recrypt 0.13.1

A pure-Rust implementation of Transform Encryption, a Proxy Re-encryption scheme
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325

use crate::internal::fp::fr_256::Fr256;
use crate::internal::fp::fr_480::Fr480;
use crate::internal::fp2elem::Fp2Elem;
use crate::internal::fp6elem::Fp6Elem;
use crate::internal::Square;
use gridiron::fp_256;
use gridiron::fp_480;
use num_traits::{Inv, Pow};
use num_traits::{One, Zero};
use std::ops::{Add, Div, Mul, Neg, Sub};

#[cfg(test)]
macro_rules! field_props {
    () => {
        #[cfg(test)]
        fn prop_semigroup(a: Self, b: Self, c: Self) -> bool {
            a + (b + c) == (a + b) + c
        }

        fn prop_monoid_identity(a: Self) -> bool {
            a + Zero::zero() == <Self as Zero>::zero() + a && a + Zero::zero() == a
        }

        fn prop_inv(a: Self, b: Self) -> bool {
            a == a * (b.inv() * b) && a == a * (b * b.inv())
        }

        fn prop_one_is_mul_identity(a: Self) -> bool {
            <Self as One>::one() * a == a && a == a * <Self as One>::one()
        }

        fn prop_zero_is_add_identity(a: Self) -> bool {
            <Self as Zero>::zero() + a == a && a == a + <Self as Zero>::zero()
        }

        fn prop_eq_reflexive(a: Self, b: Self) -> bool {
            if a == b {
                b == a
            } else {
                b != a
            }
        }

        fn prop_sub_same_as_neg_add(a: Self, b: Self) -> bool {
            a + -b == a - b
        }

        fn prop_mul_distributive(a: Self, b: Self, c: Self) -> bool {
            a * (b + c) == a * b + a * c
        }

        fn prop_mul_assoc(a: Self, b: Self, c: Self) -> bool {
            a * (b * c) == a * b * c
        }

        #[allow(clippy::eq_op)] // necessary for commutative props
        fn prop_mul_commutative(a: Self, b: Self, c: Self) -> bool {
            b * a * c == a * b * c
        }

        fn prop_add_assoc(a: Self, b: Self, c: Self) -> bool {
            a + (b + c) == a + b + c
        }

        #[allow(clippy::eq_op)] // necessary for commutative props
        fn prop_add_commutative(a: Self, b: Self, c: Self) -> bool {
            b + a + c == a + b + c
        }

        fn prop_pow_is_mul(a: Self) -> bool {
            a * a == a.pow(2) && a * a * a == a.pow(3)
        }

        fn prop_x_sub_y_eq_x_plus_y_mul_neg1(x: Self, y: Self) -> bool {
            // x - y == x + y * (-1)
            let expected = x - y;
            let result = x + y * -<Self as One>::one();

            expected == result
        }

        fn prop_square_same_as_mul_self(a: Self) -> bool {
            let expected = a * a;
            let result = a.square();

            expected == result
        }

        fn prop_square2_same_as_pow4(a: Self) -> bool {
            let expected = a.square().square();
            let result = a.pow(4);

            expected == result
        }
    };
}

pub trait Field:
    One
    + Zero
    + Copy
    + Eq
    + Square
    + Neg<Output = Self>
    + Add<Output = Self>
    + Mul<Output = Self>
    + Div<Output = Self>
    + Mul<u32, Output = Self>
    + Inv<Output = Self>
    + Pow<u32, Output = Self>
    + Sub<Output = Self>
{
    #[cfg(test)]
    field_props!();
}

impl Field for fp_256::Monty {}
impl Field for fp_480::Monty {}
impl Field for Fr256 {}
impl Field for Fr480 {}

/// Contains the values needed to configure a new Fp type to be used as an extension field
/// (FP2Elem, FP6Elem, FP12Elem)
/// All `ExtensionField`s are `Field`s
pub trait ExtensionField: Field
where
    Self: Sized + From<u8>,
{
    ///Precomputed xi.inv() * 9
    fn xi_inv_times_9() -> Fp2Elem<Self>;

    /// Used in frobenius, this is Xi^((p-1)/3)
    /// Fp6Elem[A](Fp2Elem.Zero, Fp2Elem.One, Fp2Elem.Zero).frobenius
    /// Xi  ^ ((p - p % 3) /3) because of the prime we've chosen, p % 3 == 1
    fn frobenius_factor_1() -> Fp2Elem<Self>;

