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1
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/*
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2
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*******************************************************************************
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3
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\file belt_fmt.c
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4
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\brief STB 34.101.31 (belt): FMT (format preserving encryption)
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5
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\project bee2 [cryptographic library]
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6
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\author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}]
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7
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\created 2017.09.28
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8
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\version 2020.03.24
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9
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\license This program is released under the GNU General Public License
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10
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version 3. See Copyright Notices in bee2/info.h.
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11
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*******************************************************************************
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12
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*/
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13
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14
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#include "bee2/core/blob.h"
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15
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#include "bee2/core/err.h"
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16
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#include "bee2/core/mem.h"
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17
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#include "bee2/core/u16.h"
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18
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#include "bee2/core/u32.h"
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19
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#include "bee2/core/util.h"
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20
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#include "bee2/crypto/belt.h"
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21
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#include "bee2/math/ww.h"
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22
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#include "bee2/math/zz.h"
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23
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#include "belt_lcl.h"
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24
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25
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/*
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26
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*******************************************************************************
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27
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Минимальное число 64-битовых блоков для размещения слова из ZZ_mod^count.
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28
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29
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Необходимо вычислить ceil(log2(mod) * count / 64).
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30
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31
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Реализован следующий алгоритм:
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32
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33
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1. c <- 1588 / 2291 (диофантово приближение ln 2 через цепные дроби).
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34
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2. 2^k <- ближайшая к mod степень двойки.
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35
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3. x <- (m - 2^k)/ 2^k.
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36
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4. y <- x(60 + 60x + 11x^2)/(60 + 60x + 36x^2 + 3x^3)
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37
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(аппроксимация Паде для ln(1 + x)).
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38
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5. b <- ceil((k + y / c) * count / 64).
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39
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6. Возвратить b.
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40
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41
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Аргумент ceil() на предпоследнем шаге можно записать следующим образом:
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42
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\code
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43
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count * (4764 k (8^k + 9 4^k mod + 9 2^k mod^2 + mod^3) -
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44
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2291(11 8^k + 27 4^k mod - 27 2^k mod^2 - 11 mod^3)) /
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45
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304896 * (8^k + 9 4^k mod + 9 2^k mod^2 + mod^3)
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46
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\endcode
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47
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48
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Алгоритм правильно работает для mod <= 65536 и count <= 300 за исключением
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49
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следующих сочетаний (mod, count):
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50
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\code
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51
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(49667, 160).
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52
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\endcode
