mirror of https://git.zx2c4.com/WireGuard
1305 lines
44 KiB
C
1305 lines
44 KiB
C
/* Original author: Adam Langley <agl@imperialviolet.org>
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*
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* Copyright 2008 Google Inc. All Rights Reserved.
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* Copyright 2015-2016 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
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*/
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#include "../wireguard.h"
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#include "curve25519.h"
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#include <linux/string.h>
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#include <linux/random.h>
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#include <crypto/algapi.h>
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static __always_inline void normalize_secret(uint8_t secret[CURVE25519_POINT_SIZE])
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{
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secret[0] &= 248;
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secret[31] &= 127;
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secret[31] |= 64;
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}
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static const uint8_t zeros[CURVE25519_POINT_SIZE] = { 0 };
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#ifdef __SIZEOF_INT128__
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typedef uint64_t limb;
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typedef limb felem[5];
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typedef __uint128_t uint128_t;
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/* Sum two numbers: output += in */
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static __always_inline void fsum(limb *output, const limb *in)
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{
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output[0] += in[0];
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output[1] += in[1];
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output[2] += in[2];
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output[3] += in[3];
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output[4] += in[4];
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}
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/* Find the difference of two numbers: output = in - output
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* (note the order of the arguments!)
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*
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* Assumes that out[i] < 2**52
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* On return, out[i] < 2**55
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*/
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static __always_inline void fdifference_backwards(felem out, const felem in)
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{
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/* 152 is 19 << 3 */
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static const limb two54m152 = (((limb)1) << 54) - 152;
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static const limb two54m8 = (((limb)1) << 54) - 8;
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out[0] = in[0] + two54m152 - out[0];
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out[1] = in[1] + two54m8 - out[1];
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out[2] = in[2] + two54m8 - out[2];
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out[3] = in[3] + two54m8 - out[3];
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out[4] = in[4] + two54m8 - out[4];
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}
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/* Multiply a number by a scalar: output = in * scalar */
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static __always_inline void fscalar_product(felem output, const felem in, const limb scalar)
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{
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uint128_t a;
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a = ((uint128_t) in[0]) * scalar;
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output[0] = ((limb)a) & 0x7ffffffffffffUL;
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a = ((uint128_t) in[1]) * scalar + ((limb) (a >> 51));
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output[1] = ((limb)a) & 0x7ffffffffffffUL;
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a = ((uint128_t) in[2]) * scalar + ((limb) (a >> 51));
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output[2] = ((limb)a) & 0x7ffffffffffffUL;
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a = ((uint128_t) in[3]) * scalar + ((limb) (a >> 51));
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output[3] = ((limb)a) & 0x7ffffffffffffUL;
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a = ((uint128_t) in[4]) * scalar + ((limb) (a >> 51));
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output[4] = ((limb)a) & 0x7ffffffffffffUL;
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output[0] += (a >> 51) * 19;
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}
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/* Multiply two numbers: output = in2 * in
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*
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* output must be distinct to both inputs. The inputs are reduced coefficient
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* form, the output is not.
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*
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* Assumes that in[i] < 2**55 and likewise for in2.
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* On return, output[i] < 2**52
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*/
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static __always_inline void fmul(felem output, const felem in2, const felem in)
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{
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uint128_t t[5];
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limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
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r0 = in[0];
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r1 = in[1];
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r2 = in[2];
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r3 = in[3];
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r4 = in[4];
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s0 = in2[0];
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s1 = in2[1];
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s2 = in2[2];
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s3 = in2[3];
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s4 = in2[4];
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t[0] = ((uint128_t) r0) * s0;
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t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
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t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
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t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
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t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
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r4 *= 19;
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r1 *= 19;
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r2 *= 19;
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r3 *= 19;
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t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
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t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
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t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
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t[3] += ((uint128_t) r4) * s4;
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r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
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t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
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t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
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t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
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t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
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r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
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r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
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r2 += c;
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output[0] = r0;
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output[1] = r1;
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output[2] = r2;
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output[3] = r3;
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output[4] = r4;
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}
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static __always_inline void fsquare_times(felem output, const felem in, limb count)
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{
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uint128_t t[5];
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limb r0,r1,r2,r3,r4,c;
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limb d0,d1,d2,d4,d419;
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r0 = in[0];
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r1 = in[1];
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r2 = in[2];
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r3 = in[3];
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r4 = in[4];
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do {
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d0 = r0 * 2;
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d1 = r1 * 2;
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d2 = r2 * 2 * 19;
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d419 = r4 * 19;
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d4 = d419 * 2;
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t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
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t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
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t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
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t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
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t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
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r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
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t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
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t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
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t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
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t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
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r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
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r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
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r2 += c;
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} while(--count);
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output[0] = r0;
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output[1] = r1;
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output[2] = r2;
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output[3] = r3;
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output[4] = r4;
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}
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/* Load a little-endian 64-bit number */
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static inline limb load_limb(const uint8_t *in)
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{
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return le64_to_cpu(*(uint64_t *)in);
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}
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static inline void store_limb(uint8_t *out, limb in)
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{
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*(uint64_t *)out = cpu_to_le64(in);
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}
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/* Take a little-endian, 32-byte number and expand it into polynomial form */
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static inline void fexpand(limb *output, const uint8_t *in)
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{
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output[0] = load_limb(in) & 0x7ffffffffffffUL;
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output[1] = (load_limb(in + 6) >> 3) & 0x7ffffffffffffUL;
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output[2] = (load_limb(in + 12) >> 6) & 0x7ffffffffffffUL;
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output[3] = (load_limb(in + 19) >> 1) & 0x7ffffffffffffUL;
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output[4] = (load_limb(in + 24) >> 12) & 0x7ffffffffffffUL;
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}
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/* Take a fully reduced polynomial form number and contract it into a
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* little-endian, 32-byte array
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*/
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static void fcontract(uint8_t *output, const felem input)
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{
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uint128_t t[5];
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t[0] = input[0];
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t[1] = input[1];
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t[2] = input[2];
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t[3] = input[3];
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t[4] = input[4];
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t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
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t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
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t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
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t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
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t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
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t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
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t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
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t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
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t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
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t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
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/* now t is between 0 and 2^255-1, properly carried. */
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/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
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t[0] += 19;
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t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
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t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
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t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
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t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
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t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
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/* now between 19 and 2^255-1 in both cases, and offset by 19. */
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t[0] += 0x8000000000000UL - 19;
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t[1] += 0x8000000000000UL - 1;
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t[2] += 0x8000000000000UL - 1;
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t[3] += 0x8000000000000UL - 1;
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t[4] += 0x8000000000000UL - 1;
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/* now between 2^255 and 2^256-20, and offset by 2^255. */
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t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
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t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
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t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
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t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
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t[4] &= 0x7ffffffffffffUL;
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store_limb(output, t[0] | (t[1] << 51));
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store_limb(output+8, (t[1] >> 13) | (t[2] << 38));
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store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
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store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
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}
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/* Input: Q, Q', Q-Q'
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* Output: 2Q, Q+Q'
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*
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* x2 z3: long form
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* x3 z3: long form
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* x z: short form, destroyed
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* xprime zprime: short form, destroyed
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* qmqp: short form, preserved
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*/
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static void fmonty(limb *x2, limb *z2, /* output 2Q */
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limb *x3, limb *z3, /* output Q + Q' */
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limb *x, limb *z, /* input Q */
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limb *xprime, limb *zprime, /* input Q' */
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const limb *qmqp /* input Q - Q' */)
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{
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limb origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5];
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memcpy(origx, x, 5 * sizeof(limb));
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fsum(x, z);
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fdifference_backwards(z, origx); // does x - z
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memcpy(origxprime, xprime, sizeof(limb) * 5);
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fsum(xprime, zprime);
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fdifference_backwards(zprime, origxprime);
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fmul(xxprime, xprime, z);
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fmul(zzprime, x, zprime);
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memcpy(origxprime, xxprime, sizeof(limb) * 5);
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fsum(xxprime, zzprime);
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fdifference_backwards(zzprime, origxprime);
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fsquare_times(x3, xxprime, 1);
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fsquare_times(zzzprime, zzprime, 1);
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fmul(z3, zzzprime, qmqp);
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fsquare_times(xx, x, 1);
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fsquare_times(zz, z, 1);
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fmul(x2, xx, zz);
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fdifference_backwards(zz, xx); // does zz = xx - zz
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fscalar_product(zzz, zz, 121665);
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fsum(zzz, xx);
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fmul(z2, zz, zzz);
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}
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/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements
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* long. Perform the swap iff @swap is non-zero.
