Merge remote-tracking branch 'origin/maint-0.2.5'

  o Major bugfixes:

    - Fix a bug in the bounds-checking in the 32-bit curve25519-donna

      implementation that caused incorrect results on 32-bit

      implementations when certain malformed inputs were used along with

      a small class of private ntor keys. This bug does not currently

      appear to allow an attacker to learn private keys or impersonate a

      Tor server, but it could provide a means to distinguish 32-bit Tor

      implementations from 64-bit Tor implementations. Fixes bug 12694;

      bugfix on 0.2.4.8-alpha. Bug found by Robert Ransom; fix from

      Adam Langley.

 *

 * 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.

 */

 * from the sample implementation. */

#include "orconfig.h"

 * significant first. The value of the field element is:

 *   x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...

 *

 * i.e. the limbs are 26, 25, 26, 25, ... bits wide.

 */

 * i.e. the limbs are 26, 25, 26, 25, ... bits wide. */

/* Sum two numbers: output += in */

static void fsum(limb *output, const limb *in) {

  unsigned i;

  for (i = 0; i < 10; i += 2) {

    output[0+i] = (output[0+i] + in[0+i]);

    output[1+i] = (output[1+i] + in[1+i]);

    output[0+i] = output[0+i] + in[0+i];

    output[1+i] = output[1+i] + in[1+i];

  }

}

/* Find the difference of two numbers: output = in - output

 * (note the order of the arguments!)

 */

 * (note the order of the arguments!). */

static void fdifference(limb *output, const limb *in) {

  unsigned i;

  for (i = 0; i < 10; ++i) {

    output[i] = (in[i] - output[i]);

    output[i] = in[i] - output[i];

  }

}

 *

 * output must be distinct to both inputs. The inputs are reduced coefficient

 * form, the output is not.

 */

 *

 * output[x] <= 14 * the largest product of the input limbs. */

static void fproduct(limb *output, const limb *in2, const limb *in) {

  output[0] =       ((limb) ((s32) in2[0])) * ((s32) in[0]);

  output[1] =       ((limb) ((s32) in2[0])) * ((s32) in[1]) +

  output[18] = 2 *  ((limb) ((s32) in2[9])) * ((s32) in[9]);

}

/* Reduce a long form to a short form by taking the input mod 2^255 - 19. */

/* Reduce a long form to a short form by taking the input mod 2^255 - 19.

 *

 * On entry: |output[i]| < 14*2^54

 * On exit: |output[0..8]| < 280*2^54 */

static void freduce_degree(limb *output) {

  /* Each of these shifts and adds ends up multiplying the value by 19. */

  /* Each of these shifts and adds ends up multiplying the value by 19.

   *

   * For output[0..8], the absolute entry value is < 14*2^54 and we add, at

   * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */

  output[8] += output[18] << 4;

  output[8] += output[18] << 1;

  output[8] += output[18];

#error "This code only works on a two's complement system"

#endif

/* return v / 2^26, using only shifts and adds. */

/* return v / 2^26, using only shifts and adds.

 *

 * On entry: v can take any value. */

static inline limb

div_by_2_26(const limb v)

{

  /* High word of v; no shift needed*/

  /* High word of v; no shift needed. */

  const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);

  /* Set to all 1s if v was negative; else set to 0s. */

  const int32_t sign = ((int32_t) highword) >> 31;

  return (v + roundoff) >> 26;

}

/* return v / (2^25), using only shifts and adds. */

/* return v / (2^25), using only shifts and adds.

 *

 * On entry: v can take any value. */

static inline limb

div_by_2_25(const limb v)

{

  return (v + roundoff) >> 25;

}

#if 0

/* return v / (2^25), using only shifts and adds.

 *

 * On entry: v can take any value. */

static inline s32

div_s32_by_2_25(const s32 v)

{

   const s32 roundoff = ((uint32_t)(v >> 31)) >> 7;

   return (v + roundoff) >> 25;

}

#endif

/* Reduce all coefficients of the short form input so that |x| < 2^26.

 *

 * On entry: |output[i]| < 2^62

 */

 * On entry: |output[i]| < 280*2^54 */

static void freduce_coefficients(limb *output) {

  unsigned i;

  for (i = 0; i < 10; i += 2) {

    limb over = div_by_2_26(output[i]);

    /* The entry condition (that |output[i]| < 280*2^54) means that over is, at

     * most, 280*2^28 in the first iteration of this loop. This is added to the

     * next limb and we can approximate the resulting bound of that limb by

     * 281*2^54. */

    output[i] -= over << 26;

    output[i+1] += over;

    /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <

     * 281*2^29. When this is added to the next limb, the resulting bound can

     * be approximated as 281*2^54.

