Mercurial > dropbear
annotate libtommath/bn_mp_root_u32.c @ 1861:2b3a8026a6ce
Add re-exec for server
This allows ASLR to re-randomize the address
space for every connection, preventing some
vulnerabilities from being exploitable by
repeated probing.
Overhead (memory and time) is yet to be confirmed.
At present this is only enabled on Linux. Other BSD platforms
with fexecve() would probably also work though have not been tested.
author | Matt Johnston <matt@ucc.asn.au> |
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date | Sun, 30 Jan 2022 10:14:56 +0800 |
parents | 1051e4eea25a |
children |
rev | line source |
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1692
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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1 #include "tommath_private.h" |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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2 #ifdef BN_MP_ROOT_U32_C |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */ |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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4 /* SPDX-License-Identifier: Unlicense */ |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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5 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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6 /* find the n'th root of an integer |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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7 * |
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Update LibTomMath to 1.2.0 (#84)
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8 * Result found such that (c)**b <= a and (c+1)**b > a |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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9 * |
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Update LibTomMath to 1.2.0 (#84)
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10 * This algorithm uses Newton's approximation |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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11 * x[i+1] = x[i] - f(x[i])/f'(x[i]) |
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Update LibTomMath to 1.2.0 (#84)
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12 * which will find the root in log(N) time where |
1051e4eea25a
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parents:
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13 * each step involves a fair bit. |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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14 */ |
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Update LibTomMath to 1.2.0 (#84)
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15 mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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16 { |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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17 mp_int t1, t2, t3, a_; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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18 mp_ord cmp; |
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19 int ilog2; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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20 mp_err err; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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21 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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22 /* input must be positive if b is even */ |
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23 if (((b & 1u) == 0u) && (a->sign == MP_NEG)) { |
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Update LibTomMath to 1.2.0 (#84)
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24 return MP_VAL; |
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25 } |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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26 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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27 if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) { |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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28 return err; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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29 } |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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30 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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31 /* if a is negative fudge the sign but keep track */ |
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Update LibTomMath to 1.2.0 (#84)
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32 a_ = *a; |
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33 a_.sign = MP_ZPOS; |
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Update LibTomMath to 1.2.0 (#84)
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34 |
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Update LibTomMath to 1.2.0 (#84)
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35 /* Compute seed: 2^(log_2(n)/b + 2)*/ |
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Update LibTomMath to 1.2.0 (#84)
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36 ilog2 = mp_count_bits(a); |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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37 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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38 /* |
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Update LibTomMath to 1.2.0 (#84)
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39 If "b" is larger than INT_MAX it is also larger than |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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40 log_2(n) because the bit-length of the "n" is measured |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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41 with an int and hence the root is always < 2 (two). |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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42 */ |
1051e4eea25a
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43 if (b > (uint32_t)(INT_MAX/2)) { |
1051e4eea25a
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44 mp_set(c, 1uL); |
1051e4eea25a
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45 c->sign = a->sign; |
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Update LibTomMath to 1.2.0 (#84)
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46 err = MP_OKAY; |
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47 goto LBL_ERR; |
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48 } |
1051e4eea25a
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49 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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50 /* "b" is smaller than INT_MAX, we can cast safely */ |
1051e4eea25a
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51 if (ilog2 < (int)b) { |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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52 mp_set(c, 1uL); |
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53 c->sign = a->sign; |
1051e4eea25a
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54 err = MP_OKAY; |
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55 goto LBL_ERR; |
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56 } |
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57 ilog2 = ilog2 / ((int)b); |
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58 if (ilog2 == 0) { |
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59 mp_set(c, 1uL); |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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60 c->sign = a->sign; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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61 err = MP_OKAY; |
1051e4eea25a
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62 goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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63 } |
1051e4eea25a
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64 /* Start value must be larger than root */ |
1051e4eea25a
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65 ilog2 += 2; |
1051e4eea25a
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66 if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
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67 do { |
1051e4eea25a
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68 /* t1 = t2 */ |
1051e4eea25a
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69 if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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70 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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71 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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72 |
1051e4eea25a
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73 /* t3 = t1**(b-1) */ |
1051e4eea25a
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74 if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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75 |
1051e4eea25a
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76 /* numerator */ |
1051e4eea25a
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77 /* t2 = t1**b */ |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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78 if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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79 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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80 /* t2 = t1**b - a */ |
1051e4eea25a
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81 if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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82 |
1051e4eea25a
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83 /* denominator */ |
1051e4eea25a
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84 /* t3 = t1**(b-1) * b */ |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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85 if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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|
86 |
1051e4eea25a
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87 /* t3 = (t1**b - a)/(b * t1**(b-1)) */ |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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88 if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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89 |
1051e4eea25a
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90 if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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91 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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92 /* |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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93 Number of rounds is at most log_2(root). If it is more it |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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94 got stuck, so break out of the loop and do the rest manually. |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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95 */ |
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Steffen Jaeckel <s@jaeckel.eu>
parents:
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96 if (ilog2-- == 0) { |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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97 break; |
1051e4eea25a
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98 } |
1051e4eea25a
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99 } while (mp_cmp(&t1, &t2) != MP_EQ); |
1051e4eea25a
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parents:
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100 |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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101 /* result can be off by a few so check */ |
1051e4eea25a
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parents:
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102 /* Loop beneath can overshoot by one if found root is smaller than actual root */ |
1051e4eea25a
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parents:
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103 for (;;) { |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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104 if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; |
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Update LibTomMath to 1.2.0 (#84)
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parents:
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105 cmp = mp_cmp(&t2, &a_); |
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106 if (cmp == MP_EQ) { |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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107 err = MP_OKAY; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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108 goto LBL_ERR; |
1051e4eea25a
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parents:
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109 } |
1051e4eea25a
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parents:
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110 if (cmp == MP_LT) { |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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parents:
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111 if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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changeset
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112 } else { |
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113 break; |
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114 } |
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115 } |
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116 /* correct overshoot from above or from recurrence */ |
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117 for (;;) { |
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118 if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; |
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119 if (mp_cmp(&t2, &a_) == MP_GT) { |
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120 if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; |
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121 } else { |
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122 break; |
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123 } |
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124 } |
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125 |
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126 /* set the result */ |
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127 mp_exch(&t1, c); |
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128 |
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129 /* set the sign of the result */ |
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130 c->sign = a->sign; |
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131 |
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132 err = MP_OKAY; |
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133 |
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134 LBL_ERR: |
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135 mp_clear_multi(&t1, &t2, &t3, NULL); |
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136 return err; |
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137 } |
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138 |
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139 #endif |