hcrypto: import libtommath v1.2.0

lib/hcrypto/libtommath/bn_mp_kronecker.c

@@ -0,0 +1,129 @@
+#include "tommath_private.h"
+#ifdef BN_MP_KRONECKER_C
+
+/* LibTomMath, multiple-precision integer library -- Tom St Denis */
+/* SPDX-License-Identifier: Unlicense */
+
+/*
+   Kronecker symbol (a|p)
+   Straightforward implementation of algorithm 1.4.10 in
+   Henri Cohen: "A Course in Computational Algebraic Number Theory"
+
+   @book{cohen2013course,
+     title={A course in computational algebraic number theory},
+     author={Cohen, Henri},
+     volume={138},
+     year={2013},
+     publisher={Springer Science \& Business Media}
+    }
+ */
+mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c)
+{
+   mp_int a1, p1, r;
+   mp_err err;
+   int v, k;
+
+   static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};
+
+   if (MP_IS_ZERO(p)) {
+      if ((a->used == 1) && (a->dp[0] == 1u)) {
+         *c = 1;
+      } else {
+         *c = 0;
+      }
+      return MP_OKAY;
+   }
+
+   if (MP_IS_EVEN(a) && MP_IS_EVEN(p)) {
+      *c = 0;
+      return MP_OKAY;
+   }
+
+   if ((err = mp_init_copy(&a1, a)) != MP_OKAY) {
+      return err;
+   }
+   if ((err = mp_init_copy(&p1, p)) != MP_OKAY) {
+      goto LBL_KRON_0;
+   }
+
+   v = mp_cnt_lsb(&p1);
+   if ((err = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
+      goto LBL_KRON_1;
+   }
+
+   if ((v & 1) == 0) {
+      k = 1;
+   } else {
+      k = table[a->dp[0] & 7u];
+   }
+
+   if (p1.sign == MP_NEG) {
+      p1.sign = MP_ZPOS;
+      if (a1.sign == MP_NEG) {
+         k = -k;
+      }
+   }
+
+   if ((err = mp_init(&r)) != MP_OKAY) {
+      goto LBL_KRON_1;
+   }
+
+   for (;;) {
+      if (MP_IS_ZERO(&a1)) {
+         if (mp_cmp_d(&p1, 1uL) == MP_EQ) {
+            *c = k;
+            goto LBL_KRON;
+         } else {
+            *c = 0;
+            goto LBL_KRON;
+         }
+      }
+
+      v = mp_cnt_lsb(&a1);
+      if ((err = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
+         goto LBL_KRON;
+      }
+
+      if ((v & 1) == 1) {
+         k = k * table[p1.dp[0] & 7u];
+      }
+
+      if (a1.sign == MP_NEG) {
+         /*
+          * Compute k = (-1)^((a1)*(p1-1)/4) * k
+          * a1.dp[0] + 1 cannot overflow because the MSB
+          * of the type mp_digit is not set by definition
+          */
+         if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) {
+            k = -k;
+         }
+      } else {
+         /* compute k = (-1)^((a1-1)*(p1-1)/4) * k */
+         if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) {
+            k = -k;
+         }
+      }
+
+      if ((err = mp_copy(&a1, &r)) != MP_OKAY) {
+         goto LBL_KRON;
+      }
+      r.sign = MP_ZPOS;
+      if ((err = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
+         goto LBL_KRON;
+      }
+      if ((err = mp_copy(&r, &p1)) != MP_OKAY) {
+         goto LBL_KRON;
+      }
+   }
+
+LBL_KRON:
+   mp_clear(&r);
+LBL_KRON_1:
+   mp_clear(&p1);
+LBL_KRON_0:
+   mp_clear(&a1);
+
+   return err;
+}
+
+#endif