sizeof(uint32_t) * 10); -} - -static __always_inline void fe_copy_lt(fe_loose *h, const fe *f) -{ - memmove(h, f, sizeof(uint32_t) * 10); -} - -/* h = 0 */ -static __always_inline void fe_0(fe *h) -{ - memset(h, 0, sizeof(uint32_t) * 10); -} - -/* h = 1 */ -static __always_inline void fe_1(fe *h) -{ - memset(h, 0, sizeof(uint32_t) * 10); - h->v[0] = 1; -} - -static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) -{ - { const uint32_t x20 = in1[9]; - { const uint32_t x21 = in1[8]; - { const uint32_t x19 = in1[7]; - { const uint32_t x17 = in1[6]; - { const uint32_t x15 = in1[5]; - { const uint32_t x13 = in1[4]; - { const uint32_t x11 = in1[3]; - { const uint32_t x9 = in1[2]; - { const uint32_t x7 = in1[1]; - { const uint32_t x5 = in1[0]; - { const uint32_t x38 = in2[9]; - { const uint32_t x39 = in2[8]; - { const uint32_t x37 = in2[7]; - { const uint32_t x35 = in2[6]; - { const uint32_t x33 = in2[5]; - { const uint32_t x31 = in2[4]; - { const uint32_t x29 = in2[3]; - { const uint32_t x27 = in2[2]; - { const uint32_t x25 = in2[1]; - { const uint32_t x23 = in2[0]; - out[0] = (x5 + x23); - out[1] = (x7 + x25); - out[2] = (x9 + x27); - out[3] = (x11 + x29); - out[4] = (x13 + x31); - out[5] = (x15 + x33); - out[6] = (x17 + x35); - out[7] = (x19 + x37); - out[8] = (x21 + x39); - out[9] = (x20 + x38); - }}}}}}}}}}}}}}}}}}}} -} - -/* h = f + g - * Can overlap h with f or g. - */ -static __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g) -{ - fe_add_impl(h->v, f->v, g->v); -} - -static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) -{ - { const uint32_t x20 = in1[9]; - { const uint32_t x21 = in1[8]; - { const uint32_t x19 = in1[7]; - { const uint32_t x17 = in1[6]; - { const uint32_t x15 = in1[5]; - { const uint32_t x13 = in1[4]; - { const uint32_t x11 = in1[3]; - { const uint32_t x9 = in1[2]; - { const uint32_t x7 = in1[1]; - { const uint32_t x5 = in1[0]; - { const uint32_t x38 = in2[9]; - { const uint32_t x39 = in2[8]; - { const uint32_t x37 = in2[7]; - { const uint32_t x35 = in2[6]; - { const uint32_t x33 = in2[5]; - { const uint32_t x31 = in2[4]; - { const uint32_t x29 = in2[3]; - { const uint32_t x27 = in2[2]; - { const uint32_t x25 = in2[1]; - { const uint32_t x23 = in2[0]; - out[0] = ((0x7ffffda + x5) - x23); - out[1] = ((0x3fffffe + x7) - x25); - out[2] = ((0x7fffffe + x9) - x27); - out[3] = ((0x3fffffe + x11) - x29); - out[4] = ((0x7fffffe + x13) - x31); - out[5] = ((0x3fffffe + x15) - x33); - out[6] = ((0x7fffffe + x17) - x35); - out[7] = ((0x3fffffe + x19) - x37); - out[8] = ((0x7fffffe + x21) - x39); - out[9] = ((0x3fffffe + x20) - x38); - }}}}}}}}}}}}}}}}}}}} -} - -/* h = f - g - * Can overlap h with f or g. - */ -static __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g) -{ - fe_sub_impl(h->v, f->v, g->v); -} - -static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) -{ - { const uint32_t x20 = in1[9]; - { const uint32_t x21 = in1[8]; - { const uint32_t x19 = in1[7]; - { const uint32_t x17 = in1[6]; - { const uint32_t x15 = in1[5]; - { const uint32_t x13 = in1[4]; - { const uint32_t x11 = in1[3]; - { const uint32_t x9 = in1[2]; - { const uint32_t x7 = in1[1]; - { const uint32_t x5 = in1[0]; - { const uint32_t x38 = in2[9]; - { const uint32_t x39 = in2[8]; - { const uint32_t x37 = in2[7]; - { const uint32_t x35 = in2[6]; - { const uint32_t x33 = in2[5]; - { const uint32_t x31 = in2[4]; - { const