--- a/libtommath/bn_mp_prime_is_prime.c	Wed Feb 28 22:11:39 2018 +0800
+++ b/libtommath/bn_mp_prime_is_prime.c	Thu Oct 15 19:55:15 2020 +0800
@@ -1,83 +1,314 @@
-#include <tommath_private.h>
+#include "tommath_private.h"
 #ifdef BN_MP_PRIME_IS_PRIME_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, [email protected], http://libtom.org
- */
+/* LibTomMath, multiple-precision integer library -- Tom St Denis */
+/* SPDX-License-Identifier: Unlicense */
 
-/* performs a variable number of rounds of Miller-Rabin
- *
- * Probability of error after t rounds is no more than
+/* portable integer log of two with small footprint */
+static unsigned int s_floor_ilog2(int value)
+{
+   unsigned int r = 0;
+   while ((value >>= 1) != 0) {
+      r++;
+   }
+   return r;
+}
+
+
+mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
+{
+   mp_int  b;
+   int     ix, p_max = 0, size_a, len;
+   mp_bool res;
+   mp_err  err;
+   unsigned int fips_rand, mask;
+
+   /* default to no */
+   *result = MP_NO;
 
- *
- * Sets result to 1 if probably prime, 0 otherwise
- */
-int mp_prime_is_prime (mp_int * a, int t, int *result)
-{
-  mp_int  b;
-  int     ix, err, res;
+   /* Some shortcuts */
+   /* N > 3 */
+   if (a->used == 1) {
+      if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) {
+         *result = MP_NO;
+         return MP_OKAY;
+      }
+      if (a->dp[0] == 2u) {
+         *result = MP_YES;
+         return MP_OKAY;
+      }
+   }
 
-  /* default to no */
-  *result = MP_NO;
+   /* N must be odd */
+   if (MP_IS_EVEN(a)) {
+      return MP_OKAY;
+   }
+   /* N is not a perfect square: floor(sqrt(N))^2 != N */
+   if ((err = mp_is_square(a, &res)) != MP_OKAY) {
+      return err;
+   }
+   if (res != MP_NO) {
+      return MP_OKAY;
+   }
 
-  /* valid value of t? */
-  if ((t <= 0) || (t > PRIME_SIZE)) {
-    return MP_VAL;
-  }
-
-  /* is the input equal to one of the primes in the table? */
-  for (ix = 0; ix < PRIME_SIZE; ix++) {
-      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
-         *result = 1;
+   /* is the input equal to one of the primes in the table? */
+   for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) {
+      if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) {
+         *result = MP_YES;
          return MP_OKAY;
       }
-  }
-
-  /* first perform trial division */
-  if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
-    return err;
-  }
+   }
+#ifdef MP_8BIT
+   /* The search in the loop above was exhaustive in this case */
+   if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) {
+      return MP_OKAY;
+   }
+#endif
 
-  /* return if it was trivially divisible */
-  if (res == MP_YES) {
-    return MP_OKAY;
-  }
+   /* first perform trial division */
+   if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) {
+      return err;
+   }
 
-  /* now perform the miller-rabin rounds */
-  if ((err = mp_init (&b)) != MP_OKAY) {
-    return err;
-  }
+   /* return if it was trivially divisible */
+   if (res == MP_YES) {
+      return MP_OKAY;
+   }
+
+   /*
+       Run the Miller-Rabin test with base 2 for the BPSW test.
+    */
+   if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
+      return err;
+   }
 
-  for (ix = 0; ix < t; ix++) {
-    /* set the prime */
-    mp_set (&b, ltm_prime_tab[ix]);
-
-    if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
+   if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+      goto LBL_B;
+   }
+   if (res == MP_NO) {
       goto LBL_B;
-    }
+   }
+   /*
+      Rumours have it that Mathematica does a second M-R test with base 3.
+      Other rumours have it that their strong L-S test is slightly different.
+      It does not hurt, though, beside a bit of extra runtime.
+   */
+   b.dp[0]++;
+   if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+      goto LBL_B;
+   }
+   if (res == MP_NO) {
+      goto LBL_B;
+   }
 
-    if (res == MP_NO) {
-      goto LBL_B;
-    }
-  }
-
-  /* passed the test */
-  *result = MP_YES;
-LBL_B:mp_clear (&b);
-  return err;
-}
+   /*
+    * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
+    * slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with
+    * bases 2, 3 and t random bases.
+    */
+#ifndef LTM_USE_ONLY_MR
+   if (t >= 0) {
+      /*
+       * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for
+       * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit
+       * integers but the necesssary analysis is on the todo-list).
+       */
+#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
+      err = mp_prime_frobenius_underwood(a, &res);
+      if ((err != MP_OKAY) && (err != MP_ITER)) {
+         goto LBL_B;
+      }
+      if (res == MP_NO) {
+         goto LBL_B;
+      }
+#else
+      if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) {
+         goto LBL_B;
+      }
+      if (res == MP_NO) {
+         goto LBL_B;
+      }
+#endif
+   }
 #endif
 
