/* SPDX-License-Identifier: GPL-2.0 * * Copyright (C) 2016-2017 INRIA and Microsoft Corporation. * Copyright (C) 2015-2016 The fiat-crypto Authors. * Copyright (C) 2018 Jason A. Donenfeld . All Rights Reserved. * * This is a machine-generated formally verified implementation of curve25519 DH from: * https://github.com/mitls/hacl-star and https://github.com/mit-plv/fiat-crypto */ #include "curve25519.h" #include #include #include #ifndef __always_inline #define __always_inline __inline __attribute__((__always_inline__)) #endif #ifndef __aligned #define __aligned(x) __attribute__((aligned(x))) #endif #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); } } } #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); } #endif void curve25519_generate_public(uint8_t pub[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE]) { static const uint8_t basepoint[CURVE25519_POINT_SIZE] = { 9 }; curve25519(pub, secret, basepoint); }