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53
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54
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Проверка:
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55
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\code
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56
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#include <math.h>
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57
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...
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58
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u32 mod;
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59
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size_t count;
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60
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for (mod = 2; mod <= 65536; ++mod)
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61
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for (count = 1; count <= 300; ++count)
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62
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{
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63
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long double b = log(mod) / log(2.0);
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64
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b *= count, b /= 64.0;
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65
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if ((size_t)ceil(b) != beltFMTCalcB(mod, count))
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66
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ASSERT(0);
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67
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}
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68
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\endcode
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69
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70
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\remark Используется соглашение sizeof(word) >= sizeof(u16): mod либо
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71
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умещается в word, либо равняется 65536.
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72
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*******************************************************************************
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73
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*/
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74
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75
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1
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static size_t beltFMTCalcB(u32 mod, size_t count)
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76
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{
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77
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1
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const size_t m = W_OF_B(128);
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78
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word num[W_OF_B(128)];
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79
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word den[W_OF_B(128)];
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80
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size_t k;
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81
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word stack[W_OF_B(128) * 5];
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82
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1
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word* t0 = stack;
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83
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1
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word* t1 = t0 + m;
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84
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1
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word* t2 = t1 + m;
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85
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1
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word* t3 = t2 + m;
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86
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1
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word* t4 = t3 + m;
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87
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// pre
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88
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1
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ASSERT(2 <= mod && mod <= 65536);
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89
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1
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ASSERT(1 <= count && count <= 300);
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90
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// обработать особые сочетания (mod, count)
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91
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1
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if (mod == 49667 && count == 320)
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92
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0
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return 39;
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93
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// обработать mod, который не умещается в 16 битов
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94
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1
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if (mod == 65536)
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95
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1
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return (16 * count + 63) / 64;
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96
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// k <- ceil(log2(mod))
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97
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1
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k = B_PER_W - wordCLZ((word)mod);
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98
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1
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ASSERT(k > 0);
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99
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1
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if ((U32_1 << k) - mod > mod - (U32_1 << (k - 1)))
