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1 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
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2 * |
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3 * LibTomMath is a library that provides multiple-precision |
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4 * integer arithmetic as well as number theoretic functionality. |
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5 * |
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6 * The library was designed directly after the MPI library by |
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7 * Michael Fromberger but has been written from scratch with |
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8 * additional optimizations in place. |
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9 * |
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10 * The library is free for all purposes without any express |
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11 * guarantee it works. |
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12 * |
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13 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
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14 */ |
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15 #include <tommath.h> |
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16 |
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17 /* Miller-Rabin test of "a" to the base of "b" as described in |
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18 * HAC pp. 139 Algorithm 4.24 |
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19 * |
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20 * Sets result to 0 if definitely composite or 1 if probably prime. |
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21 * Randomly the chance of error is no more than 1/4 and often |
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22 * very much lower. |
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23 */ |
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24 int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result) |
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25 { |
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26 mp_int n1, y, r; |
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27 int s, j, err; |
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28 |
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29 /* default */ |
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30 *result = MP_NO; |
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31 |
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32 /* ensure b > 1 */ |
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33 if (mp_cmp_d(b, 1) != MP_GT) { |
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34 return MP_VAL; |
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35 } |
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36 |
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37 /* get n1 = a - 1 */ |
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38 if ((err = mp_init_copy (&n1, a)) != MP_OKAY) { |
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39 return err; |
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40 } |
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41 if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) { |
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42 goto __N1; |
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43 } |
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44 |
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45 /* set 2**s * r = n1 */ |
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46 if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) { |
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47 goto __N1; |
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48 } |
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49 |
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50 /* count the number of least significant bits |
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51 * which are zero |
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52 */ |
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53 s = mp_cnt_lsb(&r); |
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54 |
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55 /* now divide n - 1 by 2**s */ |
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56 if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) { |
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57 goto __R; |
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58 } |
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59 |
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60 /* compute y = b**r mod a */ |
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61 if ((err = mp_init (&y)) != MP_OKAY) { |
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62 goto __R; |
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63 } |
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64 if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) { |
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65 goto __Y; |
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66 } |
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67 |
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68 /* if y != 1 and y != n1 do */ |
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69 if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) { |
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70 j = 1; |
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71 /* while j <= s-1 and y != n1 */ |
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72 while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) { |
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73 if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) { |
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74 goto __Y; |
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75 } |
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76 |
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77 /* if y == 1 then composite */ |
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78 if (mp_cmp_d (&y, 1) == MP_EQ) { |
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79 goto __Y; |
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80 } |
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81 |
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82 ++j; |
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83 } |
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84 |
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85 /* if y != n1 then composite */ |
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86 if (mp_cmp (&y, &n1) != MP_EQ) { |
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87 goto __Y; |
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88 } |
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89 } |
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90 |
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91 /* probably prime now */ |
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92 *result = MP_YES; |
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93 __Y:mp_clear (&y); |
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94 __R:mp_clear (&r); |
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95 __N1:mp_clear (&n1); |
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96 return err; |
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97 } |
