Botan: src/math/numbertheory/ressol.cpp Source File

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ressol.cpp
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1 /*
2 * Shanks-Tonnelli (RESSOL)
3 * (C) 2007-2008 Falko Strenzke, FlexSecure GmbH
4 * (C) 2008 Jack Lloyd
5 *
6 * Distributed under the terms of the Botan license
7 */
8
9 #include <botan/numthry.h>
10 #include <botan/reducer.h>
11
12 namespace Botan {
13
14 /*
15 * Shanks-Tonnelli algorithm
16 */
17 BigInt ressol(const BigInt& a, const BigInt& p)
18 {
19 if(a < 0)
20 throw Invalid_Argument("ressol(): a to solve for must be positive");
21 if(p <= 1)
22 throw Invalid_Argument("ressol(): prime must be > 1");
23
24 if(a == 0)
25 return 0;
26 if(p == 2)
27 return a;
28
29 if(jacobi(a, p) != 1) // not a quadratic residue
30 return -BigInt(1);
31
32 if(p % 4 == 3)
33 return power_mod(a, ((p+1) >> 2), p);
34
35 size_t s = low_zero_bits(p - 1);
36 BigInt q = p >> s;
37
38 q -= 1;
39 q >>= 1;
40
41 Modular_Reducer mod_p(p);
42
43 BigInt r = power_mod(a, q, p);
44 BigInt n = mod_p.multiply(a, mod_p.square(r));
45 r = mod_p.multiply(r, a);
46
47 if(n == 1)
48 return r;
49
50 // find random non quadratic residue z
51 BigInt z = 2;
52 while(jacobi(z, p) == 1) // while z quadratic residue
53 ++z;
54
55 BigInt c = power_mod(z, (q << 1) + 1, p);
56
57 while(n > 1)
58 {
59 q = n;
60
61 size_t i = 0;
62 while(q != 1)
63 {
64 q = mod_p.square(q);
65 ++i;
66
67 if(i >= s)
68 return -BigInt(1);
69 }
70
71 c = power_mod(c, BigInt(BigInt::Power2, s-i-1), p);
72 r = mod_p.multiply(r, c);
73 c = mod_p.square(c);
74 n = mod_p.multiply(n, c);
75 s = i;
76 }
77
78 return r;
79 }
80
81 }
Botan::BigInt
Definition: bigint.h:22
Botan::ressol
BigInt BOTAN_DLL ressol(const BigInt &x, const BigInt &p)
Definition: ressol.cpp:17
Botan::Invalid_Argument
std::invalid_argument Invalid_Argument
Definition: exceptn.h:20
Botan::Modular_Reducer::multiply
BigInt multiply(const BigInt &x, const BigInt &y) const
Definition: reducer.h:31
Botan::jacobi
s32bit jacobi(const BigInt &a, const BigInt &n)
Definition: jacobi.cpp:15
Botan
Definition: algo_base.h:14
Botan::low_zero_bits
size_t low_zero_bits(const BigInt &n)
Definition: numthry.cpp:141
Botan::power_mod
BigInt power_mod(const BigInt &base, const BigInt &exp, const BigInt &mod)
Definition: numthry.cpp:251
Botan::BigInt::Power2
Definition: bigint.h:38
Botan::Modular_Reducer::square
BigInt square(const BigInt &x) const
Definition: reducer.h:39
Botan::Modular_Reducer
Definition: reducer.h:18