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-rw-r--r--security/nss/lib/freebl/mpi/mpprime.c599
1 files changed, 599 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/mpi/mpprime.c b/security/nss/lib/freebl/mpi/mpprime.c
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+++ b/security/nss/lib/freebl/mpi/mpprime.c
@@ -0,0 +1,599 @@
+/*
+ * 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 */
+ MP_CHECKOK(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;
+ }
+
+ for (i = offset; i < nSieve * 2; i += prime) {
+ if (i % 2 == 0) {
+ sieve[i / 2] = 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;
+ unsigned 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 originally taken from table 4.4,
+ * HandBook of Applied Cryptography, augmented by FIPS-186
+ * requirements, Table C.2 and C.3 */
+ if (nBits >= 2000) {
+ num_tests = 3;
+ } else if (nBits >= 1536) {
+ num_tests = 4;
+ } else if (nBits >= 1024) {
+ num_tests = 5;
+ } else if (nBits >= 550) {
+ num_tests = 6;
+ } else if (nBits >= 450) {
+ num_tests = 7;
+ } else if (nBits >= 400) {
+ num_tests = 8;
+ } else if (nBits >= 350) {
+ num_tests = 9;
+ } else if (nBits >= 300) {
+ num_tests = 10;
+ } else if (nBits >= 250) {
+ num_tests = 20;
+ } else if (nBits >= 200) {
+ num_tests = 41;
+ } else if (nBits >= 100) {
+ num_tests = 38; /* funny anomaly in the FIPS tables, for aux primes, the
+ * required more iterations for larger aux primes */
+ } 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 */
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