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gf2m_small_m.h
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1 /*
2 * (C) Copyright Projet SECRET, INRIA, Rocquencourt
3 * (C) Bhaskar Biswas and Nicolas Sendrier
4 *
5 * (C) 2014 cryptosource GmbH
6 * (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
7 *
8 * Botan is released under the Simplified BSD License (see license.txt)
9 *
10 */
11
12 #ifndef BOTAN_GF2M_SMALL_M_H__
13 #define BOTAN_GF2M_SMALL_M_H__
14
15 #include <vector>
16 #include <botan/types.h>
17
18 namespace Botan {
19
20 typedef uint16_t gf2m;
21
22 /**
23 * GF(2^m) field for m = [2...16]
24 */
25 class BOTAN_DLL GF2m_Field
26 {
27 public:
28 explicit GF2m_Field(size_t extdeg);
29
30 gf2m gf_mul(gf2m x, gf2m y) const
31 {
32 return ((x) ? gf_mul_fast(x, y) : 0);
33 }
34
35 gf2m gf_square(gf2m x) const
36 {
37 return ((x) ? gf_exp(_gf_modq_1(gf_log(x) << 1)) : 0);
38 }
39
40 gf2m square_rr(gf2m x) const
41 {
42 return _gf_modq_1(x << 1);
43 }
44
45 gf2m gf_mul_fast(gf2m x, gf2m y) const
46 {
47 return ((y) ? gf_exp(_gf_modq_1(gf_log(x) + gf_log(y))) : 0);
48 }
49
50 /*
51 naming convention of GF(2^m) field operations:
52 l logarithmic, unreduced
53 r logarithmic, reduced
54 n normal, non-zero
55 z normal, might be zero
56 */
57
58 gf2m gf_mul_lll(gf2m a, gf2m b) const
59 {
60 return (a + b);
61 }
62
63 gf2m gf_mul_rrr(gf2m a, gf2m b) const
64 {
65 return (_gf_modq_1(gf_mul_lll(a, b)));
66 }
67
68 gf2m gf_mul_nrr(gf2m a, gf2m b) const
69 {
70 return (gf_exp(gf_mul_rrr(a, b)));
71 }
72
73 gf2m gf_mul_rrn(gf2m a, gf2m y) const
74 {
75 return _gf_modq_1(gf_mul_lll(a, gf_log(y)));
76 }
77
78 gf2m gf_mul_rnr(gf2m y, gf2m a) const
79 {
80 return gf_mul_rrn(a, y);
81 }
82
83 gf2m gf_mul_lnn(gf2m x, gf2m y) const
84 {
85 return (gf_log(x) + gf_log(y));
86 }
87
88 gf2m gf_mul_rnn(gf2m x, gf2m y) const
89 {
90 return _gf_modq_1(gf_mul_lnn(x, y));
91 }
92
93 gf2m gf_mul_nrn(gf2m a, gf2m y) const
94 {
95 return gf_exp(_gf_modq_1((a) + gf_log(y)));
96 }
97
98 /**
99 * zero operand allowed
100 */
101 gf2m gf_mul_zrz(gf2m a, gf2m y) const
102 {
103 return ( (y == 0) ? 0 : gf_mul_nrn(a, y) );
104 }
105
106 gf2m gf_mul_zzr(gf2m a, gf2m y) const
107 {
108 return gf_mul_zrz(y, a);
109 }
110
111 /**
112 * non-zero operand
113 */
114 gf2m gf_mul_nnr(gf2m y, gf2m a) const
115 {
116 return gf_mul_nrn(a, y);
117 }
118
119 gf2m gf_sqrt(gf2m x) const
120 {
121 return ((x) ? gf_exp(_gf_modq_1(gf_log(x) << (get_extension_degree()-1))) : 0);
122 }
123
124 gf2m gf_div_rnn(gf2m x, gf2m y) const
