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 /* 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include /* computes the jacobi c = (a | n) (or Legendre if n is prime) * HAC pp. 73 Algorithm 2.149 */ int mp_jacobi (mp_int * a, mp_int * p, int *c) { mp_int a1, p1; int k, s, r, res; mp_digit residue; /* if p <= 0 return MP_VAL */ if (mp_cmp_d(p, 0) != MP_GT) { return MP_VAL; } /* step 1. if a == 0, return 0 */ if (mp_iszero (a) == 1) { *c = 0; return MP_OKAY; } /* step 2. if a == 1, return 1 */ if (mp_cmp_d (a, 1) == MP_EQ) { *c = 1; return MP_OKAY; } /* default */ s = 0; /* step 3. write a = a1 * 2**k */ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) { return res; } if ((res = mp_init (&p1)) != MP_OKAY) { goto __A1; } /* divide out larger power of two */ k = mp_cnt_lsb(&a1); if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) { goto __P1; } /* step 4. if e is even set s=1 */ if ((k & 1) == 0) { s = 1; } else { /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */ residue = p->dp[0] & 7; if (residue == 1 || residue == 7) { s = 1; } else if (residue == 3 || residue == 5) { s = -1; } } /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */ if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) { s = -s; } /* if a1 == 1 we're done */ if (mp_cmp_d (&a1, 1) == MP_EQ) { *c = s; } else { /* n1 = n mod a1 */ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) { goto __P1; } if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) { goto __P1; } *c = s * r; } /* done */ res = MP_OKAY; __P1:mp_clear (&p1); __A1:mp_clear (&a1); return res; }
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