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ea83cc0ad0
One of the disadvantages of x25519 and ℘256 is it only provides 126 bits of security, so that seems like a weak link in the chain, if we're using ECDHE-ECDSA-AES256-GCM-SHA384. The U.S. government wants classified data to be encrypted using a curve at least as strong as ℘384, which provides 192 bits of security, but if you read the consensus of stack exchange it would give you the impression that ℘384 is three times slower. This change (as well as the previous one) makes ℘384 three times as fast by tuning its modulus and multiplication subroutines with new tests that should convincingly show: the optimized code behaves the same way as the old code. Some of the diff noise from the previous change is now removed too, so that our vendored fork can be more easily compared with upstream sources. So you can now have stronger cryptography without compromises. ℘384 modulus Justine l: 28𝑐 9𝑛𝑠 ℘384 modulus MbedTLS NIST l: 127𝑐 41𝑛𝑠 ℘384 modulus MbedTLS MPI l: 1,850𝑐 597𝑛𝑠 The benchmarks above show the improvements made by secp384r1() which is an important function since it needs to be called 13,000 times whenever someone establishes a connection to your web server. The same's true of Mul6x6Adx() which is able to multiply 384-bit numbers in 73 cycles, but only if your CPU was purchased after 2014 when Broadwell was introduced
211 lines
8.7 KiB
C
211 lines
8.7 KiB
C
/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
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│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│
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╞══════════════════════════════════════════════════════════════════════════════╡
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│ Copyright 2021 Justine Alexandra Roberts Tunney │
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│ │
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│ Permission to use, copy, modify, and/or distribute this software for │
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│ any purpose with or without fee is hereby granted, provided that the │
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│ above copyright notice and this permission notice appear in all copies. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL │
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│ WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED │
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│ WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE │
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│ AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL │
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│ DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR │
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│ PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER │
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│ TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR │
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│ PERFORMANCE OF THIS SOFTWARE. │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/log/check.h"
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#include "third_party/mbedtls/bignum.h"
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#include "third_party/mbedtls/math.h"
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#include "third_party/mbedtls/platform.h"
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#define Q(i) p[i >> 1]
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#define L(w) (w & 0x00000000ffffffff)
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#define H(w) (w & 0xffffffff00000000)
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/**
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* Fastest quasi-reduction modulo ℘256.
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*
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* p = 2²⁵⁶ - 2²²⁴ + 2¹⁹² + 2⁹⁶ - 1
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* B = T + 2×S₁ + 2×S₂ + S₃ + S₄ – D₁ – D₂ – D₃ – D₄ mod p
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* T = ( A₇ ‖ A₆ ‖ A₅ ‖ A₄ ‖ A₃ ‖ A₂ ‖ A₁ ‖ A₀ )
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* S₁ = ( A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₂ ‖ A₁₁ ‖ 0 ‖ 0 ‖ 0 )
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* S₂ = ( 0 ‖ A₁₅ ‖ A₁₄‖ A₁₃ ‖ A₁₂ ‖ 0 ‖ 0 ‖ 0 )
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* S₃ = ( A₁₅ ‖ A₁₄ ‖ 0 ‖ 0 ‖ 0 ‖ A₁₀ ‖ A₉ ‖ A₈ )
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* S₄ = ( A₈ ‖ A₁₃ ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₁ ‖ A₁₀ ‖ A₉ )
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* D₁ = ( A₁₀ ‖ A₈ ‖ 0 ‖ 0 ‖ 0 ‖ A₁₃ ‖ A₁₂ ‖ A₁₁ )
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* D₂ = ( A₁₁ ‖ A₉ ‖ 0 ‖ 0 ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₂ )
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* D₃ = ( A₁₂ ‖ 0 ‖ A₁₀ ‖ A₉ ‖ A₈ ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ )
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* D₄ = ( A₁₃ ‖ 0 ‖ A₁₁ ‖ A₁₀ ‖ A₉ ‖ 0 ‖ A₁₅ ‖ A₁₄ )
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*
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* @see FIPS 186-3 §D.2.3
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*/
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void secp256r1(uint64_t p[8]) {
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int r;
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char o;
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signed char E;
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uint64_t A, B, C, D, a, b, c, d, e;
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A = Q(0);
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B = Q(2);
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C = Q(4);
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D = Q(6);
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E = 0;