     *

     * For subsequent iterations of the loop, 281*2^54 remains a conservative

     * bound and no overflow occurs. */

    over = div_by_2_25(output[i+1]);

    output[i+1] -= over << 25;

    output[i+2] += over;

  }

  /* Now |output[10]| < 2 ^ 38 and all other coefficients are reduced. */

  /* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */

  output[0] += output[10] << 4;

  output[0] += output[10] << 1;

  output[0] += output[10];

  output[10] = 0;

  /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19 * 2^38

   * So |over| will be no more than 77825  */

  /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29

   * So |over| will be no more than 2^16. */

  {

    limb over = div_by_2_26(output[0]);

    output[0] -= over << 26;

    output[1] += over;

  }

  /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 77825

   * So |over| will be no more than 1. */

  {

    /* output[1] fits in 32 bits, so we can use div_s32_by_2_25 here. */

    s32 over32 = div_s32_by_2_25((s32) output[1]);

    output[1] -= over32 << 25;

    output[2] += over32;

  }

  /* Finally, output[0,1,3..9] are reduced, and output[2] is "nearly reduced":

   * we have |output[2]| <= 2^26.  This is good enough for all of our math,

   * but it will require an extra freduce_coefficients before fcontract. */

  /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The

   * bound on |output[1]| is sufficient to meet our needs. */

}

/* A helpful wrapper around fproduct: output = in * in2.

 *

 * output must be distinct to both inputs. The output is reduced degree and

 * reduced coefficient.

 */

 * On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.

 *

 * output must be distinct to both inputs. The output is reduced degree

 * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */

static void

fmul(limb *output, const limb *in, const limb *in2) {

  limb t[19];

  fproduct(t, in, in2);

  /* |t[i]| < 14*2^54 */

  freduce_degree(t);

  freduce_coefficients(t);

  /* |t[i]| < 2^26 */

  memcpy(output, t, sizeof(limb) * 10);

}

/* Square a number: output = in**2

 *

 * output must be distinct from the input. The inputs are reduced coefficient

 * form, the output is not.

 *

 * output[x] <= 14 * the largest product of the input limbs. */

static void fsquare_inner(limb *output, const limb *in) {

  output[0] =       ((limb) ((s32) in[0])) * ((s32) in[0]);

  output[1] =  2 *  ((limb) ((s32) in[0])) * ((s32) in[1]);

  output[18] = 2 *  ((limb) ((s32) in[9])) * ((s32) in[9]);

}

/* fsquare sets output = in^2.

 *

 * On entry: The |in| argument is in reduced coefficients form and |in[i]| <

 * 2^27.

 *

 * On exit: The |output| argument is in reduced coefficients form (indeed, one

 * need only provide storage for 10 limbs) and |out[i]| < 2^26. */

static void

fsquare(limb *output, const limb *in) {

  limb t[19];

  fsquare_inner(t, in);

  /* |t[i]| < 14*2^54 because the largest product of two limbs will be <

   * 2^(27+27) and fsquare_inner adds together, at most, 14 of those

   * products. */

  freduce_degree(t);

  freduce_coefficients(t);

  /* |t[i]| < 2^26 */

  memcpy(output, t, sizeof(limb) * 10);

}

#error "This code only works when >> does sign-extension on negative numbers"

#endif

/* s32_eq returns 0xffffffff iff a == b and zero otherwise. */

static s32 s32_eq(s32 a, s32 b) {

  a = ~(a ^ b);

  a &= a << 16;

  a &= a << 8;

  a &= a << 4;

  a &= a << 2;

  a &= a << 1;

  return a >> 31;

}

/* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are

 * both non-negative. */

static s32 s32_gte(s32 a, s32 b) {

  a -= b;

  /* a >= 0 iff a >= b. */

  return ~(a >> 31);

}

/* Take a fully reduced polynomial form number and contract it into a

 * little-endian, 32-byte array

 */

 * little-endian, 32-byte array.

 *

 * On entry: |input_limbs[i]| < 2^26 */

static void

fcontract(u8 *output, limb *input) {

fcontract(u8 *output, limb *input_limbs) {

  int i;

  int j;

  s32 input[10];

  s32 mask;

  /* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */

  for (i = 0; i < 10; i++) {

    input[i] = (s32) input_limbs[i];

  }

  for (j = 0; j < 2; ++j) {

    for (i = 0; i < 9; ++i) {

      if ((i & 1) == 1) {

        /* This calculation is a time-invariant way to make input[i] positive

           by borrowing from the next-larger limb.

