--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/nss/lib/freebl/mpi/mpprime.c	Mon Jul 28 10:47:06 2014 +0200
@@ -0,0 +1,584 @@
+/*
+ *  mpprime.c
+ *
+ *  Utilities for finding and working with prime and pseudo-prime
+ *  integers
+ *
+ * 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/. */
+
+#include "mpi-priv.h"
+#include "mpprime.h"
+#include "mplogic.h"
+#include <stdlib.h>
+#include <string.h>
+
+#define SMALL_TABLE 0 /* determines size of hard-wired prime table */
+
+#define RANDOM() rand()
+
+#include "primes.c"  /* pull in the prime digit table */
+
+/* 
+   Test if any of a given vector of digits divides a.  If not, MP_NO
+   is returned; otherwise, MP_YES is returned and 'which' is set to
+   the index of the integer in the vector which divided a.
+ */
+mp_err    s_mpp_divp(mp_int *a, const mp_digit *vec, int size, int *which);
+
+/* {{{ mpp_divis(a, b) */
+
+/*
+  mpp_divis(a, b)
+
+  Returns MP_YES if a is divisible by b, or MP_NO if it is not.
+ */
+
+mp_err  mpp_divis(mp_int *a, mp_int *b)
+{
+  mp_err  res;
+  mp_int  rem;
+
+  if((res = mp_init(&rem)) != MP_OKAY)
+    return res;
+
+  if((res = mp_mod(a, b, &rem)) != MP_OKAY)
+    goto CLEANUP;
+
+  if(mp_cmp_z(&rem) == 0)
+    res = MP_YES;
+  else
+    res = MP_NO;
+
+CLEANUP:
+  mp_clear(&rem);
+  return res;
+
+} /* end mpp_divis() */
+
+/* }}} */
+
+/* {{{ mpp_divis_d(a, d) */
+
+/*
+  mpp_divis_d(a, d)
+
+  Return MP_YES if a is divisible by d, or MP_NO if it is not.
+ */
+
+mp_err  mpp_divis_d(mp_int *a, mp_digit d)
+{
+  mp_err     res;
+  mp_digit   rem;
+
+  ARGCHK(a != NULL, MP_BADARG);
+
+  if(d == 0)
+    return MP_NO;
+
+  if((res = mp_mod_d(a, d, &rem)) != MP_OKAY)
+    return res;
+
+  if(rem == 0)
+    return MP_YES;
+  else
+    return MP_NO;
+
+} /* end mpp_divis_d() */
+
+/* }}} */
+
+/* {{{ mpp_random(a) */
+
+/*
+  mpp_random(a)
+
+  Assigns a random value to a.  This value is generated using the
+  standard C library's rand() function, so it should not be used for
+  cryptographic purposes, but it should be fine for primality testing,
+  since all we really care about there is good statistical properties.
+
+  As many digits as a currently has are filled with random digits.
+ */
+
+mp_err  mpp_random(mp_int *a)
+
+{
+  mp_digit  next = 0;
+  unsigned int       ix, jx;
+
+  ARGCHK(a != NULL, MP_BADARG);
+
+  for(ix = 0; ix < USED(a); ix++) {
+    for(jx = 0; jx < sizeof(mp_digit); jx++) {
+      next = (next << CHAR_BIT) | (RANDOM() & UCHAR_MAX);
+    }
+    DIGIT(a, ix) = next;
+  }
+
+  return MP_OKAY;
+
+} /* end mpp_random() */
+
+/* }}} */
+
+/* {{{ mpp_random_size(a, prec) */
+
+mp_err  mpp_random_size(mp_int *a, mp_size prec)
+{
+  mp_err   res;
+
+  ARGCHK(a != NULL && prec > 0, MP_BADARG);
+  
+  if((res = s_mp_pad(a, prec)) != MP_OKAY)
+    return res;
+
+  return mpp_random(a);
+
+} /* end mpp_random_size() */
+
+/* }}} */
+
+/* {{{ mpp_divis_vector(a, vec, size, which) */
+
+/*
+  mpp_divis_vector(a, vec, size, which)
+
+  Determines if a is divisible by any of the 'size' digits in vec.
+  Returns MP_YES and sets 'which' to the index of the offending digit,
+  if it is; returns MP_NO if it is not.
+ */
+
+mp_err  mpp_divis_vector(mp_int *a, const mp_digit *vec, int size, int *which)
+{
+  ARGCHK(a != NULL && vec != NULL && size > 0, MP_BADARG);
+  
+  return s_mpp_divp(a, vec, size, which);
+
+} /* end mpp_divis_vector() */
+
+/* }}} */
+
+/* {{{ mpp_divis_primes(a, np) */
+
+/*
+  mpp_divis_primes(a, np)
+
+  Test whether a is divisible by any of the first 'np' primes.  If it
+  is, returns MP_YES and sets *np to the value of the digit that did
+  it.  If not, returns MP_NO.