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*
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* This function performs the swap without leaking any side-channel
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* information.
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*/
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static void swap_conditional(limb a[5], limb b[5], limb iswap)
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{
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unsigned i;
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const limb swap = -iswap;
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for (i = 0; i < 5; ++i) {
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const limb x = swap & (a[i] ^ b[i]);
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a[i] ^= x;
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b[i] ^= x;
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}
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}
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/* Calculates nQ where Q is the x-coordinate of a point on the curve
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*
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* resultx/resultz: the x coordinate of the resulting curve point (short form)
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* n: a little endian, 32-byte number
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* q: a point of the curve (short form)
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*/
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static void cmult(limb *resultx, limb *resultz, const uint8_t *n, const limb *q)
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{
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limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
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limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
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limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
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limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
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unsigned i, j;
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memcpy(nqpqx, q, sizeof(limb) * 5);
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for (i = 0; i < 32; ++i) {
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uint8_t byte = n[31 - i];
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for (j = 0; j < 8; ++j) {
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const limb bit = byte >> 7;
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swap_conditional(nqx, nqpqx, bit);
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swap_conditional(nqz, nqpqz, bit);
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fmonty(nqx2, nqz2,
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nqpqx2, nqpqz2,
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nqx, nqz,
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nqpqx, nqpqz,
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q);
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swap_conditional(nqx2, nqpqx2, bit);
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swap_conditional(nqz2, nqpqz2, bit);
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t = nqx;
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nqx = nqx2;
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nqx2 = t;
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t = nqz;
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nqz = nqz2;
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nqz2 = t;
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t = nqpqx;
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nqpqx = nqpqx2;
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nqpqx2 = t;
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t = nqpqz;
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nqpqz = nqpqz2;
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nqpqz2 = t;
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byte <<= 1;
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}
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}
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memcpy(resultx, nqx, sizeof(limb) * 5);
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memcpy(resultz, nqz, sizeof(limb) * 5);
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}
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static void crecip(felem out, const felem z)
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{
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felem a,t0,b,c;
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/* 2 */ fsquare_times(a, z, 1); // a = 2
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/* 8 */ fsquare_times(t0, a, 2);
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/* 9 */ fmul(b, t0, z); // b = 9
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/* 11 */ fmul(a, b, a); // a = 11
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/* 22 */ fsquare_times(t0, a, 1);
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/* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
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/* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
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/* 2^10 - 2^0 */ fmul(b, t0, b);
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/* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
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/* 2^20 - 2^0 */ fmul(c, t0, b);
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/* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
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/* 2^40 - 2^0 */ fmul(t0, t0, c);
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/* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
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/* 2^50 - 2^0 */ fmul(b, t0, b);
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/* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
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/* 2^100 - 2^0 */ fmul(c, t0, b);
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/* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
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/* 2^200 - 2^0 */ fmul(t0, t0, c);
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/* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
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/* 2^250 - 2^0 */ fmul(t0, t0, b);
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/* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
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/* 2^255 - 21 */ fmul(out, t0, a);
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}
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void curve25519(uint8_t mypublic[CURVE25519_POINT_SIZE], const uint8_t secret[CURVE25519_POINT_SIZE], const uint8_t basepoint[CURVE25519_POINT_SIZE])
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{
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limb bp[5], x[5], z[5], zmone[5];
|
|
uint8_t e[32];
|
|
|
|
memcpy(e, secret, 32);
|
|
normalize_secret(e);
|
|
|
|
fexpand(bp, basepoint);
|
|
cmult(x, z, e, bp);
|
|
crecip(zmone, z);
|
|
fmul(z, x, zmone);
|
|
fcontract(mypublic, z);
|
|
|
|
memzero_explicit(e, sizeof(e));
|
|
memzero_explicit(bp, sizeof(bp));
|
|
memzero_explicit(x, sizeof(x));
|
|
memzero_explicit(z, sizeof(z));
|
|
memzero_explicit(zmone, sizeof(zmone));
|
|
}
|
|
|
|
#else
|
|
typedef int64_t limb;
|
|
|
|
/* Field element representation:
|
|
*
|
|
* Field elements are written as an array of signed, 64-bit limbs, least
|
|
* significant first. The value of the field element is:
|
|
* x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
|
|
*
|
|
* i.e. the limbs are 26, 25, 26, 25, ... bits wide. */
|
|
|
|
/* Sum two numbers: output += in */
|
|
static void fsum(limb *output, const limb *in)
|
|
{
|
|
unsigned i;
|
|
for (i = 0; i < 10; i += 2) {
|
|
output[0 + i] = output[0 + i] + in[0 + i];
|
|
output[1 + i] = output[1 + i] + in[1 + i];
|
|
}
|
|
}
|
|
|
|
/* Find the difference of two numbers: output = in - output
|
|
* (note the order of the arguments!). */
|
|
static void fdifference(limb *output, const limb *in)
|
|
{
|
|
unsigned i;
|
|
for (i = 0; i < 10; ++i)
|
|
output[i] = in[i] - output[i];
|
|
}
|
|
|
|
/* Multiply a number by a scalar: output = in * scalar */
|
|
static void fscalar_product(limb *output, const limb *in, const limb scalar)
|
|
{
|
|
unsigned i;
|
|
for (i = 0; i < 10; ++i)
|
|
output[i] = in[i] * scalar;
|
|
}
|
|
|
|
/* Multiply two numbers: output = in2 * in
|
|
*
|
|
* output must be distinct to both inputs. The inputs are reduced coefficient
|
|
* form, the output is not.
