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
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
|
// luc.cpp - originally written and placed in the public domain by Wei Dai
#include "pch.h"
#include "luc.h"
#include "asn.h"
#include "sha.h"
#include "integer.h"
#include "nbtheory.h"
#include "algparam.h"
#include "pkcspad.h"
NAMESPACE_BEGIN(CryptoPP)
#if defined(CRYPTOPP_DEBUG) && !defined(CRYPTOPP_DOXYGEN_PROCESSING)
void LUC_TestInstantiations()
{
LUC_HMP<SHA1>::Signer t1;
LUCFunction t2;
InvertibleLUCFunction t3;
}
#endif
void DL_Algorithm_LUC_HMP::Sign(const DL_GroupParameters<Integer> ¶ms, const Integer &x, const Integer &k, const Integer &e, Integer &r, Integer &s) const
{
const Integer &q = params.GetSubgroupOrder();
r = params.ExponentiateBase(k);
s = (k + x*(r+e)) % q;
}
bool DL_Algorithm_LUC_HMP::Verify(const DL_GroupParameters<Integer> ¶ms, const DL_PublicKey<Integer> &publicKey, const Integer &e, const Integer &r, const Integer &s) const
{
const Integer p = params.GetGroupOrder()-1;
const Integer &q = params.GetSubgroupOrder();
Integer Vsg = params.ExponentiateBase(s);
Integer Vry = publicKey.ExponentiatePublicElement((r+e)%q);
return (Vsg*Vsg + Vry*Vry + r*r) % p == (Vsg * Vry * r + 4) % p;
}
Integer DL_BasePrecomputation_LUC::Exponentiate(const DL_GroupPrecomputation<Element> &group, const Integer &exponent) const
{
return Lucas(exponent, m_g, static_cast<const DL_GroupPrecomputation_LUC &>(group).GetModulus());
}
void DL_GroupParameters_LUC::SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
{
for (unsigned int i=0; i<exponentsCount; i++)
results[i] = Lucas(exponents[i], base, GetModulus());
}
void LUCFunction::BERDecode(BufferedTransformation &bt)
{
BERSequenceDecoder seq(bt);
m_n.BERDecode(seq);
m_e.BERDecode(seq);
seq.MessageEnd();
}
void LUCFunction::DEREncode(BufferedTransformation &bt) const
{
DERSequenceEncoder seq(bt);
m_n.DEREncode(seq);
m_e.DEREncode(seq);
seq.MessageEnd();
}
Integer LUCFunction::ApplyFunction(const Integer &x) const
{
DoQuickSanityCheck();
return Lucas(m_e, x, m_n);
}
bool LUCFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
{
CRYPTOPP_UNUSED(rng), CRYPTOPP_UNUSED(level);
bool pass = true;
pass = pass && m_n > Integer::One() && m_n.IsOdd();
CRYPTOPP_ASSERT(pass);
pass = pass && m_e > Integer::One() && m_e.IsOdd() && m_e < m_n;
CRYPTOPP_ASSERT(pass);
return pass;
}
bool LUCFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
{
return GetValueHelper(this, name, valueType, pValue).Assignable()
CRYPTOPP_GET_FUNCTION_ENTRY(Modulus)
CRYPTOPP_GET_FUNCTION_ENTRY(PublicExponent)
;
}
void LUCFunction::AssignFrom(const NameValuePairs &source)
{
AssignFromHelper(this, source)
CRYPTOPP_SET_FUNCTION_ENTRY(Modulus)
CRYPTOPP_SET_FUNCTION_ENTRY(PublicExponent)
;
}
// *****************************************************************************
// private key operations:
class LUCPrimeSelector : public PrimeSelector
{
public:
LUCPrimeSelector(const Integer &e) : m_e(e) {}
bool IsAcceptable(const Integer &candidate) const
{
return RelativelyPrime(m_e, candidate+1) && RelativelyPrime(m_e, candidate-1);
}
Integer m_e;
};
void InvertibleLUCFunction::GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg)