+ */
+mp_err  mpp_divis_primes(mp_int *a, mp_digit *np)
+{
+  int     size, which;
+  mp_err  res;
+
+  ARGCHK(a != NULL && np != NULL, MP_BADARG);
+
+  size = (int)*np;
+  if(size > prime_tab_size)
+    size = prime_tab_size;
+
+  res = mpp_divis_vector(a, prime_tab, size, &which);
+  if(res == MP_YES) 
+    *np = prime_tab[which];
+
+  return res;
+
+} /* end mpp_divis_primes() */
+
+/* }}} */
+
+/* {{{ mpp_fermat(a, w) */
+
+/*
+  Using w as a witness, try pseudo-primality testing based on Fermat's
+  little theorem.  If a is prime, and (w, a) = 1, then w^a == w (mod
+  a).  So, we compute z = w^a (mod a) and compare z to w; if they are
+  equal, the test passes and we return MP_YES.  Otherwise, we return
+  MP_NO.
+ */
+mp_err  mpp_fermat(mp_int *a, mp_digit w)
+{
+  mp_int  base, test;
+  mp_err  res;
+  
+  if((res = mp_init(&base)) != MP_OKAY)
+    return res;
+
+  mp_set(&base, w);
+
+  if((res = mp_init(&test)) != MP_OKAY)
+    goto TEST;
+
+  /* Compute test = base^a (mod a) */
+  if((res = mp_exptmod(&base, a, a, &test)) != MP_OKAY)
+    goto CLEANUP;
+
+  
+  if(mp_cmp(&base, &test) == 0)
+    res = MP_YES;
+  else
+    res = MP_NO;
+
+ CLEANUP:
+  mp_clear(&test);
+ TEST:
+  mp_clear(&base);
+
+  return res;
+
+} /* end mpp_fermat() */
+
+/* }}} */
+
+/*
+  Perform the fermat test on each of the primes in a list until
+  a) one of them shows a is not prime, or 
+  b) the list is exhausted.
+  Returns:  MP_YES if it passes tests.
+	    MP_NO  if fermat test reveals it is composite
+	    Some MP error code if some other error occurs.
+ */
+mp_err mpp_fermat_list(mp_int *a, const mp_digit *primes, mp_size nPrimes)
+{
+  mp_err rv = MP_YES;
+
+  while (nPrimes-- > 0 && rv == MP_YES) {
+    rv = mpp_fermat(a, *primes++);
+  }
+  return rv;
+}
+
+/* {{{ mpp_pprime(a, nt) */
+
+/*
+  mpp_pprime(a, nt)
+
+  Performs nt iteration of the Miller-Rabin probabilistic primality
+  test on a.  Returns MP_YES if the tests pass, MP_NO if one fails.
+  If MP_NO is returned, the number is definitely composite.  If MP_YES
+  is returned, it is probably prime (but that is not guaranteed).
+ */
+
+mp_err  mpp_pprime(mp_int *a, int nt)
+{
+  mp_err   res;
+  mp_int   x, amo, m, z;	/* "amo" = "a minus one" */
+  int      iter;
+  unsigned int jx;
+  mp_size  b;
+
+  ARGCHK(a != NULL, MP_BADARG);
+
+  MP_DIGITS(&x) = 0;
+  MP_DIGITS(&amo) = 0;
+  MP_DIGITS(&m) = 0;
+  MP_DIGITS(&z) = 0;
+
+  /* Initialize temporaries... */
+  MP_CHECKOK( mp_init(&amo));
+  /* Compute amo = a - 1 for what follows...    */
+  MP_CHECKOK( mp_sub_d(a, 1, &amo) );
+
+  b = mp_trailing_zeros(&amo);
+  if (!b) { /* a was even ? */
+    res = MP_NO;
+    goto CLEANUP;
+  }
+
+  MP_CHECKOK( mp_init_size(&x, MP_USED(a)) );
+  MP_CHECKOK( mp_init(&z) );
+  MP_CHECKOK( mp_init(&m) );
+  MP_CHECKOK( mp_div_2d(&amo, b, &m, 0) );
+
+  /* Do the test nt times... */
+  for(iter = 0; iter < nt; iter++) {
+
+    /* Choose a random value for 1 < x < a      */
+    s_mp_pad(&x, USED(a));
+    mpp_random(&x);
+    MP_CHECKOK( mp_mod(&x, a, &x) );
+    if(mp_cmp_d(&x, 1) <= 0) {
+      iter--;    /* don't count this iteration */
+      continue;  /* choose a new x */
+    }
+
+    /* Compute z = (x ** m) mod a               */
+    MP_CHECKOK( mp_exptmod(&x, &m, a, &z) );
+    
+    if(mp_cmp_d(&z, 1) == 0 || mp_cmp(&z, &amo) == 0) {
+      res = MP_YES;
+      continue;
+    }
+    
+    res = MP_NO;  /* just in case the following for loop never executes. */
