ed448-goldilocks 0.9.0

A pure-Rust implementation of Ed448 and Curve448 and Decaf
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

// Move all curve specific constants into this file
// as they will have different representations depending on the backend
use crate::curve::edwards::ExtendedPoint;
use crate::curve::twedwards::extended::ExtendedPoint as TwExtendedPoint;
use crate::field::fiat_u64::FieldElement56;

/// -4 * Twisted_D = -4 * (EDWARDS_D-1)
pub const NEG_FOUR_TIMES_TWISTED_D: FieldElement56 = FieldElement56([
    156327,
    0,
    0,
    0,
    72057594037927935,
    72057594037927935,
    72057594037927935,
    72057594037927935,
]);

/// Edwards `d`, equals to -39081
pub const EDWARDS_D: FieldElement56 = FieldElement56([
    144115188075816789,
    144115188075855870,
    144115188075855870,
    144115188075855870,
    144115188075855868,
    144115188075855870,
    144115188075855870,
    144115188075855870,
]);

/// Neg_Edwards `-d`, equals to 39081
pub const NEG_EDWARDS_D: FieldElement56 = FieldElement56([39081, 0, 0, 0, 0, 0, 0, 0]);

/// Twisted Edwards D equals `d-1`, equals to -39082
pub const TWISTED_D: FieldElement56 = FieldElement56([
    144115188075816788,
    144115188075855870,
    144115188075855870,
    144115188075855870,
    144115188075855868,
    144115188075855870,
    144115188075855870,
    144115188075855870,
]);

/// Twice the Twisted Edwards d which equals to -78164
pub const TWO_TIMES_TWISTED_D: FieldElement56 = FieldElement56([
    144115188075777706,
    144115188075855870,
    144115188075855870,
    144115188075855870,
    144115188075855868,
    144115188075855870,
    144115188075855870,
    144115188075855870,
]);

/// INVSQRT(a*d_2-1) where d_2 = 39082/39081
pub const DECAF_FACTOR: FieldElement56 = FieldElement56([
    0x42ef0f45572736,
    0x7bf6aa20ce5296,
    0xf4fd6eded26033,
    0x968c14ba839a66,
    0xb8d54b64a2d780,
    0x6aa0a1f1a7b8a5,
    0x683bf68d722fa2,
    0x22d962fbeb24f7,
]);

/// 39082 used in the doubling procedure in montgomery ladder
pub const A_PLUS_TWO_OVER_FOUR: FieldElement56 = FieldElement56([39082, 0, 0, 0, 0, 0, 0, 0]);

/// The basepoint of Ed448-Goldilocks
pub const GOLDILOCKS_BASE_POINT: ExtendedPoint = ExtendedPoint {
    X: FieldElement56([
        10880955091566686,
        36276784145337894,
        69571282115576635,
        46113124210880026,
        4247859732800292,
        15440021224255559,
        66747077793030847,
        22264495316135181,
    ]),
    Y: FieldElement56([
        2385235625966100,
        5396741696826776,
        8134720567442877,
        1584133578609663,
        46047824121994270,
        56121598560924524,
        10283140089599689,
        29624444337960636,
    ]),
    Z: FieldElement56([1, 0, 0, 0, 0, 0, 0, 0]),
    T: FieldElement56([
        1796939199780339,
        45174008172060139,
        40732174862907279,
        63672088496536030,
        37244660935497319,
        41035719659624511,
        30626637035688077,
        56117654178374172,
    ]),
};

/// The basepoint of the Twisted Edwards curve which is 2-isogenous to Ed448-Goldilocks
pub const TWISTED_EDWARDS_BASE_POINT: TwExtendedPoint = TwExtendedPoint {
    X: FieldElement56([
        0,
        72057594037927936,
        72057594037927935,
        36028797018963967,
        72057594037927934,
        72057594037927935,
        72057594037927935,
        36028797018963967,
    ]),
    Y: FieldElement56([
        27155415521118820,
        3410937204744648,
        19376965222209947,
        22594032279754776,
        21520481577673772,
        10141917371396176,
        59827755213158602,
        37445921829569158,
    ]),
    Z: FieldElement56([1, 0, 0, 0, 0, 0, 0, 0]),
    T: FieldElement56([
        64114820220813573,
        27592348249940115,
        21918321435874307,
        45908688348236165,
        34141937727972228,
        63575698147485199,
        22766751209138687,
        30740600843388580,
    ]),
};