|
|
*
|
|
* output[x] <= 14 * the largest product of the input limbs. */
|
|
static void fproduct(limb *output, const limb *in2, const limb *in)
|
|
{
|
|
output[0] = ((limb) ((int32_t) in2[0])) * ((int32_t) in[0]);
|
|
output[1] = ((limb) ((int32_t) in2[0])) * ((int32_t) in[1]) +
|
|
((limb) ((int32_t) in2[1])) * ((int32_t) in[0]);
|
|
output[2] = 2 * ((limb) ((int32_t) in2[1])) * ((int32_t) in[1]) +
|
|
((limb) ((int32_t) in2[0])) * ((int32_t) in[2]) +
|
|
((limb) ((int32_t) in2[2])) * ((int32_t) in[0]);
|
|
output[3] = ((limb) ((int32_t) in2[1])) * ((int32_t) in[2]) +
|
|
((limb) ((int32_t) in2[2])) * ((int32_t) in[1]) +
|
|
((limb) ((int32_t) in2[0])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[3])) * ((int32_t) in[0]);
|
|
output[4] = ((limb) ((int32_t) in2[2])) * ((int32_t) in[2]) +
|
|
2 * (((limb) ((int32_t) in2[1])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[3])) * ((int32_t) in[1])) +
|
|
((limb) ((int32_t) in2[0])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in2[4])) * ((int32_t) in[0]);
|
|
output[5] = ((limb) ((int32_t) in2[2])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[3])) * ((int32_t) in[2]) +
|
|
((limb) ((int32_t) in2[1])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in2[4])) * ((int32_t) in[1]) +
|
|
((limb) ((int32_t) in2[0])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[5])) * ((int32_t) in[0]);
|
|
output[6] = 2 * (((limb) ((int32_t) in2[3])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[1])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[5])) * ((int32_t) in[1])) +
|
|
((limb) ((int32_t) in2[2])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in2[4])) * ((int32_t) in[2]) +
|
|
((limb) ((int32_t) in2[0])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in2[6])) * ((int32_t) in[0]);
|
|
output[7] = ((limb) ((int32_t) in2[3])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in2[4])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[2])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[5])) * ((int32_t) in[2]) +
|
|
((limb) ((int32_t) in2[1])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in2[6])) * ((int32_t) in[1]) +
|
|
((limb) ((int32_t) in2[0])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[7])) * ((int32_t) in[0]);
|
|
output[8] = ((limb) ((int32_t) in2[4])) * ((int32_t) in[4]) +
|
|
2 * (((limb) ((int32_t) in2[3])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[5])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[1])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[7])) * ((int32_t) in[1])) +
|
|
((limb) ((int32_t) in2[2])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in2[6])) * ((int32_t) in[2]) +
|
|
((limb) ((int32_t) in2[0])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in2[8])) * ((int32_t) in[0]);
|
|
output[9] = ((limb) ((int32_t) in2[4])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[5])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in2[3])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in2[6])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[2])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[7])) * ((int32_t) in[2]) +
|
|
((limb) ((int32_t) in2[1])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in2[8])) * ((int32_t) in[1]) +
|
|
((limb) ((int32_t) in2[0])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[0]);
|
|
output[10] = 2 * (((limb) ((int32_t) in2[5])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[3])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[7])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[1])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[1])) +
|
|
((limb) ((int32_t) in2[4])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in2[6])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in2[2])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in2[8])) * ((int32_t) in[2]);
|
|
output[11] = ((limb) ((int32_t) in2[5])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in2[6])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[4])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[7])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in2[3])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in2[8])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in2[2])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[2]);
|
|
output[12] = ((limb) ((int32_t) in2[6])) * ((int32_t) in[6]) +
|
|
2 * (((limb) ((int32_t) in2[5])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[7])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[3])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[3])) +
|
|
((limb) ((int32_t) in2[4])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in2[8])) * ((int32_t) in[4]);
|
|
output[13] = ((limb) ((int32_t) in2[6])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[7])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in2[5])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in2[8])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in2[4])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[4]);
|
|
output[14] = 2 * (((limb) ((int32_t) in2[7])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[5])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[5])) +
|
|
((limb) ((int32_t) in2[6])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in2[8])) * ((int32_t) in[6]);
|
|
output[15] = ((limb) ((int32_t) in2[7])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in2[8])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in2[6])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[6]);
|
|
output[16] = ((limb) ((int32_t) in2[8])) * ((int32_t) in[8]) +
|
|
2 * (((limb) ((int32_t) in2[7])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[7]));
|
|
output[17] = ((limb) ((int32_t) in2[8])) * ((int32_t) in[9]) +
|
|
((limb) ((int32_t) in2[9])) * ((int32_t) in[8]);
|
|
output[18] = 2 * ((limb) ((int32_t) in2[9])) * ((int32_t) in[9]);
|
|
}
|
|
|
|
/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
|
|
*
|
|
* On entry: |output[i]| < 14*2^54
|
|
* On exit: |output[0..8]| < 280*2^54 */
|
|
static void freduce_degree(limb *output)
|
|
{
|
|
/* Each of these shifts and adds ends up multiplying the value by 19.
|
|
*
|
|
* For output[0..8], the absolute entry value is < 14*2^54 and we add, at
|
|
* most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */
|
|
output[8] += output[18] << 4;
|
|
output[8] += output[18] << 1;
|
|
output[8] += output[18];
|
|
output[7] += output[17] << 4;
|
|
output[7] += output[17] << 1;
|
|
output[7] += output[17];
|
|
output[6] += output[16] << 4;
|
|
output[6] += output[16] << 1;
|
|
output[6] += output[16];
|
|
output[5] += output[15] << 4;
|
|
output[5] += output[15] << 1;
|
|
output[5] += output[15];
|
|
output[4] += output[14] << 4;
|
|
output[4] += output[14] << 1;
|
|
output[4] += output[14];
|
|
output[3] += output[13] << 4;
|
|
output[3] += output[13] << 1;
|
|
output[3] += output[13];
|
|
output[2] += output[12] << 4;
|
|
output[2] += output[12] << 1;
|
|
output[2] += output[12];
|
|
output[1] += output[11] << 4;
|
|
output[1] += output[11] << 1;
|
|
output[1] += output[11];
|
|
output[0] += output[10] << 4;
|
|
output[0] += output[10] << 1;
|
|
output[0] += output[10];
|
|
}
|
|
|
|
#if (-1 & 3) != 3
|
|
#error "This code only works on a two's complement system"
|
|
#endif
|
|
|
|
/* return v / 2^26, using only shifts and adds.