        */

        const s32 mask = (s32)(input[i]) >> 31;

        const s32 carry = -(((s32)(input[i]) & mask) >> 25);

        input[i] = (s32)(input[i]) + (carry << 25);

        input[i+1] = (s32)(input[i+1]) - carry;

        /* This calculation is a time-invariant way to make input[i]

         * non-negative by borrowing from the next-larger limb. */

        const s32 mask = input[i] >> 31;

        const s32 carry = -((input[i] & mask) >> 25);

        input[i] = input[i] + (carry << 25);

        input[i+1] = input[i+1] - carry;

      } else {

        const s32 mask = (s32)(input[i]) >> 31;

        const s32 carry = -(((s32)(input[i]) & mask) >> 26);

        input[i] = (s32)(input[i]) + (carry << 26);

        input[i+1] = (s32)(input[i+1]) - carry;

        const s32 mask = input[i] >> 31;

        const s32 carry = -((input[i] & mask) >> 26);

        input[i] = input[i] + (carry << 26);

        input[i+1] = input[i+1] - carry;

      }

    }

    /* There's no greater limb for input[9] to borrow from, but we can multiply

     * by 19 and borrow from input[0], which is valid mod 2^255-19. */

    {

      const s32 mask = (s32)(input[9]) >> 31;

      const s32 carry = -(((s32)(input[9]) & mask) >> 25);

      input[9] = (s32)(input[9]) + (carry << 25);

      input[0] = (s32)(input[0]) - (carry * 19);

      const s32 mask = input[9] >> 31;

      const s32 carry = -((input[9] & mask) >> 25);

      input[9] = input[9] + (carry << 25);

      input[0] = input[0] - (carry * 19);

    }

    /* After the first iteration, input[1..9] are non-negative and fit within

     * 25 or 26 bits, depending on position. However, input[0] may be

     * negative. */

  }

  /* The first borrow-propagation pass above ended with every limb

     except (possibly) input[0] non-negative.

     Since each input limb except input[0] is decreased by at most 1

     by a borrow-propagation pass, the second borrow-propagation pass

     could only have wrapped around to decrease input[0] again if the

     first pass left input[0] negative *and* input[1] through input[9]

     were all zero.  In that case, input[1] is now 2^25 - 1, and this

     last borrow-propagation step will leave input[1] non-negative.

  */

     If input[0] was negative after the first pass, then it was because of a

     carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,

     one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.

     In the second pass, each limb is decreased by at most one. Thus the second

     borrow-propagation pass could only have wrapped around to decrease

     input[0] again if the first pass left input[0] negative *and* input[1]

     through input[9] were all zero.  In that case, input[1] is now 2^25 - 1,

     and this last borrow-propagation step will leave input[1] non-negative. */

  {

    const s32 mask = input[0] >> 31;

    const s32 carry = -((input[0] & mask) >> 26);

    input[0] = input[0] + (carry << 26);

    input[1] = input[1] - carry;

  }

  /* All input[i] are now non-negative. However, there might be values between

   * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */

  for (j = 0; j < 2; j++) {

    for (i = 0; i < 9; i++) {

      if ((i & 1) == 1) {

        const s32 carry = input[i] >> 25;

        input[i] &= 0x1ffffff;

        input[i+1] += carry;

      } else {

        const s32 carry = input[i] >> 26;

        input[i] &= 0x3ffffff;

        input[i+1] += carry;

      }

    }

    {

    const s32 mask = (s32)(input[0]) >> 31;

    const s32 carry = -(((s32)(input[0]) & mask) >> 26);

    input[0] = (s32)(input[0]) + (carry << 26);

    input[1] = (s32)(input[1]) - carry;

      const s32 carry = input[9] >> 25;

      input[9] &= 0x1ffffff;

      input[0] += 19*carry;

    }

  }

  /* Both passes through the above loop, plus the last 0-to-1 step, are

     necessary: if input[9] is -1 and input[0] through input[8] are 0,

     negative values will remain in the array until the end.

   */

  /* If the first carry-chain pass, just above, ended up with a carry from

   * input[9], and that caused input[0] to be out-of-bounds, then input[0] was

   * < 2^26 + 2*19, because the carry was, at most, two.

   *

   * If the second pass carried from input[9] again then input[0] is < 2*19 and

   * the input[9] -> input[0] carry didn't push input[0] out of bounds. */

  /* It still remains the case that input might be between 2^255-19 and 2^255.

