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Diffstat (limited to 'src/crypto/curve25519.c')
-rw-r--r-- | src/crypto/curve25519.c | 1304 |
1 files changed, 1304 insertions, 0 deletions
diff --git a/src/crypto/curve25519.c b/src/crypto/curve25519.c new file mode 100644 index 0000000..8b75aa0 --- /dev/null +++ b/src/crypto/curve25519.c @@ -0,0 +1,1304 @@ +/* Original author: Adam Langley <agl@imperialviolet.org> + * + * Copyright 2008 Google Inc. All Rights Reserved. + * Copyright 2015-2016 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved. + */ + +#include "../wireguard.h" +#include "curve25519.h" +#include <linux/string.h> +#include <linux/random.h> +#include <crypto/algapi.h> + +static __always_inline void normalize_secret(uint8_t secret[CURVE25519_POINT_SIZE]) +{ + secret[0] &= 248; + secret[31] &= 127; + secret[31] |= 64; +} + +static const uint8_t zeros[CURVE25519_POINT_SIZE] = { 0 }; + +#ifdef __SIZEOF_INT128__ +typedef uint64_t limb; +typedef limb felem[5]; +typedef __uint128_t uint128_t; + +/* Sum two numbers: output += in */ +static __always_inline void fsum(limb *output, const limb *in) +{ + output[0] += in[0]; + output[1] += in[1]; + output[2] += in[2]; + output[3] += in[3]; + output[4] += in[4]; +} + +/* Find the difference of two numbers: output = in - output + * (note the order of the arguments!) + * + * Assumes that out[i] < 2**52 + * On return, out[i] < 2**55 + */ +static __always_inline void fdifference_backwards(felem out, const felem in) +{ + /* 152 is 19 << 3 */ + static const limb two54m152 = (((limb)1) << 54) - 152; + static const limb two54m8 = (((limb)1) << 54) - 8; + + out[0] = in[0] + two54m152 - out[0]; + out[1] = in[1] + two54m8 - out[1]; + out[2] = in[2] + two54m8 - out[2]; + out[3] = in[3] + two54m8 - out[3]; + out[4] = in[4] + two54m8 - out[4]; +} + +/* Multiply a number by a scalar: output = in * scalar */ +static __always_inline void fscalar_product(felem output, const felem in, const limb scalar) +{ + uint128_t a; + + a = ((uint128_t) in[0]) * scalar; + output[0] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((uint128_t) in[1]) * scalar + ((limb) (a >> 51)); + output[1] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((uint128_t) in[2]) * scalar + ((limb) (a >> 51)); + output[2] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((uint128_t) in[3]) * scalar + ((limb) (a >> 51)); + output[3] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((uint128_t) in[4]) * scalar + ((limb) (a >> 51)); + output[4] = ((limb)a) & 0x7ffffffffffffUL; + + output[0] += (a >> 51) * 19; +} + +/* Multiply two numbers: output = in2 * in + * + * output must be distinct to both inputs. The inputs are reduced coefficient + * form, the output is not. + * + * Assumes that in[i] < 2**55 and likewise for in2. + * On return, output[i] < 2**52 + */ +static __always_inline void fmul(felem output, const felem in2, const felem in) +{ + uint128_t t[5]; + limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + + s0 = in2[0]; + s1 = in2[1]; + s2 = in2[2]; + s3 = in2[3]; + s4 = in2[4]; + + t[0] = ((uint128_t) r0) * s0; + t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0; + t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1; + t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1; + t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2; + + r4 *= 19; + r1 *= 19; + r2 *= 19; + r3 *= 19; + + t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2; + t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3; + t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4; + t[3] += ((uint128_t) r4) * s4; + + r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51); + t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51); + t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51); + t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51); + t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51); + r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL; + r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL; + r2 += c; + + output[0] = r0; + output[1] = r1; + output[2] = r2; + output[3] = r3; + output[4] = r4; +} + +static __always_inline void fsquare_times(felem output, const felem in, limb count) +{ + uint128_t t[5]; + limb r0,r1,r2,r3,r4,c; + limb d0,d1,d2,d4,d419; + + r0 = in[0]; + r1 = in[1]; + r2 = in[2]; + r3 = in[3]; + r4 = in[4]; + + do { + d0 = r0 * 2; + d1 = r1 * 2; + d2 = r2 * 2 * 19; + d419 = r4 * 19; + d4 = d419 * 2; + + t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 )); + t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19)); + t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 )); + t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 )); + t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 )); + + r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51); + t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51); + t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51); + t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51); + t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51); + r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL; + r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL; + r2 += c; + } while(--count); + + output[0] = r0; + output[1] = r1; + output[2] = r2; + output[3] = r3; + output[4] = r4; +} + +/* Load a little-endian 64-bit number */ +static inline limb load_limb(const uint8_t *in) +{ + return le64_to_cpu(*(uint64_t *)in); +} + +static inline void store_limb(uint8_t *out, limb in) +{ + *(uint64_t *)out = cpu_to_le64(in); +} + +/* Take a little-endian, 32-byte number and expand it into polynomial form */ +static inline void fexpand(limb *output, const uint8_t *in) +{ + output[0] = load_limb(in) & 0x7ffffffffffffUL; + output[1] = (load_limb(in + 6) >> 3) & 0x7ffffffffffffUL; + output[2] = (load_limb(in + 12) >> 6) & 0x7ffffffffffffUL; + output[3] = (load_limb(in + 19) >> 1) & 0x7ffffffffffffUL; + output[4] = (load_limb(in + 24) >> 12) & 0x7ffffffffffffUL; +} + +/* Take a fully reduced polynomial form number and contract it into a + * little-endian, 32-byte array + */ +static void fcontract(uint8_t *output, const felem input) +{ + uint128_t t[5]; + + t[0] = input[0]; + t[1] = input[1]; + t[2] = input[2]; + t[3] = input[3]; + t[4] = input[4]; + + t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; + t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; + t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; + t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; + t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; + + t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; + t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; + t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; + t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; + t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; + + /* now t is between 0 and 2^255-1, properly carried. */ + /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ + + t[0] += 19; + + t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; + t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; + t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; + t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; + t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL; + + /* now between 19 and 2^255-1 in both cases, and offset by 19. */ + + t[0] += 0x8000000000000UL - 19; + t[1] += 0x8000000000000UL - 1; + t[2] += 0x8000000000000UL - 1; + t[3] += 0x8000000000000UL - 1; + t[4] += 0x8000000000000UL - 1; + + /* now between 2^255 and 2^256-20, and offset by 2^255. */ + + t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL; + t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL; + t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL; + t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL; + t[4] &= 0x7ffffffffffffUL; + + store_limb(output, t[0] | (t[1] << 51)); + store_limb(output+8, (t[1] >> 13) | (t[2] << 38)); + store_limb(output+16, (t[2] >> 26) | (t[3] << 25)); + store_limb(output+24, (t[3] >> 39) | (t[4] << 12)); +} + +/* 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 + */ +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[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5]; + + memcpy(origx, x, 5 * sizeof(limb)); + fsum(x, z); + fdifference_backwards(z, origx); // does x - z + + memcpy(origxprime, xprime, sizeof(limb) * 5); + fsum(xprime, zprime); + fdifference_backwards(zprime, origxprime); + fmul(xxprime, xprime, z); + fmul(zzprime, x, zprime); + memcpy(origxprime, xxprime, sizeof(limb) * 5); + fsum(xxprime, zzprime); + fdifference_backwards(zzprime, origxprime); + fsquare_times(x3, xxprime, 1); + fsquare_times(zzzprime, zzprime, 1); + fmul(z3, zzzprime, qmqp); + + fsquare_times(xx, x, 1); + fsquare_times(zz, z, 1); + fmul(x2, xx, zz); + fdifference_backwards(zz, xx); // does zz = xx - zz + fscalar_product(zzz, zz, 121665); + fsum(zzz, xx); + fmul(z2, zz, zzz); +} + +/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements + * long. Perform the swap iff @swap is non-zero. + * + * This function performs the swap without leaking any side-channel + * information. + */ +static void swap_conditional(limb a[5], limb b[5], limb iswap) +{ + unsigned i; + const limb swap = -iswap; + + for (i = 0; i < 5; ++i) { + const limb x = swap & (a[i] ^ b[i]); + a[i] ^= x; + 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[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0}; + limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; + limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1}; + limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; + + unsigned i, j; + + memcpy(nqpqx, q, sizeof(limb) * 5); + + 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) * 5); + memcpy(resultz, nqz, sizeof(limb) * 5); +} + +static void crecip(felem out, const felem z) +{ + felem a,t0,b,c; + + /* 2 */ fsquare_times(a, z, 1); // a = 2 + /* 8 */ fsquare_times(t0, a, 2); + /* 9 */ fmul(b, t0, z); // b = 9 + /* 11 */ fmul(a, b, a); // a = 11 + /* 22 */ fsquare_times(t0, a, 1); + /* 2^5 - 2^0 = 31 */ fmul(b, t0, b); + /* 2^10 - 2^5 */ fsquare_times(t0, b, 5); + /* 2^10 - 2^0 */ fmul(b, t0, b); + /* 2^20 - 2^10 */ fsquare_times(t0, b, 10); + /* 2^20 - 2^0 */ fmul(c, t0, b); + /* 2^40 - 2^20 */ fsquare_times(t0, c, 20); + /* 2^40 - 2^0 */ fmul(t0, t0, c); + /* 2^50 - 2^10 */ fsquare_times(t0, t0, 10); + /* 2^50 - 2^0 */ fmul(b, t0, b); + /* 2^100 - 2^50 */ fsquare_times(t0, b, 50); + /* 2^100 - 2^0 */ fmul(c, t0, b); + /* 2^200 - 2^100 */ fsquare_times(t0, c, 100); + /* 2^200 - 2^0 */ fmul(t0, t0, c); + /* 2^250 - 2^50 */ fsquare_times(t0, t0, 50); + /* 2^250 - 2^0 */ fmul(t0, t0, b); + /* 2^255 - 2^5 */ fsquare_times(t0, t0, 5); + /* 2^255 - 21 */ fmul(out, t0, a); +} + +void curve25519(uint8_t mypublic[CURVE25519_POINT_SIZE], const uint8_t secret[CURVE25519_POINT_SIZE], const uint8_t basepoint[CURVE25519_POINT_SIZE]) +{ + 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 |