|
|
*
|
|
* On entry: v can take any value. */
|
|
static inline limb div_by_2_26(const limb v)
|
|
{
|
|
/* High word of v; no shift needed. */
|
|
const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
|
|
/* Set to all 1s if v was negative; else set to 0s. */
|
|
const int32_t sign = ((int32_t) highword) >> 31;
|
|
/* Set to 0x3ffffff if v was negative; else set to 0. */
|
|
const int32_t roundoff = ((uint32_t) sign) >> 6;
|
|
/* Should return v / (1<<26) */
|
|
return (v + roundoff) >> 26;
|
|
}
|
|
|
|
/* return v / (2^25), using only shifts and adds.
|
|
*
|
|
* On entry: v can take any value. */
|
|
static inline limb div_by_2_25(const limb v)
|
|
{
|
|
/* High word of v; no shift needed*/
|
|
const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
|
|
/* Set to all 1s if v was negative; else set to 0s. */
|
|
const int32_t sign = ((int32_t) highword) >> 31;
|
|
/* Set to 0x1ffffff if v was negative; else set to 0. */
|
|
const int32_t roundoff = ((uint32_t) sign) >> 7;
|
|
/* Should return v / (1<<25) */
|
|
return (v + roundoff) >> 25;
|
|
}
|
|
|
|
/* Reduce all coefficients of the short form input so that |x| < 2^26.
|
|
*
|
|
* On entry: |output[i]| < 280*2^54 */
|
|
static void freduce_coefficients(limb *output)
|
|
{
|
|
unsigned i;
|
|
|
|
output[10] = 0;
|
|
|
|
for (i = 0; i < 10; i += 2) {
|
|
limb over = div_by_2_26(output[i]);
|
|
/* The entry condition (that |output[i]| < 280*2^54) means that over is, at
|
|
* most, 280*2^28 in the first iteration of this loop. This is added to the
|
|
* next limb and we can approximate the resulting bound of that limb by
|
|
* 281*2^54. */
|
|
output[i] -= over << 26;
|
|
output[i+1] += over;
|
|
|
|
/* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
|
|
* 281*2^29. When this is added to the next limb, the resulting bound can
|
|
* be approximated as 281*2^54.
|
|
*
|
|
* For subsequent iterations of the loop, 281*2^54 remains a conservative
|
|
* bound and no overflow occurs. */
|
|
over = div_by_2_25(output[i+1]);
|
|
output[i+1] -= over << 25;
|
|
output[i+2] += over;
|
|
}
|
|
/* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
|
|
output[0] += output[10] << 4;
|
|
output[0] += output[10] << 1;
|
|
output[0] += output[10];
|
|
|
|
output[10] = 0;
|
|
|
|
/* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
|
|
* So |over| will be no more than 2^16. */
|
|
{
|
|
limb over = div_by_2_26(output[0]);
|
|
output[0] -= over << 26;
|
|
output[1] += over;
|
|
}
|
|
|
|
/* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
|
|
* bound on |output[1]| is sufficient to meet our needs. */
|
|
}
|
|
|
|
/* A helpful wrapper around fproduct: output = in * in2.
|
|
*
|
|
* On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
|
|
*
|
|
* output must be distinct to both inputs. The output is reduced degree
|
|
* (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */
|
|
static void fmul(limb *output, const limb *in, const limb *in2)
|
|
{
|
|
limb t[19];
|
|
fproduct(t, in, in2);
|
|
/* |t[i]| < 14*2^54 */
|
|
freduce_degree(t);
|
|
freduce_coefficients(t);
|
|
/* |t[i]| < 2^26 */
|
|
memcpy(output, t, sizeof(limb) * 10);
|
|
}
|
|
|
|
/* Square a number: output = in**2
|
|
*
|
|
* output must be distinct from the input. The inputs are reduced coefficient
|
|
* form, the output is not.
|
|
*
|
|
* output[x] <= 14 * the largest product of the input limbs. */
|
|
static void fsquare_inner(limb *output, const limb *in)
|
|
{
|
|
output[0] = ((limb) ((int32_t) in[0])) * ((int32_t) in[0]);
|
|
output[1] = 2 * ((limb) ((int32_t) in[0])) * ((int32_t) in[1]);
|
|
output[2] = 2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[1]) +
|
|
((limb) ((int32_t) in[0])) * ((int32_t) in[2]));
|
|
output[3] = 2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[2]) +
|
|
((limb) ((int32_t) in[0])) * ((int32_t) in[3]));
|
|
output[4] = ((limb) ((int32_t) in[2])) * ((int32_t) in[2]) +
|
|
4 * ((limb) ((int32_t) in[1])) * ((int32_t) in[3]) +
|
|
2 * ((limb) ((int32_t) in[0])) * ((int32_t) in[4]);
|
|
output[5] = 2 * (((limb) ((int32_t) in[2])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in[1])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in[0])) * ((int32_t) in[5]));
|
|
output[6] = 2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[3]) +
|
|
((limb) ((int32_t) in[2])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in[0])) * ((int32_t) in[6]) +
|
|
2 * ((limb) ((int32_t) in[1])) * ((int32_t) in[5]));
|
|
output[7] = 2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[4]) +
|
|
((limb) ((int32_t) in[2])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in[1])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in[0])) * ((int32_t) in[7]));
|
|
output[8] = ((limb) ((int32_t) in[4])) * ((int32_t) in[4]) +
|
|
2 * (((limb) ((int32_t) in[2])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in[0])) * ((int32_t) in[8]) +
|
|
2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in[3])) * ((int32_t) in[5])));
|
|
output[9] = 2 * (((limb) ((int32_t) in[4])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in[3])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in[2])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in[1])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in[0])) * ((int32_t) in[9]));
|
|
output[10] = 2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[5]) +
|
|
((limb) ((int32_t) in[4])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in[2])) * ((int32_t) in[8]) +
|
|
2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in[1])) * ((int32_t) in[9])));
|
|
output[11] = 2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[6]) +
|
|
((limb) ((int32_t) in[4])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in[3])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in[2])) * ((int32_t) in[9]));
|
|
output[12] = ((limb) ((int32_t) in[6])) * ((int32_t) in[6]) +
|
|
2 * (((limb) ((int32_t) in[4])) * ((int32_t) in[8]) +
|
|
2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in[3])) * ((int32_t) in[9])));
|
|
output[13] = 2 * (((limb) ((int32_t) in[6])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in[5])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in[4])) * ((int32_t) in[9]));
|
|
output[14] = 2 * (((limb) ((int32_t) in[7])) * ((int32_t) in[7]) +
|
|
((limb) ((int32_t) in[6])) * ((int32_t) in[8]) +
|
|
2 * ((limb) ((int32_t) in[5])) * ((int32_t) in[9]));
|
|
output[15] = 2 * (((limb) ((int32_t) in[7])) * ((int32_t) in[8]) +
|
|
((limb) ((int32_t) in[6])) * ((int32_t) in[9]));
|
|
output[16] = ((limb) ((int32_t) in[8])) * ((int32_t) in[8]) +
|
|
4 * ((limb) ((int32_t) in[7])) * ((int32_t) in[9]);
|
|
output[17] = 2 * ((limb) ((int32_t) in[8])) * ((int32_t) in[9]);
|
|
output[18] = 2 * ((limb) ((int32_t) in[9])) * ((int32_t) in[9]);
|
|
}
|
|
|
|
/* fsquare sets output = in^2.
|
|
*
|
|
* On entry: The |in| argument is in reduced coefficients form and |in[i]| <
|
|
* 2^27.
|
|
*
|
|
* On exit: The |output| argument is in reduced coefficients form (indeed, one
|
|
* need only provide storage for 10 limbs) and |out[i]| < 2^26. */
|
|
static void fsquare(limb *output, const limb *in)
|
|
{
|
|
limb t[19];
|
|
fsquare_inner(t, in);
|
|
/* |t[i]| < 14*2^54 because the largest product of two limbs will be <
|
|
* 2^(27+27) and fsquare_inner adds together, at most, 14 of those
|
|
* products. */
|
|
freduce_degree(t);
|
|
freduce_coefficients(t);
|
|
/* |t[i]| < 2^26 */
|
|
memcpy(output, t, sizeof(limb) * 10);
|
|
}
|
|
|
|
/* Take a little-endian, 32-byte number and expand it into polynomial form */
|
|
static inline void fexpand(limb *output, const uint8_t *input)
|
|
{
|
|
#define F(n,start,shift,mask) \
|
|
output[n] = ((((limb) input[start + 0]) | \
|
|
((limb) input[start + 1]) << 8 | \
|
|
((limb) input[start + 2]) << 16 | \
|
|
((limb) input[start + 3]) << 24) >> shift) & mask;
|
|
F(0, 0, 0, 0x3ffffff);
|
|
F(1, 3, 2, 0x1ffffff);
|
|
F(2, 6, 3, 0x3ffffff);
|
|
F(3, 9, 5, 0x1ffffff);
|
|
F(4, 12, 6, 0x3ffffff);
|
|
F(5, 16, 0, 0x1ffffff);
|
|
F(6, 19, 1, 0x3ffffff);
|
|
F(7, 22, 3, 0x1ffffff);
|
|
F(8, 25, 4, 0x3ffffff);
|
|
F(9, 28, 6, 0x1ffffff);
|
|
#undef F
|
|
}
|
|
|
|
#if (-32 >> 1) != -16
|
|
#error "This code only works when >> does sign-extension on negative numbers"
|
|
#endif
|
|
|
|
/* int32_t_eq returns 0xffffffff iff a == b and zero otherwise. */
|
|
static int32_t int32_t_eq(int32_t a, int32_t b)
|
|
{
|
|
a = ~(a ^ b);
|
|
a &= a << 16;
|
|
a &= a << 8;
|
|
a &= a << 4;
|
|
a &= a << 2;
|
|
a &= a << 1;
|
|
return a >> 31;
|
|
}
|
|
|
|
/* int32_t_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
|
|
* both non-negative. */
|
|
static int32_t int32_t_gte(int32_t a, int32_t b)
|
|
{
|
|
a -= b;
|
|
/* a >= 0 iff a >= b. */
|
|
return ~(a >> 31);
|
|
}
|
|
|
|
/* Take a fully reduced polynomial form number and contract it into a
|
|
* little-endian, 32-byte array.
|
|
*
|
|
* On entry: |input_limbs[i]| < 2^26 */
|
|
static void fcontract(uint8_t *output, limb *input_limbs)
|
|
{
|
|
int i;
|
|
int j;
|
|
int32_t input[10];
|
|
int32_t mask;
|
|
|
|
/* |input_limbs[i]| < 2^26, so it's valid to convert to an int32_t. */
|
|
for (i = 0; i < 10; i++) {
|
|
input[i] = input_limbs[i];
|
|
}
|
|
|
|
for (j = 0; j < 2; ++j) {
|
|
for (i = 0; i < 9; ++i) {
|
|
if ((i & 1) == 1) {
|
|
/* This calculation is a time-invariant way to make input[i]
|
|
* non-negative by borrowing from the next-larger limb. */
|
|
const int32_t mask = input[i] >> 31;
|
|
const int32_t carry = -((input[i] & mask) >> 25);
|
|
input[i] = input[i] + (carry << 25);
|
|
input[i+1] = input[i+1] - carry;
|
|
} else {
|
|
const int32_t mask = input[i] >> 31;
|
|
const int32_t carry = -((input[i] & mask) >> 26);
|
|
input[i] = input[i] + (carry << 26);
|
|
input[i+1] = input[i+1] - carry;
|
|
}
|
|
}
|
|
|
|
/* There's no greater limb for input[9] to borrow from, but we can multiply
|
|
* by 19 and borrow from input[0], which is valid mod 2^255-19. */
|
|
{
|
|
const int32_t mask = input[9] >> 31;
|
|
const int32_t carry = -((input[9] & mask) >> 25);
|
|
input[9] = input[9] + (carry << 25);
|
|
input[0] = input[0] - (carry * 19);
|
|
}
|
|
|
|
/* After the first iteration, input[1..9] are non-negative and fit within
|
|
* 25 or 26 bits, depending on position. However, input[0] may be
|
|
* negative. */
|
|
}
|
|
|
|
/* The first borrow-propagation pass above ended with every limb
|
|
except (possibly) input[0] non-negative.
|
|
If input[0] was negative after the first pass, then it was because of a
|
|
carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
|
|
one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
|
|
In the second pass, each limb is decreased by at most one. Thus the second
|
|
borrow-propagation pass could only have wrapped around to decrease
|
|
input[0] again if the first pass left input[0] negative *and* input[1]
|
|
through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
|
|
and this last borrow-propagation step will leave input[1] non-negative. */
|
|
{
|
|
const int32_t mask = input[0] >> 31;
|
|
const int32_t carry = -((input[0] & mask) >> 26);
|
|
input[0] = input[0] + (carry << 26);
|
|
input[1] = input[1] - carry;
|
|
}
|
|
|
|
/* All input[i] are now non-negative. However, there might be values between
|
|
* 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */
|
|
for (j = 0; j < 2; j++) {
|
|
for (i = 0; i < 9; i++) {
|
|
if ((i & 1) == 1) {
|
|
const int32_t carry = input[i] >> 25;
|
|
input[i] &= 0x1ffffff;
|
|
input[i+1] += carry;
|
|
} else {
|
|
const int32_t carry = input[i] >> 26;
|
|
input[i] &= 0x3ffffff;
|
|
input[i+1] += carry;
|
|
}
|
|
}
|
|
|
|
{
|
|
const int32_t carry = input[9] >> 25;
|
|
input[9] &= 0x1ffffff;
|
|
input[0] += 19*carry;
|
|
}
|
|
}
|
|
|
|
/* If the first carry-chain pass, just above, ended up with a carry from
|
|
* input[9], and that caused input[0] to be out-of-bounds, then input[0] was
|
|
* < 2^26 + 2*19, because the carry was, at most, two.