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100
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1
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--k;
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101
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// t0 <- 8^k
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102
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1
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wwSetZero(t0, m);
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103
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1
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wwSetBit(t0, 3 * k, 1);
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104
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// t1 <- 4^k mod
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105
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1
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wwSetZero(t1, m);
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106
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1
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wwSetBit(t1, 2 * k, 1);
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107
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1
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zzMulW(t1, t1, m, mod);
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108
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// t2 <- 2^k mod^2
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109
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1
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wwSetZero(t2, m);
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110
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1
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wwSetBit(t2, k, 1);
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111
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1
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zzMulW(t2, t2, m, mod);
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112
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1
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zzMulW(t2, t2, m, mod);
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113
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// t3 <- mod^3
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114
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1
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wwSetW(t3, m, mod);
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115
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1
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zzMulW(t3, t3, m, mod);
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116
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1
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zzMulW(t3, t3, m, mod);
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117
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// den <- t0 + 9 * t1 + 9 * t2 + t3
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118
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1
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wwCopy(den, t0, m);
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119
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1
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zzAdd2(den, t3, m);
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120
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1
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wwCopy(t4, t1, m);
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121
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1
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zzAdd2(t4, t2, m);
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122
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1
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zzMulW(t4, t4, m, 9);
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123
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1
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zzAdd2(den, t4, m);
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124
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// num <- den * 4767 k
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125
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1
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wwCopy(num, den, m);
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126
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1
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zzMulW(num, num, m, 4764);
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127
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1
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zzMulW(num, num, m, (word)k);
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128
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// num <- count * (num - 25201 t0 - 61857 t1 + 61857 t2 + 25201 t3)
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129
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1
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zzMulW(t3, t3, m, 25201);
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130
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1
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zzAdd2(num, t3, m);
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131
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1
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zzMulW(t2, t2, m, 61857u);
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132
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1
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zzAdd2(num, t2, m);
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133
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1
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zzMulW(t1, t1, m, 61857u);
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134
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1
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zzSub2(num, t1, m);
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135
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1
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zzMulW(t0, t0, m, 25201);
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136
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1
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zzSub2(num, t0, m);
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137
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1
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zzMulW(num, num, m, (word)count);
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138
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// den <- 304896 * den
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139
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1
