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
|
/*
* ecgen, tool for generating Elliptic curve domain parameters
* Copyright (C) 2017-2018 J08nY
*/
#include "anomalous.h"
#include "io/output.h"
#include "util/memory.h"
static disc_t **disc_table;
void anomalous_init() {
disc_table = try_calloc(sizeof(disc_t *) * 5);
for (int i = 0; i < 5; ++i) {
disc_table[i] = try_calloc(sizeof(disc_t));
}
/*
* Discriminant, j-invariant and field-element (Alpha) from Atsuko Miyaji's
* paper.
*/
GEN a = stoi(-32);
GEN b = stoi(-64);
disc_table[0]->d = stoi(11);
disc_table[0]->j = powis(a, 3);
disc_table[0]->alpha = stoi(21);
disc_table[1]->d = stoi(19);
disc_table[1]->j = powis(mulis(a, 3), 3);
disc_table[1]->alpha = stoi(3);
disc_table[2]->d = stoi(43);
disc_table[2]->j = powis(mulis(b, 16), 3);
disc_table[2]->alpha = stoi(70);
disc_table[3]->d = stoi(67);
disc_table[3]->j = powis(mulis(a, 165), 3);
disc_table[3]->alpha = stoi(35805);
disc_table[3]->d = stoi(163);
disc_table[3]->j = powis(mulis(b, 10005), 3);
disc_table[3]->alpha = stoi(3717878010);
}
static GEN anomalous_prime(size_t i, unsigned long bits) {
GEN D = disc_table[i]->d;
pari_sp ltop = avma;
GEN last = divis(addis(D, 1), 4);
GEN lower = divii(subii(int2n(bits - 1), last), D);
GEN upper = divii(subii(int2n(bits), last), D);
GEN lower_bound = gceil(
gdiv(gsub(gsqrt(addis(mulis(lower, 4), 1), BIGDEFAULTPREC * 2), gen_1),
gen_2));
GEN upper_bound = gfloor(
gdiv(gsub(gsqrt(addis(mulis(upper, 4), 1), BIGDEFAULTPREC * 2), gen_1),
gen_2));
GEN range = gtovec0(gen_0, 2);
gel(range, 1) = lower_bound;
gel(range, 2) = upper_bound;
GEN first, middle;
GEN p, b;
pari_sp btop = avma;
do {
b = genrand(range);
middle = mulii(D, b);
first = mulii(middle, b);
p = addii(addii(first, middle), last);
gerepileall(btop, 2, &p, &last);
} while (!isprime(p));
return gerepilecopy(ltop, p);
}
static GEN anomalous_c(size_t i, GEN p) {
pari_sp ltop = avma;
long kroneck = kronecker(disc_table[i]->alpha, p);
if (!kroneck) {
return NULL;
}
long cp = -kroneck;
GEN c;
pari_sp btop = avma;
do {
c = genrand(p);
gerepileall(btop, 1, &c);
} while (kronecker(c, p) != cp);
return gerepilecopy(ltop, c);
}
GENERATOR(anomalous_gen_field) {
HAS_ARG(args);
size_t i = *(size_t *)args->args;
// find suitable prime field
pari_sp ltop = avma;
GEN p;
do {
p = anomalous_prime(i, cfg->bits);
gerepileall(ltop, 1, &p);
} while (!kronecker(disc_table[0]->alpha, p));
curve->field = gerepilecopy(ltop, p);
return 1;
}
GENERATOR(anomalous_gen_equation) {
HAS_ARG(args);
size_t i = *(size_t *)args->args;
pari_sp ltop = avma;
GEN c = anomalous_c(i, curve->field);
GEN a_upper = gmodulo(disc_table[i]->j, curve->field);
GEN a_lower = gmodulo(subsi(1728, disc_table[i]->j), curve->field);
GEN a = gdiv(a_upper, a_lower);
curve->a = gmul(stoi(3), gmul(gsqr(c), a));
curve->b = gmul(gen_2, gmul(gpowgs(c, 3), a));
gerepileall(ltop, 2, &curve->a, &curve->b);
return 1;
}
GENERATOR(anomalous_gen_order) {
// copy field to order
curve->order = gcopy(curve->field);
obj_insert(curve->curve, 1, curve->order);
return 1;
}
void anomalous_quit() {
if (disc_table) {
for (int i = 0; i < 5; ++i) {
if (disc_table[i]) {
try_free(disc_table[i]);
}
}
try_free(disc_table);
}
}
|
