Add fallback implementations for curve25519: curve25519_donna

    sys/queue.h, and the ones that do have diverged in incompatible

    ways.  (CIRCLEQ or no CIRCLEQ? SIMPLQ or STAILQ?)

curve25519_donna/*.c

    A copy of Adam Langley's curve25519-donna mostly-portable

    implementations of curve25519.

See http://code.google.com/p/curve25519-donna/ for details.

BUILDING:

If you run `make`, two .a archives will be built, similar to djb's curve25519

code. Alternatively, read on:

The C implementation is contained within curve25519-donna.c. It has no external

dependancies and is BSD licenced. You can copy/include/link it directly in with

your program. Recommended C flags: -O2

The x86-64 bit implementation is contained within curve25519-donna-x86-64.c and

curve25519-donna-x86-64.s. Build like this:

% cpp curve25519-donna-x86-64.s > curve25519-donna-x86-64.s.pp

% as -o curve25519-donna-x86-64.s.o curve25519-donna-x86-64.s.pp

% gcc -O2 -c curve25519-donna-x86-64.c

Then the two .o files can be linked in

USAGE:

The usage is exactly the same as djb's code (as described at

http://cr.yp.to/ecdh.html) expect that the function is called curve25519_donna.

In short,

To generate a private key, generate 32 random bytes and:

  mysecret[0] &= 248;

  mysecret[31] &= 127;

  mysecret[31] |= 64;

To generate the public key, just do

  static const uint8_t basepoint[32] = {9};

  curve25519_donna(mypublic, mysecret, basepoint);

To generate an agreed key do:

  uint8_t shared_key[32];

  curve25519_donna(shared_key, mysecret, theirpublic);

And hash the shared_key with a cryptographic hash function before using.

/* 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>

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 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 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 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 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 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;

}

/* Take a little-endian, 32-byte number and expand it into polynomial form */

static void

fexpand(limb *output, const u8 *in) {

  output[0] = *((const uint64_t *)(in)) & 0x7ffffffffffff;

  output[1] = (*((const uint64_t *)(in+6)) >> 3) & 0x7ffffffffffff;

  output[2] = (*((const uint64_t *)(in+12)) >> 6) & 0x7ffffffffffff;

  output[3] = (*((const uint64_t *)(in+19)) >> 1) & 0x7ffffffffffff;

  output[4] = (*((const uint64_t *)(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;

  *((uint64_t *)(output)) = t[0] | (t[1] << 51);

  *((uint64_t *)(output+8)) = (t[1] >> 13) | (t[2] << 38);

  *((uint64_t *)(output+16)) = (t[2] >> 26) | (t[3] << 25);

  *((uint64_t *)(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

curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) {

  limb bp[5], x[5], z[5], zmone[5];

  uint8_t e[32];

  int i;

  for (i = 0;i < 32;++i) e[i] = secret[i];

  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;

}