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 /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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 b is prime) * HAC pp. 73 Algorithm 2.149 */ int mp_jacobi (mp_int * a, mp_int * n, int *c) { mp_int a1, n1, e; int s, r, res; mp_digit residue; /* 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^e */ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) { return res; } if ((res = mp_init (&n1)) != MP_OKAY) { goto __A1; } if ((res = mp_init (&e)) != MP_OKAY) { goto __N1; } while (mp_iseven (&a1) == 1) { if ((res = mp_add_d (&e, 1, &e)) != MP_OKAY) { goto __E; } if ((res = mp_div_2 (&a1, &a1)) != MP_OKAY) { goto __E; } } /* step 4. if e is even set s=1 */ if (mp_iseven (&e) == 1) { s = 1; } else { /* else set s=1 if n = 1/7 (mod 8) or s=-1 if n = 3/5 (mod 8) */ if ((res = mp_mod_d (n, 8, &residue)) != MP_OKAY) { goto __E; } if (residue == 1 || residue == 7) { s = 1; } else if (residue == 3 || residue == 5) { s = -1; } } /* step 5. if n == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */ if ((res = mp_mod_d (n, 4, &residue)) != MP_OKAY) { goto __E; } if (residue == 3) { if ((res = mp_mod_d (&a1, 4, &residue)) != MP_OKAY) { goto __E; } if (residue == 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 (n, &a1, &n1)) != MP_OKAY) { goto __E; } if ((res = mp_jacobi (&n1, &a1, &r)) != MP_OKAY) { goto __E; } *c = s * r; } /* done */ res = MP_OKAY; __E:mp_clear (&e); __N1:mp_clear (&n1); __A1:mp_clear (&a1); return res; }
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