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zzMulW(den, den, m, 768);
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140
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1
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zzMulW(den, den, m, 397);
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141
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// num <- num + den - 1
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142
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1
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zzAdd2(num, den, m);
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143
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1
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zzSubW2(num, m, 1);
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144
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// num <- num / den
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145
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1
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for (k = m; den[k - 1] == 0; --k);
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146
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1
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ASSERT(zzDiv_deep(m, k) <= sizeof(stack));
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147
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1
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zzDiv(den, num, num, m, den, k, stack);
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148
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// возврат
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149
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1
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return (size_t)den[0];
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150
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}
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151
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152
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/*
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153
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*******************************************************************************
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154
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belt-32block
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155
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*******************************************************************************
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156
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*/
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157
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158
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1
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void belt32BlockEncr(octet block[24], const u32 key[8])
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159
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{
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160
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1
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u32* t = (u32*)block;
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161
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1
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u32From(t, block, 24);
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162
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// round #1
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163
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1
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beltBlockEncr3(t + 2, t + 3, t + 4, t + 5, key);
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164
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1
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t[2] ^= 1, t[0] ^= t[2], t[1] ^= t[3];
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165
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// round #2
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166
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1
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beltBlockEncr3(t + 4, t + 5, t + 0, t + 1, key);
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167
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1
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t[4] ^= 2, t[2] ^= t[4], t[3] ^= t[5];
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168
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// round #3
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169
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1
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beltBlockEncr3(t + 0, t + 1, t + 2, t + 3, key);
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170
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1
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t[0] ^= 3, t[4] ^= t[0], t[5] ^= t[1];
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171
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// возврат
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172
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1
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u32To(block, 24, t);
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173
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}
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174
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175
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/*
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176
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*******************************************************************************
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177
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Конвертации
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|
178
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|
*******************************************************************************
|
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179
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|
*/
|
|
180
|
|
|
|
181
|
1
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static void beltStr2Bin(octet bin[], size_t b, u32 mod,
|
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182
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const u16 str[], size_t count)
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183
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{
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184
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word* a;
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185
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size_t m;
|