    /// Used in frobenius, this is frobeniusFactor1^2
    fn frobenius_factor_2() -> Fp2Elem<Self>;
    // if q = (p-1)/2
    // q % 3 == 0  -- For our p
    // Xi ^ ((q - q % 3)/3)
    fn frobenius_factor_fp12() -> Fp2Elem<Self>;

    ///v is the thing that cubes to xi
    ///v^3 = u+3, because by definition it is a solution to the equation y^3 - (u + 3)
    #[inline]
    fn v() -> Fp6Elem<Self> {
        Fp6Elem {
            elem1: Zero::zero(),
            elem2: One::one(),
            elem3: Zero::zero(),
        }
    }

    /// 3 / (u+3)
    /// pre-calculate as an optimization
    /// ExtensionField::xi().inv() * 3;
    fn twisted_curve_const_coeff() -> Fp2Elem<Self>;
}

impl ExtensionField for fp_256::Monty {
    //precalculate this since it's used in every double and add operation in the extension field.
    //xi is u + 3 or Fp2Elem(1, 3)
    // Fp256::xi().inv() * 9
    fn xi_inv_times_9() -> Fp2Elem<Self> {
        Fp2Elem {
            //19500164908693981119838931622707971722847607432286901071563143508059255221534.str
            elem1: fp_256::Monty::new([
                2050346385, 731299471, 959575992, 34915099, 1787054046, 707674376, 1189605443,
                44293910, 138,
            ]),
            //6500054969564660373279643874235990574282535810762300357187714502686418407181
            elem2: fp_256::Monty::new([
                729307778, 258461402, 1559141440, 1381403208, 157052610, 1802371594, 636365429,
                127350700, 17,
            ]),
        }
    }
    #[inline]
    fn frobenius_factor_1() -> Fp2Elem<Self> {
        Fp2Elem {
            // 26098034838977895781559542626833399156321265654106457577426020397262786167059
            // num.digits(2^31) in sage gives the array
            elem1: fp_256::Monty::new([
                12717650, 1979656862, 1972108829, 1559171847, 290869350, 694266310, 579853055,
                1597302116, 4,
            ]),
            // 15931493369629630809226283458085260090334794394361662678240713231519278691715
            elem2: fp_256::Monty::new([
                916222744, 723717387, 574787027, 1552331516, 1261698828, 887614939, 1510504974,
                237248389, 8,
            ]),
        }
    }
    #[inline]
    fn frobenius_factor_2() -> Fp2Elem<Self> {
        Fp2Elem {
            // 19885131339612776214803633203834694332692106372356013117629940868870585019582
            elem1: fp_256::Monty::new([
                15189756, 1959629061, 767155255, 1427131279, 513871136, 1996531885, 1401068065,
                1422686260, 66,
            ]),
            // 21645619881471562101905880913352894726728173167203616652430647841922248593627
            elem2: fp_256::Monty::new([
                656635847, 1575335407, 606381995, 1750621660, 1486126693, 503904416, 1955368925,
                270969940, 28,
            ]),
        }
    }
    #[inline]
    fn frobenius_factor_fp12() -> Fp2Elem<Self> {
        Fp2Elem {
            // 8669379979083712429711189836753509758585994370025260553045152614783263110636
            elem1: fp_256::Monty::new([
                454717458, 161507933, 804946138, 817080316, 1413496639, 904558052, 1356825578,
                765259087, 11,
            ]),
            // 19998038925833620163537568958541907098007303196759855091367510456613536016040
            elem2: fp_256::Monty::new([
                392395988, 386079276, 1435458002, 829532913, 1153717094, 1170750470, 311764801,
                1868664732, 53,
            ]),
        }
    }

