text: /* 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>
   * Parts optimised by floodyberry
   * 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>
  
  #ifdef HAVE_TI_MODE
  
  #include "utils.h"
  #include "curve25519_donna_c64.h"
  #include "../scalarmult_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)));
  
  /* Sum two numbers: output += in */
  static 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 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 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) & 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
  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
  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;
  }
  
  #ifdef NATIVE_LITTLE_ENDIAN
  static inline limb
  load_limb(const u8 *in) {
      limb out;
      memcpy(&out, in, sizeof (limb));
      return out;
  }
  static inline void
  store_limb(u8 *out, limb in) {
      memcpy(out, &in, sizeof (limb));
  }
  #else
  static inline 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 inline 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;
  }
  #endif
  
  /* 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);
  }
  
  static const unsigned char basepoint[32] = {9};
  
  static int
  crypto_scalarmult_curve25519_donna_c64(unsigned char *mypublic,
                                         const unsigned char *secret,
                                         const unsigned char *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;
  }
  
  static int
  crypto_scalarmult_curve25519_donna_c64_base(unsigned char *q,
                                              const unsigned char *n)
  {
    return crypto_scalarmult_curve25519_donna_c64(q, n, basepoint);
  }
  
  struct crypto_scalarmult_curve25519_implementation
  crypto_scalarmult_curve25519_donna_c64_implementation = {
      SODIUM_C99(.mult = ) crypto_scalarmult_curve25519_donna_c64,
      SODIUM_C99(.mult_base = ) crypto_scalarmult_curve25519_donna_c64_base
  };
  
  #endif
  