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186
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// подготовить память
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187
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1
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memSetZero(bin, 8 * b);
|
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188
|
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// особый случай: mod может не уложиться в word
|
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189
|
1
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if (mod == 65536)
|
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190
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{
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191
|
1
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u16To(bin, 2 * count, str);
|
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192
|
1
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return;
|
|
193
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}
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194
|
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// конвертировать
|
|
195
|
1
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ASSERT(2 <= mod && mod < 65536);
|
|
196
|
1
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ASSERT(count >= 1);
|
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197
|
1
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--count;
|
|
198
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EXPECT(str[count] < mod);
|
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199
|
1
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a = (word*)bin;
|
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200
|
1
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m = W_OF_O(8 * b);
|
|
201
|
1
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a[0] = (word)str[count];
|
|
202
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1
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while (count--)
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203
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{
|
|
204
|
1
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zzMulW(a, a, m, mod);
|
|
205
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EXPECT(str[count] < mod);
|
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206
|
1
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zzAddW2(a, m, (word)str[count]);
|
|
207
|
|
}
|
|
208
|
1
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wwTo(bin, 8 * b, a);
|
|
209
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|
}
|
|
210
|
|
|
|
211
|
1
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static void beltBin2StrAdd(u32 mod, u16 str[], size_t count,
|
|
212
|
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octet bin[], size_t b)
|
|
213
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{
|
|
214
|
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register u32 t;
|
|
215
|
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word* a;
|
|
216
|
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size_t m;
|
|
217
|
|
// особый случай: mod может не уложиться в word
|
|
218
|
1
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if (mod == 65536)
|
|
219
|
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{
|
|
220
|
1
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u16* uu = (u16*)bin;
|
|
221
|
1
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u16From(uu, bin, 8 * b);
|
|
222
|
1
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while (count--)
|
|
223
|
1
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str[count] += uu[count];
|
|
224
|
1
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return;
|
|
225
|
|
}
|
|
226
|
|
// настроить память
|
|
227
|
1
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m = W_OF_O(8 * b);
|
|
228
|
1
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a = (word*)bin;
|
|
229
|
1
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wwFrom(a, bin, 8 * b);
|
|
230
|
|
// конвертировать и сложить
|
|
231
|
1
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ASSERT(2 <= mod && mod < 65536);
|
|
232
|
1
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while (count--)
|
|
233
|
|
{
|
|
234
|
1
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t = (u32)zzModW(a, m, mod);
|
|
235
|
1
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t += str[0], t %= mod;
|
|
236
|
1
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str[0] = (u16)t, ++str;
|
|
237
|
1
|
zzDivW(a, a, m, mod);
|
|
238
|
|
}
|
|
239
|
1
|
t = 0;
|
|
240
|
|
}
|
|
241
|
|
|
|
242
|
1
|
static void beltBin2StrSub(word mod, u16 str[], size_t count,
|
|
243
|
|
octet bin[], size_t b)
|
|
244
|
|
{
|
|
245
|
|
register u32 t;
|
|
246
|
|
word* a;
|
|
247
|
|
size_t m;
|
|
248
|
|
// особый случай: mod может не уложиться в word
|
|
249
|
1
|
if (mod == 65536)
|
|
250
|
|
{
|
|
251
|
1
|
u16* uu = (u16*)bin;
|
|
252
|
1
|
u16From(uu, bin, 8 * b);
|
|
253
|
1
|
while (count--)
|
|
254
|
1
|
str[count] -= uu[count];
|
|
255
|
1
|
return;
|
|
256
|
|
}
|
|
257
|
|
// настроить память
|
|
258
|
1
|
m = W_OF_O(8 * b);
|
|
259
|
1
|
a = (word*)bin;
|
|
260
|
1
|
wwFrom(a, bin, 8 * b);
|
|
261
|
|
// конвертировать и вычесть
|
|
262
|
1
|
ASSERT(2 <= mod && mod <= 65536);
|
|
263
|
1
|
while (count--)
|
|
264
|
|
{
|
|
265
|
1
|
t = (u32)zzModW(a, m, mod);
|
|
266
|
1
|
t = str[0] + mod - t, t %= mod;
|
|
267
|
1
|
str[0] = (u16)t, ++str;
|
|
268
|
1
|
zzDivW(a, a, m, mod);
|
|
269
|
|
}
|
|
270
|
1
|
t = 0;
|
|
271
|
|
}
|
|
272
|
|
|
|
273
|
|
/*
|
|
274
|
|
*******************************************************************************
|
|
275
|
|
Шифрование с сохранением формата (FMT)
|
|
276
|
|
|
|
277
|
|
\remark После одного beltKWPStart() выполняются многократные обращения
|
|
278
|
|
к beltKWPStepE(). Для корректной работы перед каждым обращением в состоянии
|
|
279
|
|
механизма KWP сбрасывается счетчик тактов:
|
|
280
|
|
\code
|
|
281
|
|
st->kwp->round = 0;
|
|
282
|
|
\endcode
|
|
283
|
|
*******************************************************************************
|
|
284
|
|
*/
|
|
285
|
|
|
|
286
|
|
typedef struct
|
|
287
|
|
{
|
|
288
|
|
belt_wbl_st wbl[1]; /*< состояние механизма WBL */
|
|
289
|
|
u32 mod; /*< модуль */
|
|
290
|
|
size_t n1; /*< длина левой половинки */
|
|
291
|
|
size_t n2; /*< длина правой половинки */
|
|
292
|
|
size_t b1; /*< число блоков для обработки левой половинки */
|
|
293
|
|
size_t b2; /*< число блоков для обработки правой половинки */
|
|
294
|
|
octet iv[4 + 16 + 4]; /*< формат || синхропосылка || формат */
|
|
295
|
|
octet buf[]; /*< вспомогательный буфер */
|
|
296
|
|
} belt_fmt_st;
|
|
297
|
|
|
|
298
|
1
|
size_t beltFMT_keep(u32 mod, size_t count)
|
|
299
|
|
{
|
|
300
|
1
|
ASSERT(2 <= mod && mod <= 65536);
|
|
301
|
1
|
ASSERT(2 <= count && count <= 600);