+    for (jx = 1; jx < b; jx++) {
+      /* z = z^2 (mod a) */
+      MP_CHECKOK( mp_sqrmod(&z, a, &z) );
+      res = MP_NO;	/* previous line set res to MP_YES */
+
+      if(mp_cmp_d(&z, 1) == 0) {
+	break;
+      }
+      if(mp_cmp(&z, &amo) == 0) {
+	res = MP_YES;
+	break;
+      } 
+    } /* end testing loop */
+
+    /* If the test passes, we will continue iterating, but a failed
+       test means the candidate is definitely NOT prime, so we will
+       immediately break out of this loop
+     */
+    if(res == MP_NO)
+      break;
+
+  } /* end iterations loop */
+  
+CLEANUP:
+  mp_clear(&m);
+  mp_clear(&z);
+  mp_clear(&x);
+  mp_clear(&amo);
+  return res;
+
+} /* end mpp_pprime() */
+
+/* }}} */
+
+/* Produce table of composites from list of primes and trial value.  
+** trial must be odd. List of primes must not include 2.
+** sieve should have dimension >= MAXPRIME/2, where MAXPRIME is largest 
+** prime in list of primes.  After this function is finished,
+** if sieve[i] is non-zero, then (trial + 2*i) is composite.
+** Each prime used in the sieve costs one division of trial, and eliminates
+** one or more values from the search space. (3 eliminates 1/3 of the values
+** alone!)  Each value left in the search space costs 1 or more modular 
+** exponentations.  So, these divisions are a bargain!
+*/
+mp_err mpp_sieve(mp_int *trial, const mp_digit *primes, mp_size nPrimes, 
+		 unsigned char *sieve, mp_size nSieve)
+{
+  mp_err       res;
+  mp_digit     rem;
+  mp_size      ix;
+  unsigned long offset;
+
+  memset(sieve, 0, nSieve);
+
+  for(ix = 0; ix < nPrimes; ix++) {
+    mp_digit prime = primes[ix];
+    mp_size  i;
+    if((res = mp_mod_d(trial, prime, &rem)) != MP_OKAY) 
+      return res;
+
+    if (rem == 0) {
+      offset = 0;
+    } else {
+      offset = prime - (rem / 2);
+    }
+    for (i = offset; i < nSieve ; i += prime) {
+      sieve[i] = 1;
+    }
+  }
+
+  return MP_OKAY;
+}
+
+#define SIEVE_SIZE 32*1024
+
+mp_err mpp_make_prime(mp_int *start, mp_size nBits, mp_size strong,
+		      unsigned long * nTries)
+{
+  mp_digit      np;
+  mp_err        res;
+  int           i	= 0;
+  mp_int        trial;
+  mp_int        q;
+  mp_size       num_tests;
+  unsigned char *sieve;
+  
+  ARGCHK(start != 0, MP_BADARG);
+  ARGCHK(nBits > 16, MP_RANGE);
+
+  sieve = malloc(SIEVE_SIZE);
+  ARGCHK(sieve != NULL, MP_MEM);
+
+  MP_DIGITS(&trial) = 0;
+  MP_DIGITS(&q) = 0;
+  MP_CHECKOK( mp_init(&trial) );
+  MP_CHECKOK( mp_init(&q)     );
+  /* values taken from table 4.4, HandBook of Applied Cryptography */
+  if (nBits >= 1300) {
+    num_tests = 2;
+  } else if (nBits >= 850) {
+    num_tests = 3;
+  } else if (nBits >= 650) {
+    num_tests = 4;
+  } else if (nBits >= 550) {
+    num_tests = 5;
+  } else if (nBits >= 450) {
+    num_tests = 6;
+  } else if (nBits >= 400) {
+    num_tests = 7;
+  } else if (nBits >= 350) {
+    num_tests = 8;
+  } else if (nBits >= 300) {
+    num_tests = 9;
+  } else if (nBits >= 250) {
+    num_tests = 12;
+  } else if (nBits >= 200) {
+    num_tests = 15;
+  } else if (nBits >= 150) {
+    num_tests = 18;
+  } else if (nBits >= 100) {
+    num_tests = 27;
+  } else
+    num_tests = 50;
+
+  if (strong) 
+    --nBits;
+  MP_CHECKOK( mpl_set_bit(start, nBits - 1, 1) );
+  MP_CHECKOK( mpl_set_bit(start,         0, 1) );
+  for (i = mpl_significant_bits(start) - 1; i >= nBits; --i) {
+    MP_CHECKOK( mpl_set_bit(start, i, 0) );
+  }
