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secp256r1.c
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secp256r1.c
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/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
│ vi: set et ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi │
╞══════════════════════════════════════════════════════════════════════════════╡
│ Copyright 2021 Justine Alexandra Roberts Tunney │
│ │
│ Permission to use, copy, modify, and/or distribute this software for │
│ any purpose with or without fee is hereby granted, provided that the │
│ above copyright notice and this permission notice appear in all copies. │
│ │
│ THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL │
│ WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED │
│ WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE │
│ AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL │
│ DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR │
│ PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER │
│ TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR │
│ PERFORMANCE OF THIS SOFTWARE. │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/log/check.h"
#include "third_party/mbedtls/bignum.h"
#include "third_party/mbedtls/math.h"
#include "third_party/mbedtls/platform.h"
#define Q(i) p[i >> 1]
#define L(w) (w & 0x00000000ffffffff)
#define H(w) (w & 0xffffffff00000000)
/**
* Fastest quasi-reduction modulo ℘256.
*
* p = 2²⁵⁶ - 2²²⁴ + 2¹⁹² + 2⁹⁶ - 1
* B = T + 2×S₁ + 2×S₂ + S₃ + S₄ – D₁ – D₂ – D₃ – D₄ mod p
* T = ( A₇ ‖ A₆ ‖ A₅ ‖ A₄ ‖ A₃ ‖ A₂ ‖ A₁ ‖ A₀ )
* S₁ = ( A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₂ ‖ A₁₁ ‖ 0 ‖ 0 ‖ 0 )
* S₂ = ( 0 ‖ A₁₅ ‖ A₁₄‖ A₁₃ ‖ A₁₂ ‖ 0 ‖ 0 ‖ 0 )
* S₃ = ( A₁₅ ‖ A₁₄ ‖ 0 ‖ 0 ‖ 0 ‖ A₁₀ ‖ A₉ ‖ A₈ )
* S₄ = ( A₈ ‖ A₁₃ ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₁ ‖ A₁₀ ‖ A₉ )
* D₁ = ( A₁₀ ‖ A₈ ‖ 0 ‖ 0 ‖ 0 ‖ A₁₃ ‖ A₁₂ ‖ A₁₁ )
* D₂ = ( A₁₁ ‖ A₉ ‖ 0 ‖ 0 ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₂ )
* D₃ = ( A₁₂ ‖ 0 ‖ A₁₀ ‖ A₉ ‖ A₈ ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ )
* D₄ = ( A₁₃ ‖ 0 ‖ A₁₁ ‖ A₁₀ ‖ A₉ ‖ 0 ‖ A₁₅ ‖ A₁₄ )
*
* @see FIPS 186-3 §D.2.3
*/
void secp256r1(uint64_t p[8]) {
char o;
signed char E;
uint64_t A, B, C, D, b, c, d;
A = Q(0);
B = Q(2);
C = Q(4);
D = Q(6);
E = 0;
#if !defined(__x86_64__) || defined(__STRICT_ANSI__)
(void)b;
(void)c;
(void)d;
ADC(B, B, H(Q(10)) << 1, 0, o);
ADC(C, C, Q(12) << 1 | Q(10) >> 63, o, o);
ADC(D, D, Q(14) << 1 | Q(12) >> 63, o, o);
E += o + (Q(14) >> 63);
ADC(B, B, Q(12) << 33, 0, o);
ADC(C, C, Q(14) << 33 | Q(12) >> 31, o, o);
ADC(D, D, Q(14) >> 31, o, o);
E += o;
ADC(A, A, Q(8), 0, o);
ADC(B, B, L(Q(10)), o, o);
ADC(C, C, 0, o, o);
ADC(D, D, Q(14), o, o);
E += o;
ADC(A, A, Q(10) << 32 | Q(8) >> 32, 0, o);
ADC(B, B, H(Q(12)) | Q(10) >> 32, o, o);
ADC(C, C, Q(14), o, o);
ADC(D, D, Q(8) << 32 | Q(12) >> 32, o, o);
E += o;
SBB(A, A, Q(12) << 32 | Q(10) >> 32, 0, o);
SBB(B, B, Q(12) >> 32, o, o);
SBB(C, C, 0, o, o);
SBB(D, D, Q(10) << 32 | L(Q(8)), o, o);
E -= o;
SBB(A, A, Q(12), 0, o);
SBB(B, B, Q(14), o, o);
SBB(C, C, 0, o, o);
