Tg2giDQZ

1#include <boost/multiprecision/cpp_int.hpp>
2#include <boost/random.hpp>
3#include <iostream>
4
5
6using namespace boost::multiprecision;
7
8
9struct OpenKey {
10    cpp_int p; // usually 1024 bits (prime!)
11    cpp_int q; // usually 160 bits; (p - 1) % q == 0
12    // w < q
13    cpp_int g; // (g^q) % p == 1
14    cpp_int y; // y = g^(-w) % p
15};
16
17struct SecretKey {
18    cpp_int w;
19};
20
21
22auto init_random_value_gen(const OpenKey &open_key) {
23    using namespace boost::random;
24    return uniform_int_distribution<cpp_int>(0, open_key.q);
25}
26
27
28cpp_int pre_signing(const OpenKey &open_key, const cpp_int &rand_power) {
29    namespace mp = boost::multiprecision;
30    return mp::powm(open_key.g, rand_power, open_key.p);
31}
32
33
34template<typename T>
35auto init_random_value_gen(T bits_count) {
36    // multiprecision do not allow cpp_int as exponent, because https://stackoverflow.com/a/43508036
37    using namespace boost::random;
38    namespace mp = boost::multiprecision;
39    const cpp_int &base = 2;
40    return uniform_int_distribution<cpp_int>(0, mp::pow(base, bits_count) - 1);
41}
42
43cpp_int sign(const OpenKey &open_key, const SecretKey &secret_key, const cpp_int &r, const cpp_int &e) {
44    return (r + e * secret_key.w) % open_key.q;
45}
46
47bool check_sign(const OpenKey &open_key, const cpp_int &e, const cpp_int &x, const cpp_int &s) {
48    namespace mp = boost::multiprecision;
49    using namespace std;
50
51    auto maybe_x = (
52            mp::powm(open_key.g, s, open_key.p) * mp::powm(open_key.y, e, open_key.p)
53            ) % open_key.p;
54   return maybe_x == x;
55}
56
57
58void singing(const OpenKey &open_key, const SecretKey &secret_key) {
59    // Note: Alice has secret key
60    using namespace boost::multiprecision;
61    using namespace boost::random;
62
63    mt19937 mt;
64
65    auto rand_power_gen = init_random_value_gen(open_key);
66    cpp_int r = rand_power_gen(mt);
67    auto x = pre_signing(open_key, r);
68
69    int bit_count = 72;
70    auto e_gen = init_random_value_gen(bit_count);
71    cpp_int e = e_gen(mt);
72    cpp_int s = sign(open_key, secret_key, r, e);
73    check_sign(open_key, e, x, s);
74
75};
76
77
78int main() {
79    using namespace std;
80    namespace mp = boost::multiprecision;
81
82    mp::cpp_int x = mp::pow(mp::cpp_int(2), 1024);
83    std::cout << x << "\n";
84    cpp_int v = 1;
85
86    // Do some arithmetic:
87    for (unsigned i = 1; i <= 1000; ++i)
88        v *= i;
89
90    std::cout << v << std::endl; // prints 1000! / 10
91
92    cpp_rational w(2, 3);  // component wise constructor
93    std::cout << w << std::endl; // prints 2/3
94
95    OpenKey open_key{100, 234, 23452, 15434};
96
97    cout << "";
98    return 0;
99}