    #[inline]
    fn twisted_curve_const_coeff() -> Fp2Elem<Self> {
        Fp2Elem {
            elem1: fp_256::Monty::new([
                1925150376, 516250914, 1051564560, 1369812449, 731601065, 672046428, 625168271,
                1952553705, 93,
            ]),
            elem2: fp_256::Monty::new([
                1674758358, 86153800, 1235541696, 1892123501, 768178752, 600790531, 1643777575,
                1474105998, 5,
            ]),
        }
    }
}

impl ExtensionField for fp_480::Monty {
    // precalculate this since it's used in every double and add operation in the extension field.
    // xi is u + 3 or Fp2Elem(1, 3)
    // Fp480::xi().inv() * 9
    fn xi_inv_times_9() -> Fp2Elem<Self> {
        Fp2Elem {
            elem1: fp_480::Monty::new([
                1671524251, 1452836661, 1514278714, 1089055752, 983710563, 1342902855, 1277558075,
                1876974179, 947518822, 981090444, 247487949, 1283900828, 1334523677, 1392777601,
                1513546415, 5235,
            ]),
            elem2: fp_480::Monty::new([
                335877574, 1323354927, 650625437, 272173725, 1832380438, 2065643415, 655409061,
                1376608173, 1642768871, 464289801, 840813404, 665753910, 1051781983, 447188070,
                183786362, 17059,
            ]),
        }
    }
    fn frobenius_factor_1() -> Fp2Elem<Self> {
        Fp2Elem {
            // 2705020609406098470693743943193507017690525853579041639836321147125100162418094245778443957282985233325521741487078451689773015537700623376387510
            elem1: fp_480::Monty::new([
                1789717966, 1667803516, 415596737, 273473839, 86323342, 1847146047, 411641533,
                883838890, 333532818, 2020025246, 1090726896, 1144837448, 1056047014, 650675300,
                1518220857, 28583,
            ]),
            // 1651643729828744562959031609260204931467006255025965356538853937438900508750440674159520451455470865884696804132950675577710427706655106873786415
            elem2: fp_480::Monty::new([
                1463808839, 1670428701, 447968177, 1822223094, 1576270537, 1038296259, 66655687,
                578662642, 153246326, 1500216407, 53886423, 1315635309, 1456804263, 176996090,
                1710325846, 31113,
            ]),
        }
    }

    fn frobenius_factor_2() -> Fp2Elem<Self> {
        Fp2Elem {
            // 2306651261022207350847683647334036061609898996050387019709069937614457385067216464366007100887697910705559503143400341307341852524867445116042081
            elem1: fp_480::Monty::new([
                721025432, 530063334, 1045885399, 453726440, 2141696003, 1626330876, 1074975251,
                1714081964, 1995410861, 609055642, 2058665923, 1876157870, 937690781, 1255299233,
                741827240, 14111,
            ]),
            // 2700715513864156317217817646762981219394581764002749630356081821581587105847754189716578562648186994801551242072586877237522675959303129100251619
            elem2: fp_480::Monty::new([
                147532118, 4451373, 893741577, 424324553, 481155820, 353715416, 620523272,
                346497951, 1670022807, 1427377181, 732861676, 2088692375, 582789470, 669478976,
                249410141, 28740,
            ]),
        }
    }

    fn frobenius_factor_fp12() -> Fp2Elem<Self> {
        Fp2Elem {
            // 1656507924366244928424688705439191250492553228839737584554076474712325077234544758394965182643615114744030751122897661836350026981040666763359635
            elem1: fp_480::Monty::new([
                736041138, 285900164, 1852287620, 1099722104, 1782561133, 1457388007, 1874229037,
                1965266811, 1231149838, 771491782, 467524787, 1737481601, 782773382, 79418783,
                1572898018, 31139,
            ]),
            // 411347727129503104504468123876138850111359831064167067331474757563790630947112631916366442374487601276802707186517326847256605909760387475785136
            elem2: fp_480::Monty::new([
                492638839, 304045155, 1057698408, 772372983, 1813080623, 1701111681, 801357526,
                1606643950, 1537923020, 1695901916, 157173875, 1177883133, 354458948, 163418612,
                376825454, 23056,
            ]),
        }
    }

    #[inline]
    fn twisted_curve_const_coeff() -> Fp2Elem<Self> {
        Fp2Elem {
            elem1: fp_480::Monty::new([
                1976657987, 2124705180, 1103755761, 1290923474, 2085255841, 1647224075, 1270424569,
                286550022, 1158572853, 451253923, 1853842034, 2007948773, 1667592921, 2116284018,
                790821013, 23589,
            ]),
            elem2: fp_480::Monty::new([
                1531442428, 2081544602, 1531699218, 302801582, 1652317917, 456481830, 1063041565,
                835589236, 1390322869, 278987042, 1335789303, 1086071918, 1573345690, 1085259625,
                1063395545, 27530,
            ]),
        }
    }
}