|
|
*
|
|
* If the second pass carried from input[9] again then input[0] is < 2*19 and
|
|
* the input[9] -> input[0] carry didn't push input[0] out of bounds. */
|
|
|
|
/* It still remains the case that input might be between 2^255-19 and 2^255.
|
|
* In this case, input[1..9] must take their maximum value and input[0] must
|
|
* be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */
|
|
mask = int32_t_gte(input[0], 0x3ffffed);
|
|
for (i = 1; i < 10; i++) {
|
|
if ((i & 1) == 1) {
|
|
mask &= int32_t_eq(input[i], 0x1ffffff);
|
|
} else {
|
|
mask &= int32_t_eq(input[i], 0x3ffffff);
|
|
}
|
|
}
|
|
|
|
/* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
|
|
* this conditionally subtracts 2^255-19. */
|
|
input[0] -= mask & 0x3ffffed;
|
|
|
|
for (i = 1; i < 10; i++) {
|
|
if ((i & 1) == 1) {
|
|
input[i] -= mask & 0x1ffffff;
|
|
} else {
|
|
input[i] -= mask & 0x3ffffff;
|
|
}
|
|
}
|
|
|
|
input[1] <<= 2;
|
|
input[2] <<= 3;
|
|
input[3] <<= 5;
|
|
input[4] <<= 6;
|
|
input[6] <<= 1;
|
|
input[7] <<= 3;
|
|
input[8] <<= 4;
|
|
input[9] <<= 6;
|
|
#define F(i, s) \
|
|
output[s+0] |= input[i] & 0xff; \
|
|
output[s+1] = (input[i] >> 8) & 0xff; \
|
|
output[s+2] = (input[i] >> 16) & 0xff; \
|
|
output[s+3] = (input[i] >> 24) & 0xff;
|
|
output[0] = 0;
|
|
output[16] = 0;
|
|
F(0,0);
|
|
F(1,3);
|
|
F(2,6);
|
|
F(3,9);
|
|
F(4,12);
|
|
F(5,16);
|
|
F(6,19);
|
|
F(7,22);
|
|
F(8,25);
|
|
F(9,28);
|
|
#undef F
|
|
}
|
|
|
|
/* Input: Q, Q', Q-Q'
|
|
* Output: 2Q, Q+Q'
|
|
*
|
|
* x2 z3: long form
|
|
* x3 z3: long form
|
|
* x z: short form, destroyed
|
|
* xprime zprime: short form, destroyed
|
|
* qmqp: short form, preserved
|
|
*
|
|
* On entry and exit, the absolute value of the limbs of all inputs and outputs
|
|
* are < 2^26. */
|
|
static void fmonty(limb *x2, limb *z2, /* output 2Q */
|
|
limb *x3, limb *z3, /* output Q + Q' */
|
|
limb *x, limb *z, /* input Q */
|
|
limb *xprime, limb *zprime, /* input Q' */
|
|
const limb *qmqp /* input Q - Q' */)
|
|
{
|
|
limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
|
|
zzprime[19], zzzprime[19], xxxprime[19];
|
|
|
|
memcpy(origx, x, 10 * sizeof(limb));
|
|
fsum(x, z);
|
|
/* |x[i]| < 2^27 */
|
|
fdifference(z, origx); /* does x - z */
|
|
/* |z[i]| < 2^27 */
|
|
|
|
memcpy(origxprime, xprime, sizeof(limb) * 10);
|
|
fsum(xprime, zprime);
|
|
/* |xprime[i]| < 2^27 */
|
|
fdifference(zprime, origxprime);
|
|
/* |zprime[i]| < 2^27 */
|
|
fproduct(xxprime, xprime, z);
|
|
/* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
|
|
* 2^(27+27) and fproduct adds together, at most, 14 of those products.
|
|
* (Approximating that to 2^58 doesn't work out.) */
|
|
fproduct(zzprime, x, zprime);
|
|
/* |zzprime[i]| < 14*2^54 */
|
|
freduce_degree(xxprime);
|
|
freduce_coefficients(xxprime);
|
|
/* |xxprime[i]| < 2^26 */
|
|
freduce_degree(zzprime);
|
|
freduce_coefficients(zzprime);
|
|
/* |zzprime[i]| < 2^26 */
|
|
memcpy(origxprime, xxprime, sizeof(limb) * 10);
|
|
fsum(xxprime, zzprime);
|
|
/* |xxprime[i]| < 2^27 */
|
|
fdifference(zzprime, origxprime);
|
|
/* |zzprime[i]| < 2^27 */
|
|
fsquare(xxxprime, xxprime);
|
|
/* |xxxprime[i]| < 2^26 */
|
|
fsquare(zzzprime, zzprime);
|
|
/* |zzzprime[i]| < 2^26 */
|
|
fproduct(zzprime, zzzprime, qmqp);
|
|
/* |zzprime[i]| < 14*2^52 */
|
|
freduce_degree(zzprime);
|
|
freduce_coefficients(zzprime);
|
|
/* |zzprime[i]| < 2^26 */
|
|
memcpy(x3, xxxprime, sizeof(limb) * 10);
|
|
memcpy(z3, zzprime, sizeof(limb) * 10);
|
|
|
|
fsquare(xx, x);
|
|
/* |xx[i]| < 2^26 */
|
|
fsquare(zz, z);
|
|
/* |zz[i]| < 2^26 */
|
|
fproduct(x2, xx, zz);
|
|
/* |x2[i]| < 14*2^52 */
|
|
freduce_degree(x2);
|
|
freduce_coefficients(x2);
|
|
/* |x2[i]| < 2^26 */
|
|
fdifference(zz, xx); // does zz = xx - zz
|
|
/* |zz[i]| < 2^27 */
|
|
memset(zzz + 10, 0, sizeof(limb) * 9);
|
|
fscalar_product(zzz, zz, 121665);
|
|
/* |zzz[i]| < 2^(27+17) */
|
|
/* No need to call freduce_degree here:
|
|
fscalar_product doesn't increase the degree of its input. */
|
|
freduce_coefficients(zzz);
|
|
/* |zzz[i]| < 2^26 */
|
|
fsum(zzz, xx);
|
|
/* |zzz[i]| < 2^27 */
|
|
fproduct(z2, zz, zzz);
|
|
/* |z2[i]| < 14*2^(26+27) */
|
|
freduce_degree(z2);
|
|
freduce_coefficients(z2);
|
|
/* |z2|i| < 2^26 */
|
|
}
|
|
|
|
/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
|
|
* them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
|
|
* side-channel attacks.