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#if !defined(__x86_64__) || defined(__STRICT_ANSI__)
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ADC(B, B, H(Q(10)) << 1, 0, o);
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ADC(C, C, Q(12) << 1 | Q(10) >> 63, o, o);
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ADC(D, D, Q(14) << 1 | Q(12) >> 63, o, o);
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E += o + (Q(14) >> 63);
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ADC(B, B, Q(12) << 33, 0, o);
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ADC(C, C, Q(14) << 33 | Q(12) >> 31, o, o);
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ADC(D, D, Q(14) >> 31, o, o);
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E += o;
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ADC(A, A, Q(8), 0, o);
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ADC(B, B, L(Q(10)), o, o);
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ADC(C, C, 0, o, o);
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ADC(D, D, Q(14), o, o);
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E += o;
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ADC(A, A, Q(10) << 32 | Q(8) >> 32, 0, o);
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ADC(B, B, H(Q(12)) | Q(10) >> 32, o, o);
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ADC(C, C, Q(14), o, o);
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ADC(D, D, Q(8) << 32 | Q(12) >> 32, o, o);
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E += o;
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SBB(A, A, Q(12) << 32 | Q(10) >> 32, 0, o);
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SBB(B, B, Q(12) >> 32, o, o);
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SBB(C, C, 0, o, o);
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SBB(D, D, Q(10) << 32 | L(Q(8)), o, o);
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E -= o;
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SBB(A, A, Q(12), 0, o);
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SBB(B, B, Q(14), o, o);
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SBB(C, C, 0, o, o);
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SBB(D, D, H(Q(10)) | Q(8) >> 32, o, o);
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E -= o;
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SBB(A, A, Q(14) << 32 | Q(12) >> 32, 0, o);
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SBB(B, B, Q(8) << 32 | Q(14) >> 32, o, o);
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SBB(C, C, Q(10) << 32 | Q(8) >> 32, o, o);
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SBB(D, D, Q(12) << 32, o, o);
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E -= o;
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SBB(A, A, Q(14), 0, o);
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SBB(B, B, H(Q(8)), o, o);
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SBB(C, C, Q(10), o, o);
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SBB(D, D, H(Q(12)), o, o);
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E -= o;
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#else
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asm volatile(/* x += 2 × ( A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₂ ‖ A₁₁ ‖ 0 ‖ 0 ‖ 0 ) */
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"mov\t11*4(%8),%k5\n\t"
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"mov\t12*4(%8),%6\n\t"
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"mov\t14*4(%8),%7\n\t"
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"shl\t$33,%5\n\t"
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"rcl\t%6\n\t"
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"rcl\t%7\n\t"
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"adc\t$0,%b4\n\t"
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"add\t%5,%1\n\t"
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"adc\t%6,%2\n\t"
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"adc\t%7,%3\n\t"
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"adc\t$0,%b4\n\t"
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/* x += 2 × ( 0 ‖ A₁₅ ‖ A₁₄‖ A₁₃ ‖ A₁₂ ‖ 0 ‖ 0 ‖ 0 ) */
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"mov\t12*4(%8),%k5\n\t"
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"mov\t13*4(%8),%6\n\t"
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"mov\t15*4(%8),%k7\n\t"
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"shl\t$33,%5\n\t"
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"rcl\t%6\n\t"
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"rcl\t%7\n\t"
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"add\t%5,%1\n\t"
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"adc\t%6,%2\n\t"
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"adc\t%7,%3\n\t"
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/* x += ( A₁₅ ‖ A₁₄ ‖ 0 ‖ 0 ‖ 0 ‖ A₁₀ ‖ A₉ ‖ A₈ ) */
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"mov\t10*4(%8),%k5\n\t"
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"add\t8*4(%8),%0\n\t"
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"adc\t%5,%1\n\t"
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"adc\t$0,%2\n\t"
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"adc\t14*4(%8),%3\n\t"
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"adc\t$0,%b4\n\t"
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/* x += ( A₈ ‖ A₁₃ ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₁ ‖ A₁₀ ‖ A₉ ) */
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"mov\t8*4(%8),%k7\n\t" /* A₈ ‖ A₁₃ */
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"mov\t13*4(%8),%k5\n\t" /* ... */
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"shl\t$32,%7\n\t" /* ... */
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"or\t%5,%7\n\t" /* ... */
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"shl\t$32,%5\n\t" /* A₁₃ ‖ A₁₁ */
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"mov\t11*4(%8),%k6\n\t" /* ... */