uint32_t x29 = in2[3]; - { const uint32_t x27 = in2[2]; - { const uint32_t x25 = in2[1]; - { const uint32_t x23 = in2[0]; - { uint64_t x40 = ((uint64_t)x23 * x5); - { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); - { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); - { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); - { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); - { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); - { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); - { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); - { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); - { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); - { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); - { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); - { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); - { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); - { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17)); - { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); - { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); - { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); - { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); - { uint64_t x59 = (x48 + (x58 << 0x4)); - { uint64_t x60 = (x59 + (x58 << 0x1)); - { uint64_t x61 = (x60 + x58); - { uint64_t x62 = (x47 + (x57 << 0x4)); - { uint64_t x63 = (x62 + (x57 << 0x1)); - { uint64_t x64 = (x63 + x57); - { uint64_t x65 = (x46 + (x56 << 0x4)); - { uint64_t x66 = (x65 + (x56 << 0x1)); - { uint64_t x67 = (x66 + x56); - { uint64_t x68 = (x45 + (x55 << 0x4)); - { uint64_t x69 = (x68 + (x55 << 0x1)); - { uint64_t x70 = (x69 + x55); - { uint64_t x71 = (x44 + (x54 << 0x4)); - { uint64_t x72 = (x71 + (x54 << 0x1)); - { uint64_t x73 = (x72 + x54); - { uint64_t x74 = (x43 + (x53 << 0x4)); - { uint64_t x75 = (x74 + (x53 << 0x1)); - { uint64_t x76 = (x75 + x53); - { uint64_t x77 = (x42 + (x52 << 0x4)); - { uint64_t x78 = (x77 + (x52 << 0x1)); - { uint64_t x79 = (x78 + x52); - { uint64_t x80 = (x41 + (x51 << 0x4)); - { uint64_t x81 = (x80 + (x51 << 0x1)); - { uint64_t x82 = (x81 + x51); - { uint64_t x83 = (x40 + (x50 << 0x4)); - { uint64_t x84 = (x83 + (x50 << 0x1)); - { uint64_t x85 = (x84 + x50); - { uint64_t x86 = (x85 >> 0x1a); - { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); - { uint64_t x88 = (x86 + x82); - { uint64_t x89 = (x88 >> 0x19); - { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); - { uint64_t x91 = (x89 + x79); - { uint64_t x92 = (x91 >> 0x1a); - { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); - { uint64_t x94 = (x92 + x76); - { uint64_t x95 = (x94 >> 0x19); - { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); - { uint64_t x97 = (x95 + x73); - { uint64_t x98 = (x97 >> 0x1a); - { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); - { uint64_t x100 = (x98 + x70); - { uint64_t x101 = (x100 >> 0x19); - { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); - { uint64_t x103 = (x101 + x67); - { uint64_t x104 = (x103 >> 0x1a); - { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); - { uint64_t x106 = (x104 + x64); - { uint64_t x107 = (x106 >> 0x19); - { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); - { uint64_t x109 = (x107 + x61); - { uint64_t x110 = (x109 >> 0x1a); - { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); - { uint64_t x112 = (x110 + x49); - { uint64_t x113 = (x112 >> 0x19); - { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); - { uint64_t x115 = (x87 + (0x13 * x113)); - { uint32_t x116 = (uint32_t) (x115 >> 0x1a); - { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); - { uint32_t x118 = (x116 + x90); - { uint32_t x119 = (x118 >> 0x19); - { uint32_t x120 = (x118 & 0x1ffffff); - out[0] = x117; - out[1] = x120; - out[2] = (x119 + x93); - out[3] = x96; - out[4] = x99; - out[5] = x102; - out[6] = x105; - out[7] = x108; - out[8] = x111; - out[9] = x114; - }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} -} - -static __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g) -{ - fe_mul_impl(h->v, f->v, g->v); -} - -static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) -{ - fe_mul_impl(h->v, f->v, g->v); -} - -static __always_inline void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) -{ - fe_mul_impl(h->v, f->v, g->v); -} - -static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) -{ - { const uint32_t x17 = in1[9]; - { const uint32_t x18 = in1[8]; - { const uint32_t x16 = in1[7]; - { const uint32_t x14 = in1[6]; - { const uint32_t x12 = in1[5]; - { const uint32_t x10 = in1[4]; - { const uint32_t x8 = in1[3]; - { const uint32_t x6 = in1[2]; - { const uint32_t x4 = in1[1]; - { const uint32_t x2 = in1[0]; - { uint64_t x19 = ((uint64_t)x2 * x2); - { uint64_t x20 = ((uint64_t)(0x2 * x2) * x4); - { uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6))); - { uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8))); - { uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10)); - { uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12))); - { uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12))); - { uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16))); - { uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12)))))); - { uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17))); - { uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17))))); - { uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17))); - { uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17)))))); - { uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17))); - { uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17))); - { uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17))); - { uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17)); - { uint64_t x36 = ((uint64_t)(0x2 * x18) * x17); - { uint64_t x37 = ((uint64_t)(0x2 * x17) * x17); - { uint64_t x38 = (x27 + (x37 << 0x4)); - { uint64_t x39 = (x38 + (x37 << 0x1)); - { uint64_t x40 = (x39 + x37); - { uint64_t x41 = (x26 + (x36 << 0x4)); - { uint64_t x42 = (x41 + (x36 << 0x1)); - { uint64_t x43 = (x42 + x36); - { uint64_t x44 = (x25 + (x35 << 0x4)); - { uint64_t x45 = (x44 + (x35 << 0x1)); - { uint64_t x46 = (x45 + x35); - { uint64_t x47 = (x24 + (x34 << 0x4)); - { uint64_t x48 = (x47 + (x34 << 0x1)); - { uint64_t x49 = (x48 + x34); - { uint64_t x50 = (x23 + (x33 << 0x4)); - { uint64_t x51 = (x50 + (x33 << 0x1)); - { uint64_t x52 = (x51 + x33); - { uint64_t x53 = (x22 + (x32 << 0x4)); - { uint64_t x54 = (x53 + (x32 << 0x1)); - { uint64_t x55 = (x54 + x32); - { uint64_t x56 = (x21 + (x31 << 0x4)); - { uint64_t x57 = (x56 + (x31 << 0x1)); - { uint64_t x58 = (x57 + x31); - { uint64_t x59 = (x20 + (x30 << 0x4)); - { uint64_t x60 = (x59 + (x30 << 0x1)); - { uint64_t x61 = (x60 + x30); - { uint64_t x62 = (x19 + (x29 << 0x4)); - { uint64_t x63 = (x62 + (x29 << 0x1)); - { uint64_t x64 = (x63 + x29); - { uint64_t x65 = (x64 >> 0x1a); - { uint32_t x66 = ((uint32_t)x64 & 0x3ffffff); - { uint64_t x67 = (x65 + x61); - { uint64_t x68 = (x67 >> 0x19); - { uint32_t x69 = ((uint32_t)x67 & 0x1ffffff); - { uint64_t x70 = (x68 + x58); - { uint64_t x71 = (x70 >> 0x1a); - { uint32_t x72 = ((uint32_t)x70 & 0x3ffffff); - { uint64_t x73 = (x71 + x55); - { uint64_t x74 = (x73 >> 0x19); - { uint32_t x75 = ((uint32_t)x73 & 0x1ffffff); - { uint64_t x76 = (x74 + x52); - { uint64_t x77 = (x76 >> 0x1a); - { uint32_t x78 = ((uint32_t)x76 & 0x3ffffff); - { uint64_t x79 = (x77 + x49); - { uint64_t x80 = (x79 >> 0x19); - { uint32_t x81 = ((uint32_t)x79 & 0x1ffffff); - { uint64_t x82 = (x80 + x46); - { uint64_t x83 = (x82 >> 0x1a); - { uint32_t x84 = ((uint32_t)x82 & 0x3ffffff); - { uint64_t x85 = (x83 + x43); - { uint64_t x86 = (x85 >> 0x19); - { uint32_t x87 = ((uint32_t)x85 & 0x1ffffff); - { uint64_t x88 = (x86 + x40); - { uint64_t x89 = (x88 >> 0x1a); - { uint32_t x90 = ((uint32_t)x88 & 0x3ffffff); - { uint64_t x91 = (x89 + x28); - { uint64_t x92 = (x91 >> 0x19); - { uint32_t x93 = ((uint32_t)x91 & 0x1ffffff); - { uint64_t x94 = (x66 + (0x13 * x92)); - { uint32_t x95 = (uint32_t) (x94 >> 0x1a); - { uint32_t x96 = ((uint32_t)x94 & 0x3ffffff); - { uint32_t x97 = (x95 + x69); - { uint32_t x98 = (x97 >> 0x19); - { uint32_t x99 = (x97 & 0x1ffffff); - out[0] = x96; - out[1] = x99; - out[2] = (x98 + x72); - out[3] = x75; - out[4] = x78; - out[5] = x81; - out[6] = x84; - out[7] = x87; - out[8] = x90; - out[9] = x93; - }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} -} - -static __always_inline void fe_sq_tl(fe *h, const fe_loose *f) -{ - fe_sqr_impl(h->v, f->v); -} - -static __always_inline void fe_sq_tt(fe *h, const fe *f) -{ - fe_sqr_impl(h->v, f->v); -} - -static __always_inline void fe_loose_invert(fe *out, const fe_loose *z) -{ - fe t0; - fe t1; - fe t2; - fe t3; - int i; - - fe_sq_tl(&t0, z); - fe_sq_tt(&t1, &t0); - for (i = 1; i < 2; ++i) - fe_sq_tt(&t1, &t1); - fe_mul_tlt(&t1, z, &t1); - fe_mul_ttt(&t0, &t0, &t1); - fe_sq_tt(&t2, &t0); - fe_mul_ttt(&t1, &t1, &t2); - fe_sq_tt(&t2, &t1); - for (i = 1; i < 5; ++i) - fe_sq_tt(&t2, &t2); - fe_mul_ttt(&t1, &t2, &t1); - fe_sq_tt(&t2, &t1); - for (i = 1; i < 10; ++i) - fe_sq_tt(&t2, &t2); - fe_mul_ttt(&t2, &t2, &t1); - fe_sq_tt(&t3, &t2); - for (i = 1; i < 20; ++i) - fe_sq_tt(&t3, &t3); - fe_mul_ttt(&t2, &t3, &t2); - fe_sq_tt(&t2, &t2); - for (i = 1; i < 10; ++i) - fe_sq_tt(&t2, &t2); - fe_mul_ttt(&t1, &t2, &t1); - fe_sq_tt(&t2, &t1); - for (i = 1; i < 50; ++i) - fe_sq_tt(&t2, &t2); - fe_mul_ttt(&t2, &t2, &t1); - fe_sq_tt(&t3, &t2); - for (i = 1; i < 100; ++i) - fe_sq_tt(&t3, &t3); - fe_mul_ttt(&t2, &t3, &t2); - fe_sq_tt(&t2, &t2); - for (i = 1; i < 50; ++i) - fe_sq_tt(&t2, &t2); - fe_mul_ttt(&t1, &t2, &t1); - fe_sq_tt(&t1, &t1); - for (i = 1; i < 5; ++i) - fe_sq_tt(&t1, &t1); - fe_mul_ttt(out, &t1, &t0); -} - -static __always_inline void fe_invert(fe *out, const fe *z) -{ - fe_loose l; - fe_copy_lt(&l, z); - fe_loose_invert(out, &l); -} - -/* Replace (f,g) with (g,f) if b == 1; - * replace (f,g) with (f,g) if b == 0. - * - * Preconditions: b in {0,1} - */ -static __always_inline void fe_cswap(fe *f, fe *g, unsigned int b) -{ - unsigned i; - b = 0-b; - for (i = 0; i < 10; i++) { - uint32_t