/* This Source Code Form is subject to the terms of the Mozilla Public * License, v. 2.0. If a copy of the MPL was not distributed with this * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ /* * Derived from public domain code by Matthew Dempsky and D. J. Bernstein. */ #include "ecl-priv.h" #include "mpi.h" #include <stdint.h> #include <stdio.h> typedef uint32_t elem[32]; /* * Add two field elements. * out = a + b */ static void add(elem out, const elem a, const elem b) { uint32_t j; uint32_t u = 0; for (j = 0; j < 31; ++j) { u += a[j] + b[j]; out[j] = u & 0xFF; u >>= 8; } u += a[31] + b[31]; out[31] = u; } /* * Subtract two field elements. * out = a - b */ static void sub(elem out, const elem a, const elem b) { uint32_t j; uint32_t u; u = 218; for (j = 0; j < 31; ++j) { u += a[j] + 0xFF00 - b[j]; out[j] = u & 0xFF; u >>= 8; } u += a[31] - b[31]; out[31] = u; } /* * "Squeeze" an element after multiplication (and square). */ static void squeeze(elem a) { uint32_t j; uint32_t u; u = 0; for (j = 0; j < 31; ++j) { u += a[j]; a[j] = u & 0xFF; u >>= 8; } u += a[31]; a[31] = u & 0x7F; u = 19 * (u >> 7); for (j = 0; j < 31; ++j) { u += a[j]; a[j] = u & 0xFF; u >>= 8; } a[31] += u; } static const elem minusp = { 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128 }; /* * Reduce point a by 2^255-19 */ static void reduce(elem a) { elem aorig; uint32_t j; uint32_t negative; for (j = 0; j < 32; ++j) { aorig[j] = a[j]; } add(a, a, minusp); negative = 1 + ~((a[31] >> 7) & 1); for (j = 0; j < 32; ++j) { a[j] ^= negative & (aorig[j] ^ a[j]); } } /* * Multiplication and squeeze * out = a * b */ static void mult(elem out, const elem a, const elem b) { uint32_t i; uint32_t j; uint32_t u; for (i = 0; i < 32; ++i) { u = 0; for (j = 0; j <= i; ++j) { u += a[j] * b[i - j]; } for (j = i + 1; j < 32; ++j) { u += 38 * a[j] * b[i + 32 - j]; } out[i] = u; } squeeze(out); } /* * Multiplication * out = 121665 * a */ static void mult121665(elem out, const elem a) { uint32_t j; uint32_t u; u = 0; for (j = 0; j < 31; ++j) { u += 121665 * a[j]; out[j] = u & 0xFF; u >>= 8; } u += 121665 * a[31]; out[31] = u & 0x7F; u = 19 * (u >> 7); for (j = 0; j < 31; ++j) { u += out[j]; out[j] = u & 0xFF; u >>= 8; } u += out[j]; out[j] = u; } /* * Square a and squeeze the result. * out = a * a */ static void square(elem out, const elem a) { uint32_t i; uint32_t j; uint32_t u; for (i = 0; i < 32; ++i) { u = 0; for (j = 0; j < i - j; ++j) { u += a[j] * a[i - j]; } for (j = i + 1; j < i + 32 - j; ++j) { u += 38 * a[j] * a[i + 32 - j]; } u *= 2; if ((i & 1) == 0) { u += a[i / 2] * a[i / 2]; u += 38 * a[i / 2 + 16] * a[i / 2 + 16]; } out[i] = u; } squeeze(out); } /* * Constant time swap between r and s depending on b */ static void cswap(uint32_t p[64], uint32_t q[64], uint32_t b) { uint32_t j; uint32_t swap = 1 + ~b; for (j = 0; j < 64; ++j) { const uint32_t t = swap & (p[j] ^ q[j]); p[j] ^= t; q[j] ^= t; } } /* * Montgomery ladder */ static void monty(elem x_2_out, elem z_2_out, const elem point, const elem scalar) { uint32_t x_3[64] = { 0 }; uint32_t x_2[64] = { 0 }; uint32_t a0[64]; uint32_t a1[64]; uint32_t b0[64]; uint32_t b1[64]; uint32_t c1[64]; uint32_t r[32]; uint32_t s[32]; uint32_t t[32]; uint32_t u[32]; uint32_t swap = 0; uint32_t k_t = 0; int j; for (j = 0; j < 