|
|
*
|
|
* NOTE that this function requires that 'iswap' be 1 or 0; other values give
|
|
* wrong results. Also, the two limb arrays must be in reduced-coefficient,
|
|
* reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
|
|
* and all all values in a[0..9],b[0..9] must have magnitude less than
|
|
* INT32_MAX. */
|
|
static void swap_conditional(limb a[19], limb b[19], limb iswap)
|
|
{
|
|
unsigned i;
|
|
const int32_t swap = (int32_t) -iswap;
|
|
|
|
for (i = 0; i < 10; ++i) {
|
|
const int32_t x = swap & ( ((int32_t)a[i]) ^ ((int32_t)b[i]) );
|
|
a[i] = ((int32_t)a[i]) ^ x;
|
|
b[i] = ((int32_t)b[i]) ^ x;
|
|
}
|
|
}
|
|
|
|
/* Calculates nQ where Q is the x-coordinate of a point on the curve
|
|
*
|
|
* resultx/resultz: the x coordinate of the resulting curve point (short form)
|
|
* n: a little endian, 32-byte number
|
|
* q: a point of the curve (short form) */
|
|
static void cmult(limb *resultx, limb *resultz, const uint8_t *n, const limb *q)
|
|
{
|
|
limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
|
|
limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
|
|
limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
|
|
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
|
|
|
|
unsigned i, j;
|
|
|
|
memcpy(nqpqx, q, sizeof(limb) * 10);
|
|
|
|
for (i = 0; i < 32; ++i) {
|
|
uint8_t byte = n[31 - i];
|
|
for (j = 0; j < 8; ++j) {
|
|
const limb bit = byte >> 7;
|
|
|
|
swap_conditional(nqx, nqpqx, bit);
|
|
swap_conditional(nqz, nqpqz, bit);
|
|
fmonty(nqx2, nqz2,
|
|
nqpqx2, nqpqz2,
|
|
nqx, nqz,
|
|
nqpqx, nqpqz,
|
|
q);
|
|
swap_conditional(nqx2, nqpqx2, bit);
|
|
swap_conditional(nqz2, nqpqz2, bit);
|
|
|
|
t = nqx;
|
|
nqx = nqx2;
|
|
nqx2 = t;
|
|
t = nqz;
|
|
nqz = nqz2;
|
|
nqz2 = t;
|
|
t = nqpqx;
|
|
nqpqx = nqpqx2;
|
|
nqpqx2 = t;
|
|
t = nqpqz;
|
|
nqpqz = nqpqz2;
|
|
nqpqz2 = t;
|
|
|
|
byte <<= 1;
|
|
}
|
|
}
|
|
|
|
memcpy(resultx, nqx, sizeof(limb) * 10);
|
|
memcpy(resultz, nqz, sizeof(limb) * 10);
|
|
}
|
|
|
|
static void crecip(limb *out, const limb *z)
|
|
{
|
|
limb z2[10];
|
|
limb z9[10];
|
|
limb z11[10];
|
|
limb z2_5_0[10];
|
|
limb z2_10_0[10];
|
|
limb z2_20_0[10];
|
|
limb z2_50_0[10];
|
|
limb z2_100_0[10];
|
|
limb t0[10];
|
|
limb t1[10];
|
|
int i;
|
|
|
|
/* 2 */ fsquare(z2,z);
|
|
/* 4 */ fsquare(t1,z2);
|
|
/* 8 */ fsquare(t0,t1);
|
|
/* 9 */ fmul(z9,t0,z);
|
|
/* 11 */ fmul(z11,z9,z2);
|
|
/* 22 */ fsquare(t0,z11);
|
|
/* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
|
|
|
|
/* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
|
|
/* 2^7 - 2^2 */ fsquare(t1,t0);
|
|
/* 2^8 - 2^3 */ fsquare(t0,t1);
|
|
/* 2^9 - 2^4 */ fsquare(t1,t0);
|
|
/* 2^10 - 2^5 */ fsquare(t0,t1);
|
|
/* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
|
|
|
|
/* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
|
|
/* 2^12 - 2^2 */ fsquare(t1,t0);
|
|
/* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
|
|
/* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
|
|
|
|
/* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
|
|
/* 2^22 - 2^2 */ fsquare(t1,t0);
|
|
/* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
|
|
/* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
|
|
|
|
/* 2^41 - 2^1 */ fsquare(t1,t0);
|
|
/* 2^42 - 2^2 */ fsquare(t0,t1);
|
|
/* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
|
|
/* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
|
|
|
|
/* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
|
|
/* 2^52 - 2^2 */ fsquare(t1,t0);
|
|
/* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
|
|
/* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
|
|
|
|
/* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
|
|
/* 2^102 - 2^2 */ fsquare(t0,t1);
|
|
/* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
|
|
/* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
|
|
|
|
/* 2^201 - 2^1 */ fsquare(t0,t1);
|
|
/* 2^202 - 2^2 */ fsquare(t1,t0);
|
|
/* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
|
|
/* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
|
|
|
|
/* 2^251 - 2^1 */ fsquare(t1,t0);
|
|
/* 2^252 - 2^2 */ fsquare(t0,t1);
|
|
/* 2^253 - 2^3 */ fsquare(t1,t0);
|
|
/* 2^254 - 2^4 */ fsquare(t0,t1);
|
|
/* 2^255 - 2^5 */ fsquare(t1,t0);
|
|
/* 2^255 - 21 */ fmul(out,t1,z11);
|
|
}
|
|
|
|
void curve25519(uint8_t mypublic[CURVE25519_POINT_SIZE], const uint8_t secret[CURVE25519_POINT_SIZE], const uint8_t basepoint[CURVE25519_POINT_SIZE])
|
|
{
|
|
limb bp[10], x[10], z[11], zmone[10];
|
|
uint8_t e[32];
|
|
|
|
memcpy(e, secret, 32);
|