125 {
126 return _gf_modq_1(gf_log(x) - gf_log(y));
127 }
128
129 gf2m gf_div_rnr(gf2m x, gf2m b) const
130 {
131 return _gf_modq_1(gf_log(x) - b);
132 }
133
134 gf2m gf_div_nrr(gf2m a, gf2m b) const
135 {
136 return gf_exp(_gf_modq_1(a - b));
137 }
138
139 gf2m gf_div_zzr(gf2m x, gf2m b) const
140 {
141 return ((x) ? gf_exp(_gf_modq_1(gf_log(x) - b)) : 0);
142 }
143
144 gf2m gf_inv(gf2m x) const
145 {
146 return gf_exp(gf_ord() - gf_log(x));
147 }
148
149 gf2m gf_inv_rn(gf2m x) const
150 {
151 return (gf_ord() - gf_log(x));
152 }
153
154 gf2m gf_square_ln(gf2m x) const
155 {
156 return gf_log(x) << 1;
157 }
158
159 gf2m gf_square_rr(gf2m a) const
160 {
161 return a << 1;
162 }
163
164 gf2m gf_l_from_n(gf2m x) const
165 {
166 return gf_log(x);
167 }
168
169 gf2m gf_div(gf2m x, gf2m y) const;
170
171 gf2m gf_pow(gf2m x, int i) const;
172
173 gf2m gf_exp(gf2m i) const
174 {
175 return m_gf_exp_table.at(i); /* alpha^i */
176 }
177
178 gf2m gf_log(gf2m i) const
179 {
180 return m_gf_log_table.at(i); /* return i when x=alpha^i */
181 }
182
183 gf2m gf_ord() const
184 {
185 return m_gf_multiplicative_order;
186 }
187
188 gf2m get_extension_degree() const
189 {
190 return m_gf_extension_degree;
191 }
192
193 gf2m get_cardinality() const
194 {
195 return static_cast<gf2m>(1 << get_extension_degree());
196 }
197
198 private:
199 gf2m _gf_modq_1(int32_t d) const
200 {
201 /* residual modulo q-1
202 when -q < d < 0, we get (q-1+d)
203 when 0 <= d < q, we get (d)
204 when q <= d < 2q-1, we get (d-q+1)
205 */
206 return (((d) & gf_ord()) + ((d) >> get_extension_degree()));
207 }
208
209 gf2m m_gf_extension_degree, m_gf_multiplicative_order;
210 const std::vector<gf2m>& m_gf_log_table;
211 const std::vector<gf2m>& m_gf_exp_table;
212 };
213
214 uint32_t encode_gf2m(gf2m to_enc, uint8_t* mem);
215
216 gf2m decode_gf2m(const uint8_t* mem);
217
218 }
219
220 #endif
Botan::GF2m_Field::gf_inv_rn
gf2m gf_inv_rn(gf2m x) const
Definition: gf2m_small_m.h:149
Botan::GF2m_Field::get_cardinality
gf2m get_cardinality() const
Definition: gf2m_small_m.h:193
Botan::GF2m_Field::gf_mul
gf2m gf_mul(gf2m x, gf2m y) const
Definition: gf2m_small_m.h:30
Botan::GF2m_Field::gf_mul_zzr
gf2m gf_mul_zzr(gf2m a, gf2m y) const
Definition: gf2m_small_m.h:106
Botan::GF2m_Field::gf_square
gf2m gf_square(gf2m x) const
Definition: gf2m_small_m.h:35
Botan::GF2m_Field::get_extension_degree
gf2m get_extension_degree() const
Definition: gf2m_small_m.h:188
Botan::GF2m_Field::gf_mul_lnn
gf2m gf_mul_lnn(gf2m x, gf2m y) const
