/* SPDX-License-Identifier: GPL-2.0 * * Copyright (C) 2016-2017 INRIA and Microsoft Corporation. * 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 */ typedef __uint128_t u128; static __always_inline u64 u64_eq_mask(u64 x, u64 y) { x = ~(x ^ y); x &= x << 32; x &= x << 16; x &= x << 8; x &= x << 4; x &= x << 2; x &= x << 1; return ((s64)x) >> 63; } static __always_inline u64 u64_gte_mask(u64 x, u64 y) { u64 low63 = ~((u64)((s64)((s64)(x & 0x7fffffffffffffffLLU) - (s64)(y & 0x7fffffffffffffffLLU)) >> 63)); u64 high_bit = ~((u64)((s64)((s64)(x & 0x8000000000000000LLU) - (s64)(y & 0x8000000000000000LLU)) >> 63)); return low63 & high_bit; } static __always_inline void modulo_carry_top(u64 *b) { u64 b4 = b[4]; u64 b0 = b[0]; u64 b4_ = b4 & 0x7ffffffffffffLLU; u64 b0_ = b0 + 19 * (b4 >> 51); b[4] = b4_; b[0] = b0_; } static __always_inline void fproduct_copy_from_wide_(u64 *output, u128 *input) { { u128 xi = input[0]; output[0] = ((u64)(xi)); } { u128 xi = input[1]; output[1] = ((u64)(xi)); } { u128 xi = input[2]; output[2] = ((u64)(xi)); } { u128 xi = input[3]; output[3] = ((u64)(xi)); } { u128 xi = input[4]; output[4] = ((u64)(xi)); } } static __always_inline void fproduct_sum_scalar_multiplication_(u128 *output, u64 *input, u64 s) { output[0] += (u128)input[0] * s; output[1] += (u128)input[1] * s; output[2] += (u128)input[2] * s; output[3] += (u128)input[3] * s; output[4] += (u128)input[4] * s; } static __always_inline void fproduct_carry_wide_(u128 *tmp) { { u32 ctr = 0; u128 tctr = tmp[ctr]; u128 tctrp1 = tmp[ctr + 1]; u64 r0 = ((u64)(tctr)) & 0x7ffffffffffffLLU; u128 c = ((tctr) >> (51)); tmp[ctr] = ((u128)(r0)); tmp[ctr + 1] = ((tctrp1) + (c)); } { u32 ctr = 1; u128 tctr = tmp[ctr]; u128 tctrp1 = tmp[ctr + 1]; u64 r0 = ((u64)(tctr)) & 0x7ffffffffffffLLU; u128 c = ((tctr) >> (51)); tmp[ctr] = ((u128)(r0)); tmp[ctr + 1] = ((tctrp1) + (c)); } { u32 ctr = 2; u128 tctr = tmp[ctr]; u128 tctrp1 = tmp[ctr + 1]; u64 r0 = ((u64)(tctr)) & 0x7ffffffffffffLLU; u128 c = ((tctr) >> (51)); tmp[ctr] = ((u128)(r0)); tmp[ctr + 1] = ((tctrp1) + (c)); } { u32 ctr = 3; u128 tctr = tmp[ctr]; u128 tctrp1 = tmp[ctr + 1]; u64 r0 = ((u64)(tctr)) & 0x7ffffffffffffLLU; u128 c = ((tctr) >> (51)); tmp[ctr] = ((u128)(r0)); tmp[ctr + 1] = ((tctrp1) + (c)); } } static __always_inline void fmul_shift_reduce(u64 *output) { u64 tmp = output[4]; u64 b0; { u32 ctr = 5 - 0 - 1; u64 z = output[ctr - 1]; output[ctr] = z; } { u32 ctr = 5 - 1 - 1; u64 z = output[ctr - 1]; output[ctr] = z; } { u32 ctr = 5 - 2 - 1; u64 z = output[ctr - 1]; output[ctr] = z; } { u32 ctr = 5 - 3 - 1; u64 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_(u128 *output, u64 *input, u64 *input21) { u32 i; u64 input2i; { u64 input2i = input21[0]; fproduct_sum_scalar_multiplication_(output, input, input2i); fmul_shift_reduce(input); } { u64 input2i = input21[1]; fproduct_sum_scalar_multiplication_(output, input, input2i); fmul_shift_reduce(input); } { u64 input2i = input21[2]; fproduct_sum_scalar_multiplication_(output, input, input2i); fmul_shift_reduce(input); } { u64 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(u64 *output, u64 *input, u64 *input21) { u64 tmp[5]; memcpy(tmp, input, 5 * sizeof(*input)); { u128 b4; u128 b0; u128 b4_; u128 b0_; u64 i0; u64 i1; u64 i0_; u64 i1_; u128 t[5] = { 0 }; fmul_mul_shift_reduce_(t, tmp, input21); fproduct_carry_wide_(t); b4 = t[4]; b0 = t[0]; b4_ = ((b4) & (((u128)(0x7ffffffffffffLLU)))); b0_ = ((b0) + (((u128)(19) * (((u64)(((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__(u128 *tmp, u64 *output) { u64 r0 = output[0]; u64 r1 = output[1]; u64 r2 = output[2]; u64 r3 = output[3]; u64 r4 = output[4]; u64 d0 = r0 * 2; u64 d1 = r1 * 2; u64 d2 = r2 * 2 * 19; u64 d419 = r4 * 19; u64 d4 = d419 * 2; u128 s0 = ((((((u128)(r0) * (r0))) + (((u128)(d4) * (r1))))) + (((u128)(d2) * (r3)))); u128 s1 = ((((((u128)(d0) * (r1))) + (((u128)(d4) * (r2))))) + (((u128)(r3 * 19) * (r3)))); u128 s2 = ((((((u128)(d0) * (r2))) + (((u128)(r1) * (r1))))) + (((u128)(d4) * (r3)))); u128 s3 = ((((((u128)(d0) * (r3))) + (((u128)(d1) * (r2))))) + (((u128)(r4) * (d419)))); u128 s4 = ((((((u128)(d0) * (r4))) + (((u128)(d1) * (r3))))) + (((u128)(r2) * (r2)))); tmp[0] = s0; tmp[1] = s1; tmp[2] = s2; tmp[3] = s3; tmp[4] = s4; } static __always_inline void fsquare_fsquare_(u128 *tmp, u64 *output) { u128 b4; u128 b0; u128 b4_; u128 b0_; u64 i0; u64 i1; u64 i0_; u64 i1_; fsquare_fsquare__(tmp, output); fproduct_carry_wide_(tmp); b4 = tmp[4]; b0 = tmp[0]; b4_ = ((b4) & (((u128)(0x7ffffffffffffLLU)))); b0_ = ((b0) + (((u128)(19) * (((u64)(((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_(u64 *output, u128 *tmp, u32 count1) { u32 i; fsquare_fsquare_(tmp, output); for (i = 1; i < count1; ++i) fsquare_fsquare_(tmp, output); } static __always_inline void fsquare_fsquare_times(u64 *output, u64 *input, u32 count1) { u128 t[5]; memcpy(output, input, 5 * sizeof(*input)); fsquare_fsquare_times_(output, t, count1); } static __always_inline void fsquare_fsquare_times_inplace(u64 *output, u32 count1) { u128 t[5]; fsquare_fsquare_times_(output, t, count1); } static __always_inline void crecip_crecip(u64 *out, u64 *z) { u64 buf[20] = { 0 }; u64 *a0 = buf; u64 *t00 = buf + 5; u64 *b0 = buf + 10; u64 *t01; u64 *b1; u64 *c0; u64 *a; u64 *t0; u64 *b; u64 *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(u64 *a, u64 *b) { a[0] += b[0]; a[1] += b[1]; a[2] += b[2]; a[3] += b[3]; a[4] += b[4]; } static __always_inline void fdifference(u64 *a, u64 *b) { u64 tmp[5] = { 0 }; u64 b0; u64 b1; u64 b2; u64 b3; u64 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; { u64 xi = a[0]; u64 yi = tmp[0]; a[0] = yi - xi; } { u64 xi = a[1]; u64 yi = tmp[1]; a[1] = yi - xi; } { u64 xi = a[2]; u64 yi = tmp[2]; a[2] = yi - xi; } { u64 xi = a[3]; u64 yi = tmp[3]; a[3] = yi - xi; } { u64 xi = a[4]; u64 yi = tmp[4]; a[4] = yi - xi; } } static __always_inline void fscalar(u64 *output, u64 *b, u64 s) { u128 tmp[5]; u128 b4; u128 b0; u128 b4_; u128 b0_; { u64 xi = b[0]; tmp[0] = ((u128)(xi) * (s)); } { u64 xi = b[1]; tmp[1] = ((u128)(xi) * (s)); } { u64 xi = b[2]; tmp[2] = ((u128)(xi) * (s)); } { u64 xi = b[3]; tmp[3] = ((u128)(xi) * (s)); } { u64 xi = b[4]; tmp[4] = ((u128)(xi) * (s)); } fproduct_carry_wide_(tmp); b4 = tmp[4]; b0 = tmp[0]; b4_ = ((b4) & (((u128)(0x7ffffffffffffLLU)))); b0_ = ((b0) + (((u128)(19) * (((u64)(((b4) >> (51)))))))); tmp[4] = b4_; tmp[0] = b0_; fproduct_copy_from_wide_(output, tmp); } static __always_inline void fmul(u64 *output, u64 *a, u64 *b) { fmul_fmul(output, a, b); } static __always_inline void crecip(u64 *output, u64 *input) { crecip_crecip(output, input); } static __always_inline void point_swap_conditional_step(u64 *a, u64 *b, u64 swap1, u32 ctr) { u32 i = ctr - 1; u64 ai = a[i]; u64 bi = b[i]; u64 x = swap1 & (ai ^ bi); u64 ai1 = ai ^ x; u64 bi1 = bi ^ x; a[i] = ai1; b[i] = bi1; } static __always_inline void point_swap_conditional5(u64 *a, u64 *b, u64 swap1) { point_swap_conditional_step(a, b, swap1, 5); point_swap_conditional_step(a, b, swap1, 4); point_swap_conditional_step(a, b, swap1, 3); point_swap_conditional_step(a, b, swap1, 2); point_swap_conditional_step(a, b, swap1, 1); } static __always_inline void point_swap_conditional(u64 *a, u64 *b, u64 iswap) { u64 swap1 = 0 - iswap; point_swap_conditional5(a, b, swap1); point_swap_conditional5(a + 5, b + 5, swap1); } static __always_inline void point_copy(u64 *output, u64 *input) { memcpy(output, input, 5 * sizeof(*input)); memcpy(output + 5, input + 5, 5 * sizeof(*input)); } static __always_inline void addanddouble_fmonty(u64 *pp, u64 *ppq, u64 *p, u64 *pq, u64 *qmqp) { u64 *qx = qmqp; u64 *x2 = pp; u64 *z2 = pp + 5; u64 *x3 = ppq; u64 *z3 = ppq + 5; u64 *x = p; u64 *z = p + 5; u64 *xprime = pq; u64 *zprime = pq + 5; u64 buf[40] = { 0 }; u64 *origx = buf; u64 *origxprime0 = buf + 5; u64 *xxprime0; u64 *zzprime0; u64 *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; { u64 *xx0; u64 *zz0; u64 *xxprime; u64 *zzprime; u64 *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); { u64 *zzz; u64 *xx; u64 *zz; u64 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(u64 *nq, u64 *nqpq, u64 *nq2, u64 *nqpq2, u64 *q, u8 byt) { u64 bit0 = (u64)(byt >> 7); u64 bit; point_swap_conditional(nq, nqpq, bit0); addanddouble_fmonty(nq2, nqpq2, nq, nqpq, q); bit = (u64)(byt >> 7); point_swap_conditional(nq2, nqpq2, bit); } static __always_inline void ladder_smallloop_cmult_small_loop_double_step(u64 *nq, u64 *nqpq, u64 *nq2, u64 *nqpq2, u64 *q, u8 byt) { u8 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(u64 *nq, u64 *nqpq, u64 *nq2, u64 *nqpq2, u64 *q, u8 byt, u32 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(u8 *n1, u64 *nq, u64 *nqpq, u64 *nq2, u64 *nqpq2, u64 *q, u32 i) { while (i--) { u8 byte = n1[i]; ladder_smallloop_cmult_small_loop(nq, nqpq, nq2, nqpq2, q, byte, 4); } } static __always_inline void ladder_cmult(u64 *result, u8 *n1, u64 *q) { u64 point_buf[40] = { 0 }; u64 *nq = point_buf; u64 *nqpq = point_buf + 10; u64 *nq2 = point_buf + 20; u64 *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(u64 *output, const u8 *input) { const u8 *x00 = input + 6; const u8 *x01 = input + 12; const u8 *x02 = input + 19; const u8 *x0 = input + 24; u64 i0, i1, i2, i3, i4, output0, output1, output2, output3, output4; i0 = le64_to_cpup((__force __le64 *)input); i1 = le64_to_cpup((__force __le64 *)x00); i2 = le64_to_cpup((__force __le64 *)x01); i3 = le64_to_cpup((__force __le64 *)x02); i4 = le64_to_cpup((__force __le64 *)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(u64 *input) { u64 t0 = input[0]; u64 t1 = input[1]; u64 t2 = input[2]; u64 t3 = input[3]; u64 t4 = input[4]; u64 t1_ = t1 + (t0 >> 51); u64 t0_ = t0 & 0x7ffffffffffffLLU; u64 t2_ = t2 + (t1_ >> 51); u64 t1__ = t1_ & 0x7ffffffffffffLLU; u64 t3_ = t3 + (t2_ >> 51); u64 t2__ = t2_ & 0x7ffffffffffffLLU; u64 t4_ = t4 + (t3_ >> 51); u64 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(u64 *input) { format_fcontract_first_carry_pass(input); modulo_carry_top(input); } static __always_inline void format_fcontract_second_carry_pass(u64 *input) { u64 t0 = input[0]; u64 t1 = input[1]; u64 t2 = input[2]; u64 t3 = input[3]; u64 t4 = input[4]; u64 t1_ = t1 + (t0 >> 51); u64 t0_ = t0 & 0x7ffffffffffffLLU; u64 t2_ = t2 + (t1_ >> 51); u64 t1__ = t1_ & 0x7ffffffffffffLLU; u64 t3_ = t3 + (t2_ >> 51); u64 t2__ = t2_ & 0x7ffffffffffffLLU; u64 t4_ = t4 + (t3_ >> 51); u64 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(u64 *input) { u64 i0; u64 i1; u64 i0_; u64 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(u64 *input) { u64 a0 = input[0]; u64 a1 = input[1]; u64 a2 = input[2]; u64 a3 = input[3]; u64 a4 = input[4]; u64 mask0 = u64_gte_mask(a0, 0x7ffffffffffedLLU); u64 mask1 = u64_eq_mask(a1, 0x7ffffffffffffLLU); u64 mask2 = u64_eq_mask(a2, 0x7ffffffffffffLLU); u64 mask3 = u64_eq_mask(a3, 0x7ffffffffffffLLU); u64 mask4 = u64_eq_mask(a4, 0x7ffffffffffffLLU); u64 mask = (((mask0 & mask1) & mask2) & mask3) & mask4; u64 a0_ = a0 - (0x7ffffffffffedLLU & mask); u64 a1_ = a1 - (0x7ffffffffffffLLU & mask); u64 a2_ = a2 - (0x7ffffffffffffLLU & mask); u64 a3_ = a3 - (0x7ffffffffffffLLU & mask); u64 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(u8 *output, u64 *input) { u64 t0 = input[0]; u64 t1 = input[1]; u64 t2 = input[2]; u64 t3 = input[3]; u64 t4 = input[4]; u64 o0 = t1 << 51 | t0; u64 o1 = t2 << 38 | t1 >> 13; u64 o2 = t3 << 25 | t2 >> 26; u64 o3 = t4 << 12 | t3 >> 39; u8 *b0 = output; u8 *b1 = output + 8; u8 *b2 = output + 16; u8 *b3 = output + 24; *(__force __le64 *)b0 = cpu_to_le64(o0); *(__force __le64 *)b1 = cpu_to_le64(o1); *(__force __le64 *)b2 = cpu_to_le64(o2); *(__force __le64 *)b3 = cpu_to_le64(o3); } static __always_inline void format_fcontract(u8 *output, u64 *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(u8 *scalar, u64 *point) { u64 *x = point; u64 *z = point + 5; u64 buf[10] __aligned(32) = { 0 }; u64 *zmone = buf; u64 *sc = buf + 5; crecip(zmone, z); fmul(sc, x, zmone); format_fcontract(scalar, sc); } static void curve25519_generic(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]) { u64 buf0[10] __aligned(32) = { 0 }; u64 *x0 = buf0; u64 *z = buf0 + 5; u64 *q; format_fexpand(x0, basepoint); z[0] = 1; q = buf0; { u8 e[32] __aligned(32) = { 0 }; u8 *scalar; memcpy(e, secret, 32); normalize_secret(e); scalar = e; { u64 buf[15] = { 0 }; u64 *nq = buf; u64 *x = nq; x[0] = 1; ladder_cmult(nq, scalar, q); format_scalar_of_point(mypublic, nq); memzero_explicit(buf, sizeof(buf)); } memzero_explicit(e, sizeof(e)); } memzero_explicit(buf0, sizeof(buf0)); }