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Diffstat (limited to 'src/crypto/curve25519-u128.h')
| -rw-r--r-- | src/crypto/curve25519-u128.h | 408 |
1 files changed, 408 insertions, 0 deletions
diff --git a/src/crypto/curve25519-u128.h b/src/crypto/curve25519-u128.h new file mode 100644 index 0000000..9f9ab20 --- /dev/null +++ b/src/crypto/curve25519-u128.h @@ -0,0 +1,408 @@ +/* SPDX-License-Identifier: GPL-2.0 + * + * Copyright (C) 2008 Google Inc. All Rights Reserved. + * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved. + * + * Original author: Adam Langley <agl@imperialviolet.org> + */ + +typedef u64 limb; +typedef limb felem[5]; +typedef __uint128_t u128; + +/* 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) +{ + u128 a; + + a = ((u128) in[0]) * scalar; + output[0] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((u128) in[1]) * scalar + ((limb) (a >> 51)); + output[1] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((u128) in[2]) * scalar + ((limb) (a >> 51)); + output[2] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((u128) in[3]) * scalar + ((limb) (a >> 51)); + output[3] = ((limb)a) & 0x7ffffffffffffUL; + + a = ((u128) 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) +{ + u128 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] = ((u128) r0) * s0; + t[1] = ((u128) r0) * s1 + ((u128) r1) * s0; + t[2] = ((u128) r0) * s2 + ((u128) r2) * s0 + ((u128) r1) * s1; + t[3] = ((u128) r0) * s3 + ((u128) r3) * s0 + ((u128) r1) * s2 + ((u128) r2) * s1; + t[4] = ((u128) r0) * s4 + ((u128) r4) * s0 + ((u128) r3) * s1 + ((u128) r1) * s3 + ((u128) r2) * s2; + + r4 *= 19; + r1 *= 19; + r2 *= 19; + r3 *= 19; + + t[0] += ((u128) r4) * s1 + ((u128) r1) * s4 + ((u128) r2) * s3 + ((u128) r3) * s2; + t[1] += ((u128) r4) * s2 + ((u128) r2) * s4 + ((u128) r3) * s3; + t[2] += ((u128) r4) * s3 + ((u128) r3) * s4; + t[3] += ((u128) 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) +{ + u128 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] = ((u128) r0) * r0 + ((u128) d4) * r1 + (((u128) d2) * (r3 )); + t[1] = ((u128) d0) * r1 + ((u128) d4) * r2 + (((u128) r3) * (r3 * 19)); + t[2] = ((u128) d0) * r2 + ((u128) r1) * r1 + (((u128) d4) * (r3 )); + t[3] = ((u128) d0) * r3 + ((u128) d1) * r2 + (((u128) r4) * (d419 )); + t[4] = ((u128) d0) * r4 + ((u128) d1) * r3 + (((u128) 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 u8 *in) +{ + return le64_to_cpu(*(__le64 *)in); +} + +static inline void store_limb(u8 *out, limb in) +{ + *(__le64 *)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 u8 *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(u8 *output, const felem input) +{ + u128 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 int 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 u8 *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 int i, j; + + memcpy(nqpqx, q, sizeof(limb) * 5); + + for (i = 0; i < 32; ++i) { + u8 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); +} + +static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE]) +{ + limb bp[5], x[5], z[5], zmone[5]; + u8 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)); + + return true; +} |