|
normalize_secret(e);
|
|
|
|
fexpand(bp, basepoint);
|
|
cmult(x, z, e, bp);
|
|
crecip(zmone, z);
|
|
fmul(z, x, zmone);
|
|
fcontract(mypublic, z);
|
|
|
|
memzero_explicit(e, sizeof(e));
|
|
memzero_explicit(bp, sizeof(bp));
|
|
memzero_explicit(x, sizeof(x));
|
|
memzero_explicit(z, sizeof(z));
|
|
memzero_explicit(zmone, sizeof(zmone));
|
|
}
|
|
#endif
|
|
|
|
|
|
void curve25519_generate_secret(uint8_t secret[CURVE25519_POINT_SIZE])
|
|
{
|
|
get_random_bytes(secret, CURVE25519_POINT_SIZE);
|
|
normalize_secret(secret);
|
|
}
|
|
|
|
void curve25519_generate_public(uint8_t pub[CURVE25519_POINT_SIZE], const uint8_t secret[CURVE25519_POINT_SIZE])
|
|
{
|
|
static const uint8_t basepoint[CURVE25519_POINT_SIZE] = { 9 };
|
|
curve25519(pub, secret, basepoint);
|
|
}
|
|
|
|
#ifdef DEBUG
|
|
struct curve25519_test_vector {
|
|
uint8_t private[CURVE25519_POINT_SIZE];
|
|
uint8_t public[CURVE25519_POINT_SIZE];
|
|
uint8_t result[CURVE25519_POINT_SIZE];
|
|
};
|
|
static const struct curve25519_test_vector curve25519_test_vectors[] = {
|
|
{
|
|
.private = { 0x77, 0x07, 0x6d, 0x0a, 0x73, 0x18, 0xa5, 0x7d, 0x3c, 0x16, 0xc1, 0x72, 0x51, 0xb2, 0x66, 0x45, 0xdf, 0x4c, 0x2f, 0x87, 0xeb, 0xc0, 0x99, 0x2a, 0xb1, 0x77, 0xfb, 0xa5, 0x1d, 0xb9, 0x2c, 0x2a },
|
|
.public = { 0xde, 0x9e, 0xdb, 0x7d, 0x7b, 0x7d, 0xc1, 0xb4, 0xd3, 0x5b, 0x61, 0xc2, 0xec, 0xe4, 0x35, 0x37, 0x3f, 0x83, 0x43, 0xc8, 0x5b, 0x78, 0x67, 0x4d, 0xad, 0xfc, 0x7e, 0x14, 0x6f, 0x88, 0x2b, 0x4f },
|
|
.result = { 0x4a, 0x5d, 0x9d, 0x5b, 0xa4, 0xce, 0x2d, 0xe1, 0x72, 0x8e, 0x3b, 0xf4, 0x80, 0x35, 0x0f, 0x25, 0xe0, 0x7e, 0x21, 0xc9, 0x47, 0xd1, 0x9e, 0x33, 0x76, 0xf0, 0x9b, 0x3c, 0x1e, 0x16, 0x17, 0x42 }
|
|
},
|
|
{
|
|
.private = { 0x5d, 0xab, 0x08, 0x7e, 0x62, 0x4a, 0x8a, 0x4b, 0x79, 0xe1, 0x7f, 0x8b, 0x83, 0x80, 0x0e, 0xe6, 0x6f, 0x3b, 0xb1, 0x29, 0x26, 0x18, 0xb6, 0xfd, 0x1c, 0x2f, 0x8b, 0x27, 0xff, 0x88, 0xe0, 0xeb },
|
|
.public = { 0x85, 0x20, 0xf0, 0x09, 0x89, 0x30, 0xa7, 0x54, 0x74, 0x8b, 0x7d, 0xdc, 0xb4, 0x3e, 0xf7, 0x5a, 0x0d, 0xbf, 0x3a, 0x0d, 0x26, 0x38, 0x1a, 0xf4, 0xeb, 0xa4, 0xa9, 0x8e, 0xaa, 0x9b, 0x4e, 0x6a },
|
|
.result = { 0x4a, 0x5d, 0x9d, 0x5b, 0xa4, 0xce, 0x2d, 0xe1, 0x72, 0x8e, 0x3b, 0xf4, 0x80, 0x35, 0x0f, 0x25, 0xe0, 0x7e, 0x21, 0xc9, 0x47, 0xd1, 0x9e, 0x33, 0x76, 0xf0, 0x9b, 0x3c, 0x1e, 0x16, 0x17, 0x42 }
|
|
},
|
|
{
|
|
.private = { 1 },
|
|
.public = { 0x25, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
|
|
.result = { 0x3c, 0x77, 0x77, 0xca, 0xf9, 0x97, 0xb2, 0x64, 0x41, 0x60, 0x77, 0x66, 0x5b, 0x4e, 0x22, 0x9d, 0xb, 0x95, 0x48, 0xdc, 0xc, 0xd8, 0x19, 0x98, 0xdd, 0xcd, 0xc5, 0xc8, 0x53, 0x3c, 0x79, 0x7f }
|
|
},
|
|
{
|
|
.private = { 1 },
|
|
.public = { 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff },
|
|
.result = { 0xb3, 0x2d, 0x13, 0x62, 0xc2, 0x48, 0xd6, 0x2f, 0xe6, 0x26, 0x19, 0xcf, 0xf0, 0x4d, 0xd4, 0x3d, 0xb7, 0x3f, 0xfc, 0x1b, 0x63, 0x8, 0xed, 0xe3, 0xb, 0x78, 0xd8, 0x73, 0x80, 0xf1, 0xe8, 0x34 }
|
|
},
|
|
{
|
|
.private = { 0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d, 0x3b, 0x16, 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd, 0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc, 0x5a, 0x18, 0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4 },
|
|
.public = { 0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb, 0x35, 0x94, 0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c, 0x72, 0x66, 0x24, 0xec, 0x26, 0xb3, 0x35, 0x3b, 0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c },
|
|
.result = { 0xc3, 0xda, 0x55, 0x37, 0x9d, 0xe9, 0xc6, 0x90, 0x8e, 0x94, 0xea, 0x4d, 0xf2, 0x8d, 0x08, 0x4f, 0x32, 0xec, 0xcf, 0x03, 0x49, 0x1c, 0x71, 0xf7, 0x54, 0xb4, 0x07, 0x55, 0x77, 0xa2, 0x85, 0x52 }
|
|
},
|
|
{
|
|
.private = { 1, 2, 3, 4 },
|
|
.public = { 0 },
|
|
.result = { 0 }
|
|
},
|
|
{
|
|
.private = { 2, 4, 6, 8 },
|
|
.public = { 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8 },
|
|
.result = { 0 }
|
|
}
|
|
};
|
|
void curve25519_selftest(void)
|
|
{
|
|
bool success = true;
|
|
size_t i = 0;
|
|
uint8_t out[CURVE25519_POINT_SIZE];
|
|
|
|
for (i = 0; i < ARRAY_SIZE(curve25519_test_vectors); ++i) {
|
|
memset(out, 0, CURVE25519_POINT_SIZE);
|
|
curve25519(out, curve25519_test_vectors[i].private, curve25519_test_vectors[i].public);
|
|
if (memcmp(out, curve25519_test_vectors[i].result, CURVE25519_POINT_SIZE)) {
|
|
pr_info("curve25519 self-test %zu: FAIL\n", i + 1);
|
|
success = false;
|
|
return;
|
|
}
|
|
}
|
|
|
|
if (success)
|
|
pr_info("curve25519 self-tests: pass\n");
|
|
}
|
|
#endif
|