+  /* start sieveing with prime value of 3. */
+  MP_CHECKOK(mpp_sieve(start, prime_tab + 1, prime_tab_size - 1, 
+		       sieve, SIEVE_SIZE) );
+
+#ifdef DEBUG_SIEVE
+  res = 0;
+  for (i = 0; i < SIEVE_SIZE; ++i) {
+    if (!sieve[i])
+      ++res;
+  }
+  fprintf(stderr,"sieve found %d potential primes.\n", res);
+#define FPUTC(x,y) fputc(x,y)
+#else
+#define FPUTC(x,y) 
+#endif
+
+  res = MP_NO;
+  for(i = 0; i < SIEVE_SIZE; ++i) {
+    if (sieve[i])	/* this number is composite */
+      continue;
+    MP_CHECKOK( mp_add_d(start, 2 * i, &trial) );
+    FPUTC('.', stderr);
+    /* run a Fermat test */
+    res = mpp_fermat(&trial, 2);
+    if (res != MP_OKAY) {
+      if (res == MP_NO)
+	continue;	/* was composite */
+      goto CLEANUP;
+    }
+      
+    FPUTC('+', stderr);
+    /* If that passed, run some Miller-Rabin tests	*/
+    res = mpp_pprime(&trial, num_tests);
+    if (res != MP_OKAY) {
+      if (res == MP_NO)
+	continue;	/* was composite */
+      goto CLEANUP;
+    }
+    FPUTC('!', stderr);
+
+    if (!strong) 
+      break;	/* success !! */
+
+    /* At this point, we have strong evidence that our candidate
+       is itself prime.  If we want a strong prime, we need now
+       to test q = 2p + 1 for primality...
+     */
+    MP_CHECKOK( mp_mul_2(&trial, &q) );
+    MP_CHECKOK( mp_add_d(&q, 1, &q)  );
+
+    /* Test q for small prime divisors ... */
+    np = prime_tab_size;
+    res = mpp_divis_primes(&q, &np);
+    if (res == MP_YES) { /* is composite */
+      mp_clear(&q);
+      continue;
+    }
+    if (res != MP_NO) 
+      goto CLEANUP;
+
+    /* And test with Fermat, as with its parent ... */
+    res = mpp_fermat(&q, 2);
+    if (res != MP_YES) {
+      mp_clear(&q);
+      if (res == MP_NO)
+	continue;	/* was composite */
+      goto CLEANUP;
+    }
+
+    /* And test with Miller-Rabin, as with its parent ... */
+    res = mpp_pprime(&q, num_tests);
+    if (res != MP_YES) {
+      mp_clear(&q);
+      if (res == MP_NO)
+	continue;	/* was composite */
+      goto CLEANUP;
+    }
+
+    /* If it passed, we've got a winner */
+    mp_exch(&q, &trial);
+    mp_clear(&q);
+    break;
+
+  } /* end of loop through sieved values */
+  if (res == MP_YES) 
+    mp_exch(&trial, start);
+CLEANUP:
+  mp_clear(&trial);
+  mp_clear(&q);
+  if (nTries)
+    *nTries += i;
+  if (sieve != NULL) {
+  	memset(sieve, 0, SIEVE_SIZE);
+  	free (sieve);
+  }
+  return res;
+}
+
+/*========================================================================*/
+/*------------------------------------------------------------------------*/
+/* Static functions visible only to the library internally                */
+
+/* {{{ s_mpp_divp(a, vec, size, which) */
+
+/* 
+   Test for divisibility by members of a vector of digits.  Returns
+   MP_NO if a is not divisible by any of them; returns MP_YES and sets
+   'which' to the index of the offender, if it is.  Will stop on the
+   first digit against which a is divisible.
+ */
+
+mp_err    s_mpp_divp(mp_int *a, const mp_digit *vec, int size, int *which)
+{
+  mp_err    res;
+  mp_digit  rem;
+
+  int     ix;
+
+  for(ix = 0; ix < size; ix++) {
+    if((res = mp_mod_d(a, vec[ix], &rem)) != MP_OKAY) 
+      return res;
+
+    if(rem == 0) {
+      if(which)
+	*which = ix;
+      return MP_YES;
+    }
+  }
+
+  return MP_NO;
+
+} /* end s_mpp_divp() */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* HERE THERE BE DRAGONS                                                  */