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"or\t%6,%5\n\t" /* ... */
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"add\t9*4(%8),%0\n\t" /* A₁₀ ‖ A₉ */
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"adc\t%5,%1\n\t" /* ... */
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"adc\t14*4(%8),%2\n\t" /* A₁₅ ‖ A₁₄ */
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"adc\t%7,%3\n\t"
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"adc\t$0,%b4\n\t"
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/* x -= ( A₁₀ ‖ A₈ ‖ 0 ‖ 0 ‖ 0 ‖ A₁₃ ‖ A₁₂ ‖ A₁₁ ) */
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"mov\t10*4(%8),%k6\n\t"
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"mov\t8*4(%8),%k7\n\t"
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"shl\t$32,%6\n\t"
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"or\t%6,%7\n\t"
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"mov\t13*4(%8),%k5\n\t"
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"sub\t11*4(%8),%0\n\t"
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"sbb\t%5,%1\n\t"
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"sbb\t$0,%2\n\t"
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"sbb\t%7,%3\n\t"
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"sbb\t$0,%b4\n\t"
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/* x -= ( A₁₁ ‖ A₉ ‖ 0 ‖ 0 ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ‖ A₁₂ ) */
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"mov\t11*4(%8),%k6\n\t"
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"mov\t9*4(%8),%k7\n\t"
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"shl\t$32,%6\n\t"
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"or\t%6,%7\n\t"
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"sub\t12*4(%8),%0\n\t"
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"sbb\t14*4(%8),%1\n\t"
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"sbb\t$0,%2\n\t"
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"sbb\t%7,%3\n\t"
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"sbb\t$0,%b4\n\t"
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/* x -= ( A₁₂ ‖ 0 ‖ A₁₀ ‖ A₉ ‖ A₈ ‖ A₁₅ ‖ A₁₄ ‖ A₁₃ ) */
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"mov\t12*4(%8),%k7\n\t"
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"shl\t$32,%7\n\t"
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"mov\t15*4(%8),%k6\n\t"
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"mov\t8*4(%8),%k5\n\t"
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"shl\t$32,%5\n\t"
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"or\t%5,%6\n\t"
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"sub\t13*4(%8),%0\n\t"
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"sbb\t%6,%1\n\t"
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"sbb\t9*4(%8),%2\n\t"
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"sbb\t%7,%3\n\t"
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"sbb\t$0,%b4\n\t"
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/* x -= ( A₁₃ ‖ 0 ‖ A₁₁ ‖ A₁₀ ‖ A₉ ‖ 0 ‖ A₁₅ ‖ A₁₄ ) */
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"mov\t9*4(%8),%k6\n\t"
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"shl\t$32,%6\n\t"
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"mov\t13*4(%8),%k5\n\t"
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"shl\t$32,%5\n\t"
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"sub\t14*4(%8),%0\n\t"
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"sbb\t%6,%1\n\t"
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"sbb\t10*4(%8),%2\n\t"
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"sbb\t%5,%3\n\t"
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"sbb\t$0,%b4\n\t"
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: "+r"(A), "+r"(B), "+r"(C), "+r"(D), "+&q"(E), "=&r"(b),
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"=&r"(c), "=&r"(d)
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: "r"(p)
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: "memory");
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#endif
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p[0] = A;
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p[1] = B;
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p[2] = C;
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p[3] = D;
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p[4] = E;
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p[5] = 0;
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p[6] = 0;
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p[7] = 0;
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}
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int ecp_mod_p256(mbedtls_mpi *N) {
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int r;
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char o;
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if (N->n < 8 && (r = mbedtls_mpi_grow(N, 8))) return r;
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secp256r1(N->p);
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if ((int64_t)N->p[4] < 0) {
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N->s = -1;
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SBB(N->p[0], 0, N->p[0], 0, o);
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SBB(N->p[1], 0, N->p[1], o, o);
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SBB(N->p[2], 0, N->p[2], o, o);
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SBB(N->p[3], 0, N->p[3], o, o);
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N->p[4] = 0 - (N->p[4] + o);
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} else {
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N->s = 1;
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}
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return 0;
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}
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