SBB(D, D, H(Q(10)) | Q(8) >> 32, o, o);
E -= o;
SBB(A, A, Q(14) << 32 | Q(12) >> 32, 0, o);
SBB(B, B, Q(8) << 32 | Q(14) >> 32, o, o);
SBB(C, C, Q(10) << 32 | Q(8) >> 32, o, o);
SBB(D, D, Q(12) << 32, o, o);
E -= o;
SBB(A, A, Q(14), 0, o);
SBB(B, B, H(Q(8)), o, o);
SBB(C, C, Q(10), o, o);
SBB(D, D, H(Q(12)), o, o);
E -= o;
#else
(void)o;
asm volatile(/* x += 2 × ( A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₂ ‖ A₁₁ ‖ 0 ‖ 0 ‖ 0 ) */
"mov\t11*4(%8),%k5\n\t"
"mov\t12*4(%8),%6\n\t"
"mov\t14*4(%8),%7\n\t"
"shl\t$33,%5\n\t"
"rcl\t%6\n\t"
"rcl\t%7\n\t"
"adc\t$0,%b4\n\t"
"add\t%5,%1\n\t"
"adc\t%6,%2\n\t"
"adc\t%7,%3\n\t"
"adc\t$0,%b4\n\t"
/* x += 2 × ( 0 ‖ A₁₅ ‖ A₁₄‖ A₁₃ ‖ A₁₂ ‖ 0 ‖ 0 ‖ 0 ) */
"mov\t12*4(%8),%k5\n\t"
"mov\t13*4(%8),%6\n\t"
"mov\t15*4(%8),%k7\n\t"
"shl\t$33,%5\n\t"
"rcl\t%6\n\t"
"rcl\t%7\n\t"
"add\t%5,%1\n\t"
"adc\t%6,%2\n\t"
"adc\t%7,%3\n\t"
/* x += ( A₁₅ ‖ A₁₄ ‖ 0 ‖ 0 ‖ 0 ‖ A₁₀ ‖ A₉ ‖ A₈ ) */
"mov\t10*4(%8),%k5\n\t"
"add\t8*4(%8),%0\n\t"
"adc\t%5,%1\n\t"
"adc\t$0,%2\n\t"
"adc\t14*4(%8),%3\n\t"
"adc\t$0,%b4\n\t"
/* x += ( A₈ ‖ A₁₃ ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₁ ‖ A₁₀ ‖ A₉ ) */
"mov\t8*4(%8),%k7\n\t" /* A₈ ‖ A₁₃ */
"mov\t13*4(%8),%k5\n\t" /* ... */
"shl\t$32,%7\n\t" /* ... */
"or\t%5,%7\n\t" /* ... */
"shl\t$32,%5\n\t" /* A₁₃ ‖ A₁₁ */
"mov\t11*4(%8),%k6\n\t" /* ... */
"or\t%6,%5\n\t" /* ... */
"add\t9*4(%8),%0\n\t" /* A₁₀ ‖ A₉ */
"adc\t%5,%1\n\t" /* ... */
"adc\t14*4(%8),%2\n\t" /* A₁₅ ‖ A₁₄ */
"adc\t%7,%3\n\t"
"adc\t$0,%b4\n\t"
/* x -= ( A₁₀ ‖ A₈ ‖ 0 ‖ 0 ‖ 0 ‖ A₁₃ ‖ A₁₂ ‖ A₁₁ ) */
"mov\t10*4(%8),%k6\n\t"
"mov\t8*4(%8),%k7\n\t"
"shl\t$32,%6\n\t"
"or\t%6,%7\n\t"
"mov\t13*4(%8),%k5\n\t"
"sub\t11*4(%8),%0\n\t"
"sbb\t%5,%1\n\t"
"sbb\t$0,%2\n\t"
"sbb\t%7,%3\n\t"
"sbb\t$0,%b4\n\t"
/* x -= ( A₁₁ ‖ A₉ ‖ 0 ‖ 0 ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₂ ) */
"mov\t11*4(%8),%k6\n\t"
"mov\t9*4(%8),%k7\n\t"
"shl\t$32,%6\n\t"
"or\t%6,%7\n\t"
"sub\t12*4(%8),%0\n\t"
"sbb\t14*4(%8),%1\n\t"
"sbb\t$0,%2\n\t"
"sbb\t%7,%3\n\t"
"sbb\t$0,%b4\n\t"
/* x -= ( A₁₂ ‖ 0 ‖ A₁₀ ‖ A₉ ‖ A₈ ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ) */
"mov\t12*4(%8),%k7\n\t"
"shl\t$32,%7\n\t"
"mov\t15*4(%8),%k6\n\t"
"mov\t8*4(%8),%k5\n\t"
"shl\t$32,%5\n\t"
"or\t%5,%6\n\t"
"sub\t13*4(%8),%0\n\t"
"sbb\t%6,%1\n\t"
"sbb\t9*4(%8),%2\n\t"
"sbb\t%7,%3\n\t"
"sbb\t$0,%b4\n\t"
/* x -= ( A₁₃ ‖ 0 ‖ A₁₁ ‖ A₁₀ ‖ A₉ ‖ 0 ‖ A₁₅ ‖ A₁₄ ) */
"mov\t9*4(%8),%k6\n\t"
"shl\t$32,%6\n\t"
"mov\t13*4(%8),%k5\n\t"
"shl\t$32,%5\n\t"
"sub\t14*4(%8),%0\n\t"
"sbb\t%6,%1\n\t"
"sbb\t10*4(%8),%2\n\t"
"sbb\t%5,%3\n\t"
"sbb\t$0,%b4\n\t"
: "+r"(A), "+r"(B), "+r"(C), "+r"(D), "+&q"(E), "=&r"(b),
"=&r"(c), "=&r"(d)
: "r"(p)
: "memory");
#endif
p[0] = A;
p[1] = B;
p[2] = C;
p[3] = D;
p[4] = E;
p[5] = 0;
p[6] = 0;
p[7] = 0;
}
int ecp_mod_p256(mbedtls_mpi *N) {
int r;
char o;
if (N->n < 8 && (r = mbedtls_mpi_grow(N, 8))) return r;
secp256r1(N->p);
if ((int64_t)N->p[4] < 0) {
N->s = -1;
SBB(N->p[0], 0, N->p[0], 0, o);
SBB(N->p[1], 0, N->p[1], o, o);
SBB(N->p[2], 0, N->p[2], o, o);
SBB(N->p[3], 0, N->p[3], o, o);
N->p[4] = 0 - (N->p[4] + o);
} else {
N->s = 1;
}
return 0;
}