|
|
302
|
1
|
return sizeof(belt_fmt_st) + 8 * (beltFMTCalcB(mod, (count + 1) / 2) + 1);
|
|
303
|
|
}
|
|
304
|
|
|
|
305
|
1
|
void beltFMTStart(void* state, u32 mod, size_t count, const octet key[],
|
|
306
|
|
size_t len)
|
|
307
|
|
{
|
|
308
|
1
|
belt_fmt_st* st = (belt_fmt_st*)state;
|
|
309
|
1
|
ASSERT(2 <= mod && mod <= 65536);
|
|
310
|
1
|
ASSERT(2 <= count && count <= 600);
|
|
311
|
1
|
ASSERT(memIsValid(state, beltFMT_keep(mod, count)));
|
|
312
|
|
// инициализировать состояние
|
|
313
|
1
|
beltWBLStart(st->wbl, key, len);
|
|
314
|
1
|
st->mod = mod;
|
|
315
|
1
|
st->n1 = (count + 1) / 2;
|
|
316
|
1
|
st->n2 = count / 2;
|
|
317
|
1
|
st->b1 = beltFMTCalcB(mod, st->n1);
|
|
318
|
1
|
st->b2 = beltFMTCalcB(mod, st->n2);
|
|
319
|
|
#if (OCTET_ORDER == LITTLE_ENDIAN)
|
|
320
|
1
|
((u16*)st->iv)[0] = (u16)mod;
|
|
321
|
1
|
((u16*)st->iv)[1] = (u16)count;
|
|
322
|
|
#else
|
|
323
|
|
((u16*)st->iv)[0] = u16Rev((u16)mod);
|
|
324
|
|
((u16*)st->iv)[1] = u16Rev((u16)count);
|
|
325
|
|
#endif
|
|
326
|
1
|
memCopy(st->iv + 20, st->iv, 4);
|
|
327
|
|
}
|
|
328
|
|
|
|
329
|
1
|
void beltFMTStepE(u16 buf[], const octet iv[16], void* state)
|
|
330
|
|
{
|
|
331
|
1
|
belt_fmt_st* st = (belt_fmt_st*)state;
|
|
332
|
|
size_t i;
|
|
333
|
1
|
ASSERT(memIsValid(state, sizeof(belt_fmt_st)));
|
|
334
|
1
|
ASSERT(memIsValid(state, beltFMT_keep(st->mod, st->n1 + st->n2)));
|
|
335
|
1
|
ASSERT(memIsNullOrValid(iv, 16));
|
|
336
|
1
|
ASSERT(memIsValid(buf, 2 * st->n1 + 2 * st->n2));
|
|
337
|
|
// подготовить синхропосылку
|
|
338
|
1
|
if (iv)
|
|
339
|
1
|
memCopy(st->iv + 4, iv, 16);
|
|
340
|
|
else
|
|
341
|
1
|
memSetZero(st->iv + 4, 16);
|
|
342
|
|
// такты
|
|
343
|
1
|
for (i = 0; i < 3; ++i)
|
|
344
|
|
{
|
|
345
|
|
// первая половинка
|
|
346
|
1
|
beltStr2Bin(st->buf, st->b2, st->mod, buf + st->n1, st->n2);
|
|
347
|
1
|
memCopy(st->buf + st->b2 * 8, beltH() + 8 * i, 4);
|
|
348
|
1
|
memCopy(st->buf + st->b2 * 8 + 4, st->iv + 8 * i, 4);
|
|
349
|
1
|
if (st->b2 == 1)
|
|
350
|
1
|
beltBlockEncr(st->buf, st->wbl->key);
|
|
351
|
1
|
else if (st->b2 == 2)
|
|
352
|
1
|
belt32BlockEncr(st->buf, st->wbl->key);
|
|
353
|
|
else
|
|
354
|
0
|
beltWBLStepE(st->buf, 8 * st->b2 + 8, st->wbl);
|
|
355
|
1
|
beltBin2StrAdd(st->mod, buf, st->n1, st->buf, st->b2 + 1);
|
|
356
|
|
// вторая половинка
|
|
357
|
1
|
beltStr2Bin(st->buf, st->b1, st->mod, buf, st->n1);
|
|
358
|
1
|
memCopy(st->buf + st->b1 * 8, beltH() + 8 * i + 4, 4);
|
|
359
|
1
|
memCopy(st->buf + st->b1 * 8 + 4, st->iv + 8 * i + 4, 4);
|
|
360
|
1
|
if (st->b1 == 1)
|
|
361
|
1
|
beltBlockEncr(st->buf, st->wbl->key);
|
|
362
|
1
|
else if (st->b1 == 2)
|
|
363
|
1
|
belt32BlockEncr(st->buf, st->wbl->key);
|
|
364
|
|
else
|
|
365
|
1
|
beltWBLStepE(st->buf, 8 * st->b1 + 8, st->wbl);
|
|
366
|
1
|
beltBin2StrAdd(st->mod, buf + st->n1, st->n2, st->buf, st->b1 + 1);
|
|
367
|
|
}
|
|
368
|
|
}
|
|
369
|
|
|
|
370
|
1
|
void beltFMTStepD(u16 buf[], const octet iv[16], void* state)
|
|
371
|
|
{
|
|
372
|
1
|
belt_fmt_st* st = (belt_fmt_st*)state;
|
|
373
|
|
size_t i;
|
|
374
|
1
|
ASSERT(memIsValid(state, sizeof(belt_fmt_st)));
|
|
375
|
1
|
ASSERT(memIsValid(state, beltFMT_keep(st->mod, st->n1 + st->n2)));
|
|
376
|
1
|
ASSERT(memIsNullOrValid(iv, 16));
|
|
377
|
1
|
ASSERT(memIsValid(buf, 2 * st->n1 + 2 * st->n2));
|
|
378
|
|
// подготовить синхропосылку
|
|
379
|
1
|
if (iv)
|
|
380
|
1
|
memCopy(st->iv + 4, iv, 16);
|
|
381
|
|
else
|
|
382
|
1
|
memSetZero(st->iv + 4, 16);
|
|
383
|
|
// такты
|
|
384
|
1
|
for (i = 3; i--;)
|
|
385
|
|
{
|
|
386
|
|
// вторая половинка
|
|
387
|
1
|
beltStr2Bin(st->buf, st->b1, st->mod, buf, st->n1);
|
|
388
|
1
|
memCopy(st->buf + st->b1 * 8, beltH() + 8 * i + 4, 4);
|
|
389
|
1
|
memCopy(st->buf + st->b1 * 8 + 4, st->iv + 8 * i + 4, 4);
|
|
390
|
1
|
if (st->b1 == 1)
|
|
391
|
1
|
beltBlockEncr(st->buf, st->wbl->key);
|
|
392
|
1
|
else if (st->b1 == 2)
|
|
393
|
1
|
belt32BlockEncr(st->buf, st->wbl->key);
|
|
394
|
|
else
|
|
395
|
1
|
beltWBLStepE(st->buf, 8 * st->b1 + 8, st->wbl);
|
|
396
|
1
|
beltBin2StrSub(st->mod, buf + st->n1, st->n2, st->buf, st->b1 + 1);
|
|
397
|
|
// первая половинка
|
|
398
|
1
|
beltStr2Bin(st->buf, st->b2, st->mod, buf + st->n1, st->n2);
|
|
399
|
1
|
memCopy(st->buf + st->b2 * 8, beltH() + 8 * i, 4);
|
|
400
|
1
|
memCopy(st->buf + st->b2 * 8 + 4, st->iv + 8 * i, 4);
|
|
401
|
1
|
if (st->b2 == 1)
|
|
402
|
1
|
beltBlockEncr(st->buf, st->wbl->key);
|
|
403
|
1
|
else if (st->b2 == 2)
|
|
404
|
1
|
belt32BlockEncr(st->buf, st->wbl->key);
|
|
405
|
|
else
|
|
406
|
0
|
beltWBLStepE(st->buf, 8 * st->b2 + 8, st->wbl);
|
|
407
|
1
|
beltBin2StrSub(st->mod, buf, st->n1, st->buf, st->b2 + 1);
|
|
408
|
|
}
|
|
409
|
|
}
|
|
410
|
|
|
|
411
|
1
|
err_t beltFMTEncr(u16 dest[], u32 mod, const u16 src[], size_t count,
|
|
412
|
|
const octet key[], size_t len, const octet iv[16])
|
|
413
|
|
{
|
|
414
|
|
void* state;
|
|
415
|
|
// проверить входные данные
|
|
416
|
1
|
if (count < 2 ||
|
|
417
|
1
|
len != 16 && len != 24 && len != 32 ||
|
|
418
|
1
|
!memIsValid(src, 2 * count) ||
|
|
419
|
1
|
!memIsNullOrValid(iv, 16) ||
|
|
420
|
1
|
!memIsValid(key, len) ||
|
|
421
|
1
|
!memIsValid(dest, 2 * count) ||
|
|
422
|
1
|
iv && !memIsDisjoint2(dest, 2 * count, iv, 16))
|
|
423
|
0
|
return ERR_BAD_INPUT;
|
|
424
|
1
|
if (count > 600)
|
|
425
|
0
|
return ERR_NOT_IMPLEMENTED;
|
|
426
|
|
// создать состояние
|
|
427
|
1
|
state = blobCreate(beltFMT_keep(mod, count));
|
|
428
|
1
|
if (state == 0)
|
|
429
|
0
|
return ERR_OUTOFMEMORY;
|
|
430
|
|
// зашифровать
|
|
431
|
1
|
beltFMTStart(state, mod, count, key, len);
|
|
432
|
1
|
memMove(dest, src, 2 * count);
|
|
433
|
1
|
beltFMTStepE(dest, iv, state);
|
|
434
|
|
// завершить
|
|
435
|
1
|
blobClose(state);
|
|
436
|
1
|
return ERR_OK;
|
|
437
|
|
}
|
|
438
|
|
|
|
439
|
1
|
err_t beltFMTDecr(u16 dest[], u32 mod, const u16 src[], size_t count,
|
|
440
|
|
const octet key[], size_t len, const octet iv[16])
|
|
441
|
|
{
|
|
442
|
|
void* state;
|
|
443
|
|
// проверить входные данные
|
|
444
|
1
|
if (count < 2 ||
|
|
445
|
1
|
len != 16 && len != 24 && len != 32 ||
|
|
446
|
1
|
!memIsValid(src, 2 * count) ||
|
|
447
|
1
|
!memIsNullOrValid(iv, 16) ||
|
|
448
|
1
|
!memIsValid(key, len) ||
|
|
449
|
1
|
!memIsValid(dest, 2 * count) ||
|
|
450
|
1
|
iv && !memIsDisjoint2(dest, 2 * count, iv, 16))
|
|
451
|
0
|
return ERR_BAD_INPUT;
|
|
452
|
1
|
if (count > 600)
|
|
453
|
0
|
return ERR_NOT_IMPLEMENTED;
|
|
454
|
|
// создать состояние
|
|
455
|
1
|
state = blobCreate(beltFMT_keep(mod, count));
|
|
456
|
1
|
if (state == 0)
|
|
457
|
0
|
return ERR_OUTOFMEMORY;
|
|
458
|
|
// зашифровать
|
|
459
|
1
|
beltFMTStart(state, mod, count, key, len);
|
|
460
|
1
|
memMove(dest, src, 2 * count);
|
|
461
|
1
|
beltFMTStepD(dest, iv, state);
|
|
462
|
|
// завершить
|
|
463
|
1
|
blobClose(state);
|
|
464
|
1
|
return ERR_OK;
|
|
465
|
|
}
|
agievich