x = f->v[i] ^ g->v[i]; - x &= b; - f->v[i] ^= x; - g->v[i] ^= x; - } -} - -/* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/ -static __always_inline void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) -{ - { const uint32_t x20 = in1[9]; - { const uint32_t x21 = in1[8]; - { const uint32_t x19 = in1[7]; - { const uint32_t x17 = in1[6]; - { const uint32_t x15 = in1[5]; - { const uint32_t x13 = in1[4]; - { const uint32_t x11 = in1[3]; - { const uint32_t x9 = in1[2]; - { const uint32_t x7 = in1[1]; - { const uint32_t x5 = in1[0]; - { const uint32_t x38 = 0; - { const uint32_t x39 = 0; - { const uint32_t x37 = 0; - { const uint32_t x35 = 0; - { const uint32_t x33 = 0; - { const uint32_t x31 = 0; - { const uint32_t x29 = 0; - { const uint32_t x27 = 0; - { const uint32_t x25 = 0; - { const uint32_t x23 = 121666; - { uint64_t x40 = ((uint64_t)x23 * x5); - { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); - { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); - { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); - { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); - { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); - { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); - { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); - { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); - { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); - { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); - { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); - { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); - { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); - { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17)); - { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); - { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); - { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); - { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); - { uint64_t x59 = (x48 + (x58 << 0x4)); - { uint64_t x60 = (x59 + (x58 << 0x1)); - { uint64_t x61 = (x60 + x58); - { uint64_t x62 = (x47 + (x57 << 0x4)); - { uint64_t x63 = (x62 + (x57 << 0x1)); - { uint64_t x64 = (x63 + x57); - { uint64_t x65 = (x46 + (x56 << 0x4)); - { uint64_t x66 = (x65 + (x56 << 0x1)); - { uint64_t x67 = (x66 + x56); - { uint64_t x68 = (x45 + (x55 << 0x4)); - { uint64_t x69 = (x68 + (x55 << 0x1)); - { uint64_t x70 = (x69 + x55); - { uint64_t x71 = (x44 + (x54 << 0x4)); - { uint64_t x72 = (x71 + (x54 << 0x1)); - { uint64_t x73 = (x72 + x54); - { uint64_t x74 = (x43 + (x53 << 0x4)); - { uint64_t x75 = (x74 + (x53 << 0x1)); - { uint64_t x76 = (x75 + x53); - { uint64_t x77 = (x42 + (x52 << 0x4)); - { uint64_t x78 = (x77 + (x52 << 0x1)); - { uint64_t x79 = (x78 + x52); - { uint64_t x80 = (x41 + (x51 << 0x4)); - { uint64_t x81 = (x80 + (x51 << 0x1)); - { uint64_t x82 = (x81 + x51); - { uint64_t x83 = (x40 + (x50 << 0x4)); - { uint64_t x84 = (x83 + (x50 << 0x1)); - { uint64_t x85 = (x84 + x50); - { uint64_t x86 = (x85 >> 0x1a); - { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); - { uint64_t x88 = (x86 + x82); - { uint64_t x89 = (x88 >> 0x19); - { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); - { uint64_t x91 = (x89 + x79); - { uint64_t x92 = (x91 >> 0x1a); - { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); - { uint64_t x94 = (x92 + x76); - { uint64_t x95 = (x94 >> 