   * In this case, input[1..9] must take their maximum value and input[0] must

   * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */

  mask = s32_gte(input[0], 0x3ffffed);

  for (i = 1; i < 10; i++) {

    if ((i & 1) == 1) {

      mask &= s32_eq(input[i], 0x1ffffff);

    } else {

      mask &= s32_eq(input[i], 0x3ffffff);

    }

  }

  /* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus

   * this conditionally subtracts 2^255-19. */

  input[0] -= mask & 0x3ffffed;

  for (i = 1; i < 10; i++) {

    if ((i & 1) == 1) {

      input[i] -= mask & 0x1ffffff;

    } else {

      input[i] -= mask & 0x3ffffff;

    }

  }

  input[1] <<= 2;

  input[2] <<= 3;

 *   x z: short form, destroyed

 *   xprime zprime: short form, destroyed

 *   qmqp: short form, preserved

 */

 *

 * On entry and exit, the absolute value of the limbs of all inputs and outputs

 * are < 2^26. */

static void fmonty(limb *x2, limb *z2,  /* output 2Q */

                   limb *x3, limb *z3,  /* output Q + Q' */

                   limb *x, limb *z,    /* input Q */

  memcpy(origx, x, 10 * sizeof(limb));

  fsum(x, z);

  fdifference(z, origx);  // does x - z

  /* |x[i]| < 2^27 */

  fdifference(z, origx);  /* does x - z */

  /* |z[i]| < 2^27 */

  memcpy(origxprime, xprime, sizeof(limb) * 10);

  fsum(xprime, zprime);

  /* |xprime[i]| < 2^27 */

  fdifference(zprime, origxprime);

  /* |zprime[i]| < 2^27 */

  fproduct(xxprime, xprime, z);

  /* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <

   * 2^(27+27) and fproduct adds together, at most, 14 of those products.

   * (Approximating that to 2^58 doesn't work out.) */

  fproduct(zzprime, x, zprime);

  /* |zzprime[i]| < 14*2^54 */

  freduce_degree(xxprime);

  freduce_coefficients(xxprime);

  /* |xxprime[i]| < 2^26 */

  freduce_degree(zzprime);

  freduce_coefficients(zzprime);

  /* |zzprime[i]| < 2^26 */

  memcpy(origxprime, xxprime, sizeof(limb) * 10);

  fsum(xxprime, zzprime);

  /* |xxprime[i]| < 2^27 */

  fdifference(zzprime, origxprime);

  /* |zzprime[i]| < 2^27 */

  fsquare(xxxprime, xxprime);

  /* |xxxprime[i]| < 2^26 */

  fsquare(zzzprime, zzprime);

  /* |zzzprime[i]| < 2^26 */

  fproduct(zzprime, zzzprime, qmqp);

  /* |zzprime[i]| < 14*2^52 */

  freduce_degree(zzprime);

  freduce_coefficients(zzprime);

  /* |zzprime[i]| < 2^26 */

  memcpy(x3, xxxprime, sizeof(limb) * 10);

  memcpy(z3, zzprime, sizeof(limb) * 10);

  fsquare(xx, x);

  /* |xx[i]| < 2^26 */

  fsquare(zz, z);

  /* |zz[i]| < 2^26 */

  fproduct(x2, xx, zz);

  /* |x2[i]| < 14*2^52 */

  freduce_degree(x2);

  freduce_coefficients(x2);

  /* |x2[i]| < 2^26 */

  fdifference(zz, xx);  // does zz = xx - zz

  /* |zz[i]| < 2^27 */

  memset(zzz + 10, 0, sizeof(limb) * 9);

  fscalar_product(zzz, zz, 121665);

  /* |zzz[i]| < 2^(27+17) */

  /* No need to call freduce_degree here:

     fscalar_product doesn't increase the degree of its input. */

  freduce_coefficients(zzz);

  /* |zzz[i]| < 2^26 */

  fsum(zzz, xx);

  /* |zzz[i]| < 2^27 */

  fproduct(z2, zz, zzz);

  /* |z2[i]| < 14*2^(26+27) */

  freduce_degree(z2);

  freduce_coefficients(z2);

  /* |z2|i| < 2^26 */

}

/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave

 * wrong results.  Also, the two limb arrays must be in reduced-coefficient,

 * reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,

 * and all all values in a[0..9],b[0..9] must have magnitude less than

 * INT32_MAX.

 */

 * INT32_MAX. */

static void

swap_conditional(limb a[19], limb b[19], limb iswap) {

  unsigned i;

 *

 *   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)

 */

 *   q: a point of the curve (short form) */

static void

cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) {

  limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};

  /* 2^255 - 21 */ fmul(out,t1,z11);

}

int curve25519_donna(u8 *, const u8 *, const u8 *);

int curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint);

int

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

  cmult(x, z, e, bp);

  crecip(zmone, z);

  fmul(z, x, zmone);

  freduce_coefficients(z);

  fcontract(mypublic, z);

  return 0;

}