Crypto++ 7.0 Free C++ class library of cryptographic schemes

xtr.cpp
1 // xtr.cpp - originally written and placed in the public domain by Wei Dai
2
3 #include "pch.h"
4
5 #include "xtr.h"
6 #include "nbtheory.h"
7 #include "integer.h"
8 #include "algebra.h"
9 #include "modarith.h"
10 #include "algebra.cpp"
11
12 NAMESPACE_BEGIN(CryptoPP)
13
14 const GFP2Element & GFP2Element::Zero()
15 {
16 #if defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
17 static const GFP2Element s_zero;
18 return s_zero;
19 #else
20 return Singleton<GFP2Element>().Ref();
21 #endif
22 }
23
24 void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits)
25 {
26 CRYPTOPP_ASSERT(qbits > 9); // no primes exist for pbits = 10, qbits = 9
27 CRYPTOPP_ASSERT(pbits > qbits);
28
29 const Integer minQ = Integer::Power2(qbits - 1);
30 const Integer maxQ = Integer::Power2(qbits) - 1;
31 const Integer minP = Integer::Power2(pbits - 1);
32 const Integer maxP = Integer::Power2(pbits) - 1;
33
34 top:
35
36 Integer r1, r2;
37 do
38 {
39 (void)q.Randomize(rng, minQ, maxQ, Integer::PRIME, 7, 12);
40 // Solution always exists because q === 7 mod 12.
41 (void)SolveModularQuadraticEquation(r1, r2, 1, -1, 1, q);
42 // I believe k_i, r1 and r2 are being used slightly different than the
43 // paper's algorithm. I believe it is leading to the failed asserts.
44 // Just make the assert part of the condition.
45 if(!p.Randomize(rng, minP, maxP, Integer::PRIME, CRT(rng.GenerateBit() ?
46 r1 : r2, q, 2, 3, EuclideanMultiplicativeInverse(p, 3)), 3 * q)) { continue; }
47 } while (((p % 3U) != 2) || (((p.Squared() - p + 1) % q).NotZero()));
48
49 // CRYPTOPP_ASSERT((p % 3U) == 2);
50 // CRYPTOPP_ASSERT(((p.Squared() - p + 1) % q).IsZero());
51
52 GFP2_ONB<ModularArithmetic> gfp2(p);
53 GFP2Element three = gfp2.ConvertIn(3), t;
54
55 while (true)
56 {
57 g.c1.Randomize(rng, Integer::Zero(), p-1);
58 g.c2.Randomize(rng, Integer::Zero(), p-1);
59 t = XTR_Exponentiate(g, p+1, p);
60 if (t.c1 == t.c2)
61 continue;
62 g = XTR_Exponentiate(g, (p.Squared()-p+1)/q, p);
63 if (g != three)
64 break;
65 }
66
67 if (XTR_Exponentiate(g, q, p) != three)
68 goto top;
69
70 // CRYPTOPP_ASSERT(XTR_Exponentiate(g, q, p) == three);
71 }
72
73 GFP2Element XTR_Exponentiate(const GFP2Element &b, const Integer &e, const Integer &p)
74 {
75 unsigned int bitCount = e.BitCount();
76 if (bitCount == 0)
77 return GFP2Element(-3, -3);
78
79 // find the lowest bit of e that is 1
80 unsigned int lowest1bit;
81 for (lowest1bit=0; e.GetBit(lowest1bit) == 0; lowest1bit++) {}
82
83 GFP2_ONB<MontgomeryRepresentation> gfp2(p);
84 GFP2Element c = gfp2.ConvertIn(b);
85 GFP2Element cp = gfp2.PthPower(c);
86 GFP2Element S[5] = {gfp2.ConvertIn(3), c, gfp2.SpecialOperation1(c)};
87
88 // do all exponents bits except the lowest zeros starting from the top
89 unsigned int i;
90 for (i = e.BitCount() - 1; i>lowest1bit; i--)
91 {
92 if (e.GetBit(i))
93 {
94 gfp2.RaiseToPthPower(S[0]);
95 gfp2.Accumulate(S[0], gfp2.SpecialOperation2(S[2], c, S[1]));
96 S[1] = gfp2.SpecialOperation1(S[1]);
97 S[2] = gfp2.SpecialOperation1(S[2]);
98 S[0].swap(S[1]);
99 }
100 else
101 {
102 gfp2.RaiseToPthPower(S[2]);
103 gfp2.Accumulate(S[2], gfp2.SpecialOperation2(S[0], cp, S[1]));
104 S[1] = gfp2.SpecialOperation1(S[1]);
105 S[0] = gfp2.SpecialOperation1(S[0]);
106 S[2].swap(S[1]);
107 }
108 }
109
110 // now do the lowest zeros
111 while (i--)
112 S[1] = gfp2.SpecialOperation1(S[1]);
113
114 return gfp2.ConvertOut(S[1]);
115 }
116
117 template class AbstractRing<GFP2Element>;
118 template class AbstractGroup<GFP2Element>;
119
120 NAMESPACE_END
CRT
Integer CRT(const Integer &xp, const Integer &p, const Integer &xq, const Integer &q, const Integer &u)
Chinese Remainder Theorem.
Definition: nbtheory.cpp:553
Integer::PRIME
a number which is probabilistically prime
Definition: integer.h:95
Singleton
Restricts the instantiation of a class to one static object without locks.
Definition: misc.h:291
RandomNumberGenerator
Interface for random number generators.
Definition: cryptlib.h:1349
Integer::Randomize
void Randomize(RandomNumberGenerator &rng, size_t bitCount)
Set this Integer to random integer.
Definition: integer.cpp:3497
algebra.h
Classes for performing mathematics over different fields.
AbstractRing< GFP2Element >
GFP2Element
an element of GF(p^2)
Definition: xtr.h:16
xtr.h
The XTR public key system.
Integer::Power2
static Integer Power2(size_t e)
Exponentiates to a power of 2.
Definition: integer.cpp:3076
Integer
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
pch.h
Precompiled header file.
CRYPTOPP_ASSERT
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
Definition: trap.h:60
AbstractGroup< GFP2Element >
nbtheory.h
Classes and functions for number theoretic operations.
EuclideanMultiplicativeInverse
Integer EuclideanMultiplicativeInverse(const Integer &a, const Integer &b)
Calculate multiplicative inverse.
Definition: nbtheory.h:165
Integer::Squared
Integer Squared() const
Multiply this integer by itself.
Definition: integer.h:609
RandomNumberGenerator::GenerateBit
virtual unsigned int GenerateBit()
Generate new random bit and return it.
Definition: cryptlib.cpp:271
integer.h
Multiple precision integer with arithmetic operations.
Integer::Zero
static const Integer & Zero()
Integer representing 0.
Definition: integer.cpp:4842
modarith.h
Class file for performing modular arithmetic.
CryptoPP
Crypto++ library namespace.
SolveModularQuadraticEquation
bool SolveModularQuadraticEquation(Integer &r1, Integer &r2, const Integer &a, const Integer &b, const Integer &c, const Integer &p)
Solve a Modular Quadratic Equation.
Definition: nbtheory.cpp:621
GFP2_ONB
GF(p^2), optimal normal basis.
Definition: xtr.h:46
XTR_FindPrimesAndGenerator
void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits)
Creates primes p,q and generator g for XTR.
Definition: xtr.cpp:24