0x19); - { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); - { uint64_t x97 = (x95 + x73); - { uint64_t x98 = (x97 >> 0x1a); - { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); - { uint64_t x100 = (x98 + x70); - { uint64_t x101 = (x100 >> 0x19); - { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); - { uint64_t x103 = (x101 + x67); - { uint64_t x104 = (x103 >> 0x1a); - { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); - { uint64_t x106 = (x104 + x64); - { uint64_t x107 = (x106 >> 0x19); - { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); - { uint64_t x109 = (x107 + x61); - { uint64_t x110 = (x109 >> 0x1a); - { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); - { uint64_t x112 = (x110 + x49); - { uint64_t x113 = (x112 >> 0x19); - { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); - { uint64_t x115 = (x87 + (0x13 * x113)); - { uint32_t x116 = (uint32_t) (x115 >> 0x1a); - { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); - { uint32_t x118 = (x116 + x90); - { uint32_t x119 = (x118 >> 0x19); - { uint32_t x120 = (x118 & 0x1ffffff); - out[0] = x117; - out[1] = x120; - out[2] = (x119 + x93); - out[3] = x96; - out[4] = x99; - out[5] = x102; - out[6] = x105; - out[7] = x108; - out[8] = x111; - out[9] = x114; - }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} -} - -static __always_inline void fe_mul121666(fe *h, const fe_loose *f) -{ - fe_mul_121666_impl(h->v, f->v); -} - -void curve25519(uint8_t out[static CURVE25519_POINT_SIZE], const uint8_t scalar[static CURVE25519_POINT_SIZE], const uint8_t point[static CURVE25519_POINT_SIZE]) -{ - fe x1, x2, z2, x3, z3, tmp0, tmp1; - fe_loose x2l, z2l, x3l, tmp0l, tmp1l; - unsigned swap = 0; - int pos; - uint8_t e[32]; - - memcpy(e, scalar, 32); - curve25519_normalize_secret(e); - - /* 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 - */ - fe_frombytes(&x1, point); - fe_1(&x2); - fe_0(&z2); - fe_copy(&x3, &x1); - fe_1(&z3); - - 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; - fe_cswap(&x2, &x3, swap); - fe_cswap(&z2, &z3, swap); - swap = b; - /* Coq transcription of ladderstep formula (called from transcribed loop): - * - * - * x1 != 0 - * x1 = 0 - */ - fe_sub(&tmp0l, &x3, &z3); - fe_sub(&tmp1l, &x2, &z2); - fe_add(&x2l, &x2, &z2); - fe_add(&z2l, &x3, &z3); - fe_mul_tll(&z3, &tmp0l, &x2l); - fe_mul_tll(&z2, &z2l, &tmp1l); - fe_sq_tl(&tmp0, &tmp1l); - fe_sq_tl(&tmp1, &x2l); - fe_add(&x3l, &z3, &z2); - fe_sub(&z2l, &z3, &z2); - fe_mul_ttt(&x2, &tmp1, &tmp0); - fe_sub(&tmp1l, &tmp1, &tmp0); - fe_sq_tl(&z2, &z2l); - fe_mul121666(&z3, &tmp1l); - fe_sq_tl(&x3, &x3l); - fe_add(&tmp0l, &tmp0, &z3); - fe_mul_ttt(&z3, &x1, &z2); - fe_mul_tll(&z2, &tmp1l, &tmp0l); - } - /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) else (x2, z2) */ - fe_cswap(&x2, &x3, swap); - fe_cswap(&z2, &z3, swap); - - fe_invert(&z2, &z2); - fe_mul_ttt(&x2, &x2, &z2); - fe_tobytes(out, &x2); -} +#include "../crypto/curve25519-fiat32.h" #endif void curve25519_generate_public(uint8_t pub[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE]) @@ -1575,3 +61,8 @@ void curve25519_generate_public(uint8_t pub[static CURVE25519_POINT_SIZE], const curve25519(pub, secret, basepoint); } + +void curve25519(uint8_t mypublic[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE], const uint8_t basepoint[static CURVE25519_POINT_SIZE]) +{ + curve25519_generic(mypublic, secret, basepoint); +}