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-rw-r--r--src/libcryptobox/curve25519/curve25519-donna-c64.c505
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diff --git a/src/libcryptobox/curve25519/curve25519-donna-c64.c b/src/libcryptobox/curve25519/curve25519-donna-c64.c
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-/* Copyright 2008, Google Inc.
- * All rights reserved.
- *
- * Code released into the public domain.
- *
- * curve25519-donna: Curve25519 elliptic curve, public key function
- *
- * http://code.google.com/p/curve25519-donna/
- *
- * Adam Langley <agl@imperialviolet.org>
- *
- * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
- *
- * More information about curve25519 can be found here
- * http://cr.yp.to/ecdh.html
- *
- * djb's sample implementation of curve25519 is written in a special assembly
- * language called qhasm and uses the floating point registers.
- *
- * This is, almost, a clean room reimplementation from the curve25519 paper. It
- * uses many of the tricks described therein. Only the crecip function is taken
- * from the sample implementation.
- */
-
-#include <string.h>
-#include <stdint.h>
-#include "curve25519.h"
-
-typedef uint8_t u8;
-typedef uint64_t limb;
-typedef limb felem[5];
-// This is a special gcc mode for 128-bit integers. It's implemented on 64-bit
-// platforms only as far as I know.
-typedef unsigned uint128_t __attribute__((mode(TI)));
-
-#undef force_inline
-#define force_inline __attribute__((always_inline))
-
-/* Sum two numbers: output += in */
-static inline void force_inline
-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 inline void force_inline
-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 inline void force_inline
-fscalar_product (felem output, const felem in, const limb scalar)
-{
- uint128_t a;
-
- a = ((uint128_t) in[0]) * scalar;
- output[0] = ((limb) a) & 0x7ffffffffffff;
-
- a = ((uint128_t) in[1]) * scalar + ((limb) (a >> 51));
- output[1] = ((limb) a) & 0x7ffffffffffff;
-
- a = ((uint128_t) in[2]) * scalar + ((limb) (a >> 51));
- output[2] = ((limb) a) & 0x7ffffffffffff;
-
- a = ((uint128_t) in[3]) * scalar + ((limb) (a >> 51));
- output[3] = ((limb) a) & 0x7ffffffffffff;
-
- a = ((uint128_t) in[4]) * scalar + ((limb) (a >> 51));
- output[4] = ((limb) a) & 0x7ffffffffffff;
-
- 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 inline void force_inline
-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] & 0x7ffffffffffff;
- c = (limb) (t[0] >> 51);
- t[1] += c;
- r1 = (limb) t[1] & 0x7ffffffffffff;
- c = (limb) (t[1] >> 51);
- t[2] += c;
- r2 = (limb) t[2] & 0x7ffffffffffff;
- c = (limb) (t[2] >> 51);
- t[3] += c;
- r3 = (limb) t[3] & 0x7ffffffffffff;
- c = (limb) (t[3] >> 51);
- t[4] += c;
- r4 = (limb) t[4] & 0x7ffffffffffff;
- c = (limb) (t[4] >> 51);
- r0 += c * 19;
- c = r0 >> 51;
- r0 = r0 & 0x7ffffffffffff;
- r1 += c;
- c = r1 >> 51;
- r1 = r1 & 0x7ffffffffffff;
- r2 += c;
-
- output[0] = r0;
- output[1] = r1;
- output[2] = r2;
- output[3] = r3;
- output[4] = r4;
-}
-
-static inline void force_inline
-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] & 0x7ffffffffffff;
- c = (limb) (t[0] >> 51);
- t[1] += c;
- r1 = (limb) t[1] & 0x7ffffffffffff;
- c = (limb) (t[1] >> 51);
- t[2] += c;
- r2 = (limb) t[2] & 0x7ffffffffffff;
- c = (limb) (t[2] >> 51);
- t[3] += c;
- r3 = (limb) t[3] & 0x7ffffffffffff;
- c = (limb) (t[3] >> 51);
- t[4] += c;
- r4 = (limb) t[4] & 0x7ffffffffffff;
- c = (limb) (t[4] >> 51);
