Mercurial > dropbear
annotate libtommath/bn_mp_prime_frobenius_underwood.c @ 1723:5386011b740d
Disable toom and karatsuba for new libtommath
author | Matt Johnston <matt@ucc.asn.au> |
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date | Thu, 18 Jun 2020 19:12:07 +0800 |
parents | 1051e4eea25a |
children |
rev | line source |
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1 #include "tommath_private.h" |
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2 #ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_C |
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3 |
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4 /* LibTomMath, multiple-precision integer library -- Tom St Denis */ |
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5 /* SPDX-License-Identifier: Unlicense */ |
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6 |
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7 /* |
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8 * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details |
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9 */ |
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10 #ifndef LTM_USE_ONLY_MR |
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11 |
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12 #ifdef MP_8BIT |
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13 /* |
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14 * floor of positive solution of |
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15 * (2^16)-1 = (a+4)*(2*a+5) |
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16 * TODO: Both values are smaller than N^(1/4), would have to use a bigint |
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17 * for a instead but any a biger than about 120 are already so rare that |
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18 * it is possible to ignore them and still get enough pseudoprimes. |
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19 * But it is still a restriction of the set of available pseudoprimes |
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20 * which makes this implementation less secure if used stand-alone. |
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21 */ |
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22 #define LTM_FROBENIUS_UNDERWOOD_A 177 |
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23 #else |
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24 #define LTM_FROBENIUS_UNDERWOOD_A 32764 |
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25 #endif |
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26 mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result) |
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27 { |
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28 mp_int T1z, T2z, Np1z, sz, tz; |
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29 |
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30 int a, ap2, length, i, j; |
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31 mp_err err; |
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32 |
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33 *result = MP_NO; |
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34 |
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35 if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) { |
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36 return err; |
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37 } |
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38 |
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39 for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) { |
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40 /* TODO: That's ugly! No, really, it is! */ |
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41 if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) || |
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42 (a==14) || (a==18) || (a==23) || (a==26) || (a==28)) { |
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43 continue; |
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44 } |
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45 /* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */ |
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46 mp_set_u32(&T1z, (uint32_t)a); |
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47 |
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48 if ((err = mp_sqr(&T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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49 |
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50 if ((err = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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51 |
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52 if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR; |
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53 |
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54 if (j == -1) { |
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55 break; |
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56 } |
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57 |
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58 if (j == 0) { |
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59 /* composite */ |
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60 goto LBL_FU_ERR; |
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61 } |
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62 } |
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63 /* Tell it a composite and set return value accordingly */ |
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64 if (a >= LTM_FROBENIUS_UNDERWOOD_A) { |
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65 err = MP_ITER; |
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66 goto LBL_FU_ERR; |
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67 } |
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68 /* Composite if N and (a+4)*(2*a+5) are not coprime */ |
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69 mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5))); |
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70 |
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71 if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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72 |
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73 if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR; |
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74 |
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75 ap2 = a + 2; |
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76 if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR; |
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77 |
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78 mp_set(&sz, 1uL); |
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79 mp_set(&tz, 2uL); |
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80 length = mp_count_bits(&Np1z); |
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81 |
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82 for (i = length - 2; i >= 0; i--) { |
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83 /* |
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84 * temp = (sz*(a*sz+2*tz))%N; |
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85 * tz = ((tz-sz)*(tz+sz))%N; |
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86 * sz = temp; |
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87 */ |
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88 if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; |
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89 |
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90 /* a = 0 at about 50% of the cases (non-square and odd input) */ |
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91 if (a != 0) { |
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92 if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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93 if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR; |
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94 } |
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95 |
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96 if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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97 if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; |
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98 if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR; |
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99 if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR; |
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100 if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR; |
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101 if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR; |
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102 if (s_mp_get_bit(&Np1z, (unsigned int)i) == MP_YES) { |
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103 /* |
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104 * temp = (a+2) * sz + tz |
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105 * tz = 2 * tz - sz |
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106 * sz = temp |
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107 */ |
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108 if (a == 0) { |
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109 if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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110 } else { |
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111 if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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112 } |
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113 if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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114 if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; |
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115 if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR; |
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116 mp_exch(&sz, &T1z); |
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117 } |
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118 } |
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119 |
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120 mp_set_u32(&T1z, (uint32_t)((2 * a) + 5)); |
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121 if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR; |
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122 if (MP_IS_ZERO(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) { |
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123 *result = MP_YES; |
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124 } |
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125 |
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126 LBL_FU_ERR: |
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127 mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL); |
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128 return err; |
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129 } |
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130 |
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131 #endif |
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132 #endif |