32; ++j) { x_3[j] = point[j]; } x_3[32] = 1; x_2[0] = 1; for (j = 254; j >= 0; --j) { k_t = (scalar[j >> 3] >> (j & 7)) & 1; swap ^= k_t; cswap(x_2, x_3, swap); swap = k_t; add(a0, x_2, x_2 + 32); sub(a0 + 32, x_2, x_2 + 32); add(a1, x_3, x_3 + 32); sub(a1 + 32, x_3, x_3 + 32); square(b0, a0); square(b0 + 32, a0 + 32); mult(b1, a1, a0 + 32); mult(b1 + 32, a1 + 32, a0); add(c1, b1, b1 + 32); sub(c1 + 32, b1, b1 + 32); square(r, c1 + 32); sub(s, b0, b0 + 32); mult121665(t, s); add(u, t, b0); mult(x_2, b0, b0 + 32); mult(x_2 + 32, s, u); square(x_3, c1); mult(x_3 + 32, r, point); } cswap(x_2, x_3, swap); for (j = 0; j < 32; ++j) { x_2_out[j] = x_2[j]; } for (j = 0; j < 32; ++j) { z_2_out[j] = x_2[j + 32]; } } static void recip(elem out, const elem z) { elem z2; elem z9; elem z11; elem z2_5_0; elem z2_10_0; elem z2_20_0; elem z2_50_0; elem z2_100_0; elem t0; elem t1; int i; /* 2 */ square(z2, z); /* 4 */ square(t1, z2); /* 8 */ square(t0, t1); /* 9 */ mult(z9, t0, z); /* 11 */ mult(z11, z9, z2); /* 22 */ square(t0, z11); /* 2^5 - 2^0 = 31 */ mult(z2_5_0, t0, z9); /* 2^6 - 2^1 */ square(t0, z2_5_0); /* 2^7 - 2^2 */ square(t1, t0); /* 2^8 - 2^3 */ square(t0, t1); /* 2^9 - 2^4 */ square(t1, t0); /* 2^10 - 2^5 */ square(t0, t1); /* 2^10 - 2^0 */ mult(z2_10_0, t0, z2_5_0); /* 2^11 - 2^1 */ square(t0, z2_10_0); /* 2^12 - 2^2 */ square(t1, t0); /* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) { square(t0, t1); square(t1, t0); } /* 2^20 - 2^0 */ mult(z2_20_0, t1, z2_10_0); /* 2^21 - 2^1 */ square(t0, z2_20_0); /* 2^22 - 2^2 */ square(t1, t0); /* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) { square(t0, t1); square(t1, t0); } /* 2^40 - 2^0 */ mult(t0, t1, z2_20_0); /* 2^41 - 2^1 */ square(t1, t0); /* 2^42 - 2^2 */ square(t0, t1); /* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) { square(t1, t0); square(t0, t1); } /* 2^50 - 2^0 */ mult(z2_50_0, t0, z2_10_0); /* 2^51 - 2^1 */ square(t0, z2_50_0); /* 2^52 - 2^2 */ square(t1, t0); /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) { square(t0, t1); square(t1, t0); } /* 2^100 - 2^0 */ mult(z2_100_0, t1, z2_50_0); /* 2^101 - 2^1 */ square(t1, z2_100_0); /* 2^102 - 2^2 */ square(t0, t1); /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) { square(t1, t0); square(t0, t1); } /* 2^200 - 2^0 */ mult(t1, t0, z2_100_0); /* 2^201 - 2^1 */ square(t0, t1); /* 2^202 - 2^2 */ square(t1, t0); /* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) { square(t0, t1); square(t1, t0); } /* 2^250 - 2^0 */ mult(t0, t1, z2_50_0); /* 2^251 - 2^1 */ square(t1, t0); /* 2^252 - 2^2 */ square(t0, t1); /* 2^253 - 2^3 */ square(t1, t0); /* 2^254 - 2^4 */ square(t0, t1); /* 2^255 - 2^5 */ square(t1, t0); /* 2^255 - 21 */ mult(out, t1, z11); } /* * Computes q = Curve25519(p, s) */ SECStatus ec_Curve25519_mul(PRUint8 *q, const PRUint8 *s, const PRUint8 *p) { elem point = { 0 }; elem x_2 = { 0 }; elem z_2 = { 0 }; elem X = { 0 }; elem scalar = { 0 }; uint32_t i; /* read and mask scalar */ for (i = 0; i < 32; ++i) { scalar[i] = s[i]; } scalar[0] &= 0xF8; scalar[31] &= 0x7F; scalar[31] |= 64; /* read and mask point */ for (i = 0; i < 32; ++i) { point[i] = p[i]; } point[31] &= 0x7F; monty(x_2, z_2, point, scalar); recip(z_2, z_2); mult(X, x_2, z_2); reduce(X); for (i = 0; i < 32; ++i) { q[i] = X[i]; } return 0; }