- r0 += c * 19;
- c = r0 >> 51;
- r0 = r0 & 0x7ffffffffffff;
- r1 += c;
- c = r1 >> 51;
- r1 = r1 & 0x7ffffffffffff;
- 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 limb load_limb (const u8 *in)
-{
- return ((limb) in[0]) | (((limb) in[1]) << 8) | (((limb) in[2]) << 16)
- | (((limb) in[3]) << 24) | (((limb) in[4]) << 32)
- | (((limb) in[5]) << 40) | (((limb) in[6]) << 48)
- | (((limb) in[7]) << 56);
-}
-
-static void store_limb (u8 *out, limb in)
-{
- out[0] = in & 0xff;
- out[1] = (in >> 8) & 0xff;
- out[2] = (in >> 16) & 0xff;
- out[3] = (in >> 24) & 0xff;
- out[4] = (in >> 32) & 0xff;
- out[5] = (in >> 40) & 0xff;
- out[6] = (in >> 48) & 0xff;
- out[7] = (in >> 56) & 0xff;
-}
-
-/* Take a little-endian, 32-byte number and expand it into polynomial form */
-static void fexpand (limb *output, const u8 *in)
-{
- output[0] = load_limb (in) & 0x7ffffffffffff;
- output[1] = (load_limb (in + 6) >> 3) & 0x7ffffffffffff;
- output[2] = (load_limb (in + 12) >> 6) & 0x7ffffffffffff;
- output[3] = (load_limb (in + 19) >> 1) & 0x7ffffffffffff;
- output[4] = (load_limb (in + 24) >> 12) & 0x7ffffffffffff;
-}
-
-/* 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)
-{
- 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] &= 0x7ffffffffffff;
- t[2] += t[1] >> 51;
- t[1] &= 0x7ffffffffffff;
- t[3] += t[2] >> 51;
- t[2] &= 0x7ffffffffffff;
- t[4] += t[3] >> 51;
- t[3] &= 0x7ffffffffffff;
- t[0] += 19 * (t[4] >> 51);
- t[4] &= 0x7ffffffffffff;
-
- t[1] += t[0] >> 51;
- t[0] &= 0x7ffffffffffff;
- t[2] += t[1] >> 51;
- t[1] &= 0x7ffffffffffff;
- t[3] += t[2] >> 51;
- t[2] &= 0x7ffffffffffff;
- t[4] += t[3] >> 51;
- t[3] &= 0x7ffffffffffff;
- t[0] += 19 * (t[4] >> 51);
- t[4] &= 0x7ffffffffffff;
-
- /* 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] &= 0x7ffffffffffff;
- t[2] += t[1] >> 51;
- t[1] &= 0x7ffffffffffff;
- t[3] += t[2] >> 51;
- t[2] &= 0x7ffffffffffff;
- t[4] += t[3] >> 51;
- t[3] &= 0x7ffffffffffff;
- t[0] += 19 * (t[4] >> 51);
- t[4] &= 0x7ffffffffffff;
-
- /* now between 19 and 2^255-1 in both cases, and offset by 19. */
-
- t[0] += 0x8000000000000 - 19;
- t[1] += 0x8000000000000 - 1;
- t[2] += 0x8000000000000 - 1;
- t[3] += 0x8000000000000 - 1;
- t[4] += 0x8000000000000 - 1;
-
- /* now between 2^255 and 2^256-20, and offset by 2^255. */
-
- t[1] += t[0] >> 51;
- t[0] &= 0x7ffffffffffff;
- t[2] += t[1] >> 51;
- t[1] &= 0x7ffffffffffff;
- t[3] += t[2] >> 51;
- t[2] &= 0x7ffffffffffff;
- t[4] += t[3] >> 51;
- t[3] &= 0x7ffffffffffff;
- t[4] &= 0x7ffffffffffff;
-
- 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 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 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);
-}
-
-// -----------------------------------------------------------------------------
-// Shamelessly copied from djb's code, tightened a little
-// -----------------------------------------------------------------------------
-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);
-}
-
-int scalarmult_donna (u8 *mypublic, const u8 *secret, const u8 *basepoint)
-{
- limb bp[5], x[5], z[5], zmone[5];
- unsigned char e[32];
-
- memcpy (e, secret, 32);
- e[0] &= 248;
- e[31] &= 127;
- e[31] |= 64;
-
- fexpand (bp, basepoint);
- cmult (x, z, e, bp);
- crecip (zmone, z);
- fmul (z, x, zmone);
- fcontract (mypublic, z);
-
- return 0;
-}
-
-int
-scalarmult_base_donna (u8 *mypublic, const u8 *secret)
-{
- return scalarmult_donna (mypublic, secret,
- curve25519_basepoint);
-}