-/* ref:         $Format:%D$ */
-/* git commit:  $Format:%H$ */
-/* commit time: $Format:%ai$ */
+   /* run at least one Miller-Rabin test with a random base */
+   if (t == 0) {
+      t = 1;
+   }
+
+   /*
+      Only recommended if the input range is known to be < 3317044064679887385961981
+
+      It uses the bases necessary for a deterministic M-R test if the input is
+      smaller than  3317044064679887385961981
+      The caller has to check the size.
+      TODO: can be made a bit finer grained but comparing is not free.
+   */
+   if (t < 0) {
+      /*
+          Sorenson, Jonathan; Webster, Jonathan (2015).
+           "Strong Pseudoprimes to Twelve Prime Bases".
+       */
+      /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */
+      if ((err =   mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) {
+         goto LBL_B;
+      }
+
+      if (mp_cmp(a, &b) == MP_LT) {
+         p_max = 12;
+      } else {
+         /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */
+         if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) {
+            goto LBL_B;
+         }
+
+         if (mp_cmp(a, &b) == MP_LT) {
+            p_max = 13;
+         } else {
+            err = MP_VAL;
+            goto LBL_B;
+         }
+      }
+
+      /* we did bases 2 and 3  already, skip them */
+      for (ix = 2; ix < p_max; ix++) {
+         mp_set(&b, s_mp_prime_tab[ix]);
+         if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+            goto LBL_B;
+         }
+         if (res == MP_NO) {
+            goto LBL_B;
+         }
+      }
+   }
+   /*
+       Do "t" M-R tests with random bases between 3 and "a".
+       See Fips 186.4 p. 126ff
+   */
+   else if (t > 0) {
+      /*
+       * The mp_digit's have a defined bit-size but the size of the
+       * array a.dp is a simple 'int' and this library can not assume full
+       * compliance to the current C-standard (ISO/IEC 9899:2011) because
+       * it gets used for small embeded processors, too. Some of those MCUs
+       * have compilers that one cannot call standard compliant by any means.
+       * Hence the ugly type-fiddling in the following code.
+       */
+      size_a = mp_count_bits(a);
+      mask = (1u << s_floor_ilog2(size_a)) - 1u;
+      /*
+         Assuming the General Rieman hypothesis (never thought to write that in a
+         comment) the upper bound can be lowered to  2*(log a)^2.
+         E. Bach, "Explicit bounds for primality testing and related problems,"
+         Math. Comp. 55 (1990), 355-380.
+
+            size_a = (size_a/10) * 7;
+            len = 2 * (size_a * size_a);
+
+         E.g.: a number of size 2^2048 would be reduced to the upper limit
+
+            floor(2048/10)*7 = 1428
+            2 * 1428^2       = 4078368
+
+         (would have been ~4030331.9962 with floats and natural log instead)
+         That number is smaller than 2^28, the default bit-size of mp_digit.
+      */
+
+      /*
+        How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
+        does exactly 1. In words: one. Look at the end of _GMP_is_prime() in
+        Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.
+
+        The function mp_rand() goes to some length to use a cryptographically
+        good PRNG. That also means that the chance to always get the same base
+        in the loop is non-zero, although very low.
+        If the BPSW test and/or the addtional Frobenious test have been
+        performed instead of just the Miller-Rabin test with the bases 2 and 3,
+        a single extra test should suffice, so such a very unlikely event
+        will not do much harm.
+
+        To preemptivly answer the dangling question: no, a witness does not
+        need to be prime.
+      */
+      for (ix = 0; ix < t; ix++) {
+         /* mp_rand() guarantees the first digit to be non-zero */
+         if ((err = mp_rand(&b, 1)) != MP_OKAY) {
+            goto LBL_B;
+         }
+         /*
+          * Reduce digit before casting because mp_digit might be bigger than
+          * an unsigned int and "mask" on the other side is most probably not.
+          */
+         fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask);
+#ifdef MP_8BIT
+         /*
+          * One 8-bit digit is too small, so concatenate two if the size of
+          * unsigned int allows for it.
+          */
+         if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) {
+            if ((err = mp_rand(&b, 1)) != MP_OKAY) {
+               goto LBL_B;
+            }
+            fips_rand <<= MP_SIZEOF_BITS(mp_digit);
+            fips_rand |= (unsigned int) b.dp[0];
+            fips_rand &= mask;
+         }
+#endif
+         if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) {
+            len = INT_MAX / MP_DIGIT_BIT;
+         } else {
+            len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT);
+         }
+         /*  Unlikely. */
+         if (len < 0) {
+            ix--;
+            continue;
+         }
+         /*
+          * As mentioned above, one 8-bit digit is too small and
+          * although it can only happen in the unlikely case that
+          * an "unsigned int" is smaller than 16 bit a simple test
+          * is cheap and the correction even cheaper.
+          */
+#ifdef MP_8BIT
+         /* All "a" < 2^8 have been caught before */
+         if (len == 1) {
+            len++;
+         }
+#endif
+         if ((err = mp_rand(&b, len)) != MP_OKAY) {
+            goto LBL_B;
+         }
+         /*
+          * That number might got too big and the witness has to be
+          * smaller than "a"
+          */
+         len = mp_count_bits(&b);
+         if (len >= size_a) {
+            len = (len - size_a) + 1;
+            if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) {
+               goto LBL_B;
+            }
+         }
+         /* Although the chance for b <= 3 is miniscule, try again. */
+         if (mp_cmp_d(&b, 3uL) != MP_GT) {
+            ix--;
+            continue;
+         }
+         if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+            goto LBL_B;
+         }
+         if (res == MP_NO) {
+            goto LBL_B;
+         }
+      }
+   }
+
+   /* passed the test */
+   *result = MP_YES;
+LBL_B:
+   mp_clear(&b);
+   return err;
+}
+
+#endif