Definition: gf2m_small_m.h:83
Botan::GF2m_Field::gf_mul_rnn
gf2m gf_mul_rnn(gf2m x, gf2m y) const
Definition: gf2m_small_m.h:88
Botan::decode_gf2m
gf2m decode_gf2m(const uint8_t *mem)
Definition: gf2m_small_m.cpp:104
Botan::GF2m_Field::gf_mul_rnr
gf2m gf_mul_rnr(gf2m y, gf2m a) const
Definition: gf2m_small_m.h:78
Botan::GF2m_Field::gf_mul_fast
gf2m gf_mul_fast(gf2m x, gf2m y) const
Definition: gf2m_small_m.h:45
Botan::GF2m_Field
Definition: gf2m_small_m.h:25
Botan::GF2m_Field::gf_mul_lll
gf2m gf_mul_lll(gf2m a, gf2m b) const
Definition: gf2m_small_m.h:58
Botan::GF2m_Field::gf_mul_rrn
gf2m gf_mul_rrn(gf2m a, gf2m y) const
Definition: gf2m_small_m.h:73
Botan::GF2m_Field::gf_div_rnn
gf2m gf_div_rnn(gf2m x, gf2m y) const
Definition: gf2m_small_m.h:124
Botan::GF2m_Field::gf_square_rr
gf2m gf_square_rr(gf2m a) const
Definition: gf2m_small_m.h:159
Botan::GF2m_Field::gf_inv
gf2m gf_inv(gf2m x) const
Definition: gf2m_small_m.h:144
Botan::GF2m_Field::gf_log
gf2m gf_log(gf2m i) const
Definition: gf2m_small_m.h:178
Botan::GF2m_Field::gf_mul_nrr
gf2m gf_mul_nrr(gf2m a, gf2m b) const
Definition: gf2m_small_m.h:68
Botan::GF2m_Field::gf_mul_nrn
gf2m gf_mul_nrn(gf2m a, gf2m y) const
Definition: gf2m_small_m.h:93
Botan::gf2m
uint16_t gf2m
Definition: gf2m_small_m.h:20
Botan
Definition: alg_id.cpp:13
Botan::GF2m_Field::gf_l_from_n
gf2m gf_l_from_n(gf2m x) const
Definition: gf2m_small_m.h:164
Botan::GF2m_Field::gf_mul_nnr
gf2m gf_mul_nnr(gf2m y, gf2m a) const
Definition: gf2m_small_m.h:114
Botan::encode_gf2m
uint32_t encode_gf2m(gf2m to_enc, uint8_t *mem)
Definition: gf2m_small_m.cpp:97
Botan::GF2m_Field::gf_mul_zrz
gf2m gf_mul_zrz(gf2m a, gf2m y) const
Definition: gf2m_small_m.h:101
Botan::GF2m_Field::gf_square_ln
gf2m gf_square_ln(gf2m x) const
Definition: gf2m_small_m.h:154
Botan::GF2m_Field::gf_ord
gf2m gf_ord() const
Definition: gf2m_small_m.h:183
Botan::GF2m_Field::gf_sqrt
gf2m gf_sqrt(gf2m x) const
Definition: gf2m_small_m.h:119
Botan::GF2m_Field::gf_exp
gf2m gf_exp(gf2m i) const
Definition: gf2m_small_m.h:173
Botan::GF2m_Field::gf_mul_rrr
gf2m gf_mul_rrr(gf2m a, gf2m b) const
Definition: gf2m_small_m.h:63
Botan::GF2m_Field::square_rr
gf2m square_rr(gf2m x) const
Definition: gf2m_small_m.h:40
Botan::GF2m_Field::gf_div_nrr
gf2m gf_div_nrr(gf2m a, gf2m b) const
Definition: gf2m_small_m.h:134
Botan::GF2m_Field::gf_div_rnr
gf2m gf_div_rnr(gf2m x, gf2m b) const
Definition: gf2m_small_m.h:129
Botan::GF2m_Field::gf_div_zzr
gf2m gf_div_zzr(gf2m x, gf2m b) const
Definition: gf2m_small_m.h:139