{
int modulusSize = 2048;
alg.GetIntValue("ModulusSize", modulusSize) || alg.GetIntValue("KeySize", modulusSize);
if (modulusSize < 16)
throw InvalidArgument("InvertibleLUCFunction: specified modulus size is too small");
m_e = alg.GetValueWithDefault("PublicExponent", Integer(17));
if (m_e < 5 || m_e.IsEven())
throw InvalidArgument("InvertibleLUCFunction: invalid public exponent");
LUCPrimeSelector selector(m_e);
AlgorithmParameters primeParam = MakeParametersForTwoPrimesOfEqualSize(modulusSize)
("PointerToPrimeSelector", selector.GetSelectorPointer());
m_p.GenerateRandom(rng, primeParam);
m_q.GenerateRandom(rng, primeParam);
m_n = m_p * m_q;
m_u = m_q.InverseMod(m_p);
}
void InvertibleLUCFunction::Initialize(RandomNumberGenerator &rng, unsigned int keybits, const Integer &e)
{
GenerateRandom(rng, MakeParameters("ModulusSize", (int)keybits)("PublicExponent", e));
}
void InvertibleLUCFunction::BERDecode(BufferedTransformation &bt)
{
BERSequenceDecoder seq(bt);
Integer version(seq);
if (!!version) // make sure version is 0
BERDecodeError();
m_n.BERDecode(seq);
m_e.BERDecode(seq);
m_p.BERDecode(seq);
m_q.BERDecode(seq);
m_u.BERDecode(seq);
seq.MessageEnd();
}
void InvertibleLUCFunction::DEREncode(BufferedTransformation &bt) const
{
DERSequenceEncoder seq(bt);
const byte version[] = {INTEGER, 1, 0};
seq.Put(version, sizeof(version));
m_n.DEREncode(seq);
m_e.DEREncode(seq);
m_p.DEREncode(seq);
m_q.DEREncode(seq);
m_u.DEREncode(seq);
seq.MessageEnd();
}
Integer InvertibleLUCFunction::CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const
{
// not clear how to do blinding with LUC
CRYPTOPP_UNUSED(rng);
DoQuickSanityCheck();
return InverseLucas(m_e, x, m_q, m_p, m_u);
}
bool InvertibleLUCFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
{
bool pass = LUCFunction::Validate(rng, level);
CRYPTOPP_ASSERT(pass);
pass = pass && m_p > Integer::One() && m_p.IsOdd() && m_p < m_n;
CRYPTOPP_ASSERT(pass);
pass = pass && m_q > Integer::One() && m_q.IsOdd() && m_q < m_n;
CRYPTOPP_ASSERT(pass);
pass = pass && m_u.IsPositive() && m_u < m_p;
CRYPTOPP_ASSERT(pass);
if (level >= 1)
{
pass = pass && m_p * m_q == m_n;
CRYPTOPP_ASSERT(pass);
pass = pass && RelativelyPrime(m_e, m_p+1);
CRYPTOPP_ASSERT(pass);
pass = pass && RelativelyPrime(m_e, m_p-1);
CRYPTOPP_ASSERT(pass);
pass = pass && RelativelyPrime(m_e, m_q+1);
CRYPTOPP_ASSERT(pass);
pass = pass && RelativelyPrime(m_e, m_q-1);
CRYPTOPP_ASSERT(pass);
pass = pass && m_u * m_q % m_p == 1;
CRYPTOPP_ASSERT(pass);
}
if (level >= 2)
{
pass = pass && VerifyPrime(rng, m_p, level-2) && VerifyPrime(rng, m_q, level-2);
CRYPTOPP_ASSERT(pass);
}
return pass;
}
bool InvertibleLUCFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
{
return GetValueHelper<LUCFunction>(this, name, valueType, pValue).Assignable()
CRYPTOPP_GET_FUNCTION_ENTRY(Prime1)
CRYPTOPP_GET_FUNCTION_ENTRY(Prime2)
CRYPTOPP_GET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
;
}
void InvertibleLUCFunction::AssignFrom(const NameValuePairs &source)
{
AssignFromHelper<LUCFunction>(this, source)
CRYPTOPP_SET_FUNCTION_ENTRY(Prime1)
CRYPTOPP_SET_FUNCTION_ENTRY(Prime2)
CRYPTOPP_SET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
;
}
NAMESPACE_END
|
