Update libtommath to latest stable release (1.1.0)

1 files changed, 131 insertions, 0 deletions

diff --git a/libtommath/bn_mp_sqrtmod_prime.c b/libtommath/bn_mp_sqrtmod_prime.c
new file mode 100644
index 0000000..cc4da3b
--- /dev/null
+++ b/libtommath/bn_mp_sqrtmod_prime.c
@@ -0,0 +1,131 @@
+#include "tommath_private.h"
+#ifdef BN_MP_SQRTMOD_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.
+ *
+ * SPDX-License-Identifier: Unlicense
+ */
+
+/* Tonelli-Shanks algorithm
+ * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
+ * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
+ *
+ */
+
+int mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret)
+{
+   int res, legendre;
+   mp_int t1, C, Q, S, Z, M, T, R, two;
+   mp_digit i;
+
+   /* first handle the simple cases */
+   if (mp_cmp_d(n, 0uL) == MP_EQ) {
+      mp_zero(ret);
+      return MP_OKAY;
+   }
+   if (mp_cmp_d(prime, 2uL) == MP_EQ)                            return MP_VAL; /* prime must be odd */
+   if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY)        return res;
+   if (legendre == -1)                                           return MP_VAL; /* quadratic non-residue mod prime */
+
+   if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
+      return res;
+   }
+
+   /* SPECIAL CASE: if prime mod 4 == 3
+    * compute directly: res = n^(prime+1)/4 mod prime
+    * Handbook of Applied Cryptography algorithm 3.36
+    */
+   if ((res = mp_mod_d(prime, 4uL, &i)) != MP_OKAY)               goto cleanup;
+   if (i == 3u) {
+      if ((res = mp_add_d(prime, 1uL, &t1)) != MP_OKAY)           goto cleanup;
+      if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                  goto cleanup;
+      if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                  goto cleanup;
+      if ((res = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY)      goto cleanup;
+      res = MP_OKAY;
+      goto cleanup;
+   }
+
+   /* NOW: Tonelli-Shanks algorithm */
+
+   /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */
+   if ((res = mp_copy(prime, &Q)) != MP_OKAY)                    goto cleanup;
+   if ((res = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY)                 goto cleanup;
+   /* Q = prime - 1 */
+   mp_zero(&S);
+   /* S = 0 */
+   while (mp_iseven(&Q) != MP_NO) {
+      if ((res = mp_div_2(&Q, &Q)) != MP_OKAY)                    goto cleanup;
+      /* Q = Q / 2 */
+      if ((res = mp_add_d(&S, 1uL, &S)) != MP_OKAY)               goto cleanup;
+      /* S = S + 1 */
+   }
+
+   /* find a Z such that the Legendre symbol (Z|prime) == -1 */
+   if ((res = mp_set_int(&Z, 2uL)) != MP_OKAY)                    goto cleanup;
+   /* Z = 2 */
+   while (1) {
+      if ((res = mp_jacobi(&Z, prime, &legendre)) != MP_OKAY)     goto cleanup;
+      if (legendre == -1) break;
+      if ((res = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY)               goto cleanup;
+      /* Z = Z + 1 */
+   }
+
+   if ((res = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY)         goto cleanup;
+   /* C = Z ^ Q mod prime */
+   if ((res = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY)                goto cleanup;
+   if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                    goto cleanup;
+   /* t1 = (Q + 1) / 2 */
+   if ((res = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY)         goto cleanup;
+   /* R = n ^ ((Q + 1) / 2) mod prime */
+   if ((res = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY)          goto cleanup;
+   /* T = n ^ Q mod prime */
+   if ((res = mp_copy(&S, &M)) != MP_OKAY)                       goto cleanup;
+   /* M = S */
+   if ((res = mp_set_int(&two, 2uL)) != MP_OKAY)                 goto cleanup;
+
+   res = MP_VAL;
+   while (1) {
+      if ((res = mp_copy(&T, &t1)) != MP_OKAY)                    goto cleanup;
+      i = 0;
+      while (1) {
+         if (mp_cmp_d(&t1, 1uL) == MP_EQ) break;
+         if ((res = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
+         i++;
+      }
+      if (i == 0u) {
+         if ((res = mp_copy(&R, ret)) != MP_OKAY)                  goto cleanup;
+         res = MP_OKAY;
+         goto cleanup;
+      }
+      if ((res = mp_sub_d(&M, i, &t1)) != MP_OKAY)                goto cleanup;
+      if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY)             goto cleanup;
+      if ((res = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY)   goto cleanup;
+      /* t1 = 2 ^ (M - i - 1) */
+      if ((res = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY)     goto cleanup;
+      /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
+      if ((res = mp_sqrmod(&t1, prime, &C)) != MP_OKAY)           goto cleanup;
+      /* C = (t1 * t1) mod prime */
+      if ((res = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY)       goto cleanup;
+      /* R = (R * t1) mod prime */
+      if ((res = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY)        goto cleanup;
+      /* T = (T * C) mod prime */
+      mp_set(&M, i);
+      /* M = i */
+   }
+
+cleanup:
+   mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
+   return res;
+}
+
+#endif
+
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */