Crypto++ 8.1 Free C++ class library of cryptographic schemes

rabin.cpp
1 // rabin.cpp - originally written and placed in the public domain by Wei Dai
2
3 #include "pch.h"
4 #include "rabin.h"
5 #include "integer.h"
6 #include "nbtheory.h"
7 #include "modarith.h"
8 #include "asn.h"
9 #include "sha.h"
10
11 NAMESPACE_BEGIN(CryptoPP)
12
13 void RabinFunction::BERDecode(BufferedTransformation &bt)
14 {
15 BERSequenceDecoder seq(bt);
16 m_n.BERDecode(seq);
17 m_r.BERDecode(seq);
18 m_s.BERDecode(seq);
19 seq.MessageEnd();
20 }
21
22 void RabinFunction::DEREncode(BufferedTransformation &bt) const
23 {
24 DERSequenceEncoder seq(bt);
25 m_n.DEREncode(seq);
26 m_r.DEREncode(seq);
27 m_s.DEREncode(seq);
28 seq.MessageEnd();
29 }
30
31 Integer RabinFunction::ApplyFunction(const Integer &in) const
32 {
33 DoQuickSanityCheck();
34
35 Integer out = in.Squared()%m_n;
36 if (in.IsOdd())
37 out = out*m_r%m_n;
38 if (Jacobi(in, m_n)==-1)
39 out = out*m_s%m_n;
40 return out;
41 }
42
43 bool RabinFunction::Validate(RandomNumberGenerator& /*rng*/, unsigned int level) const
44 {
45 bool pass = true;
46 pass = pass && m_n > Integer::One() && m_n%4 == 1;
47 CRYPTOPP_ASSERT(pass);
48 pass = pass && m_r > Integer::One() && m_r < m_n;
49 CRYPTOPP_ASSERT(pass);
50 pass = pass && m_s > Integer::One() && m_s < m_n;
51 CRYPTOPP_ASSERT(pass);
52 if (level >= 1)
53 {
54 pass = pass && Jacobi(m_r, m_n) == -1 && Jacobi(m_s, m_n) == -1;
55 CRYPTOPP_ASSERT(pass);
56 }
57 return pass;
58 }
59
60 bool RabinFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
61 {
62 return GetValueHelper(this, name, valueType, pValue).Assignable()
63 CRYPTOPP_GET_FUNCTION_ENTRY(Modulus)
64 CRYPTOPP_GET_FUNCTION_ENTRY(QuadraticResidueModPrime1)
65 CRYPTOPP_GET_FUNCTION_ENTRY(QuadraticResidueModPrime2)
66 ;
67 }
68
69 void RabinFunction::AssignFrom(const NameValuePairs &source)
70 {
71 AssignFromHelper(this, source)
72 CRYPTOPP_SET_FUNCTION_ENTRY(Modulus)
73 CRYPTOPP_SET_FUNCTION_ENTRY(QuadraticResidueModPrime1)
74 CRYPTOPP_SET_FUNCTION_ENTRY(QuadraticResidueModPrime2)
75 ;
76 }
77
78 // *****************************************************************************
79 // private key operations:
80
81 // generate a random private key
82 void InvertibleRabinFunction::GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg)
83 {
84 int modulusSize = 2048;
85 alg.GetIntValue("ModulusSize", modulusSize) || alg.GetIntValue("KeySize", modulusSize);
86
87 if (modulusSize < 16)
88 throw InvalidArgument("InvertibleRabinFunction: specified modulus size is too small");
89
90 // VC70 workaround: putting these after primeParam causes overlapped stack allocation
91 bool rFound=false, sFound=false;
92 Integer t=2;
93
94 AlgorithmParameters primeParam = MakeParametersForTwoPrimesOfEqualSize(modulusSize)
95 ("EquivalentTo", 3)("Mod", 4);
96 m_p.GenerateRandom(rng, primeParam);
97 m_q.GenerateRandom(rng, primeParam);
98
99 while (!(rFound && sFound))
100 {
101 int jp = Jacobi(t, m_p);
102 int jq = Jacobi(t, m_q);
103
104 if (!rFound && jp==1 && jq==-1)
105 {
106 m_r = t;
107 rFound = true;
108 }
109
110 if (!sFound && jp==-1 && jq==1)
111 {
112 m_s = t;
113 sFound = true;
114 }
115
116 ++t;
117 }
118
119 m_n = m_p * m_q;
120 m_u = m_q.InverseMod(m_p);
121 }
122
123 void InvertibleRabinFunction::BERDecode(BufferedTransformation &bt)
124 {
125 BERSequenceDecoder seq(bt);
126 m_n.BERDecode(seq);
127 m_r.BERDecode(seq);
128 m_s.BERDecode(seq);
129 m_p.BERDecode(seq);
130 m_q.BERDecode(seq);
131 m_u.BERDecode(seq);
132 seq.MessageEnd();
133 }
134
135 void InvertibleRabinFunction::DEREncode(BufferedTransformation &bt) const
136 {
137 DERSequenceEncoder seq(bt);
138 m_n.DEREncode(seq);
139 m_r.DEREncode(seq);
140 m_s.DEREncode(seq);
141 m_p.DEREncode(seq);
142 m_q.DEREncode(seq);
143 m_u.DEREncode(seq);
144 seq.MessageEnd();
145 }
146
147 Integer InvertibleRabinFunction::CalculateInverse(RandomNumberGenerator &rng, const Integer &in) const
148 {
149 DoQuickSanityCheck();
150
151 ModularArithmetic modn(m_n);
152 Integer r(rng, Integer::One(), m_n - Integer::One());
153 r = modn.Square(r);
154 Integer r2 = modn.Square(r);
155 Integer c = modn.Multiply(in, r2); // blind
156
157 Integer cp=c%m_p, cq=c%m_q;
158
159 int jp = Jacobi(cp, m_p);
160 int jq = Jacobi(cq, m_q);
161
162 if (jq==-1)
163 {
164 cp = cp*EuclideanMultiplicativeInverse(m_r, m_p)%m_p;
165 cq = cq*EuclideanMultiplicativeInverse(m_r, m_q)%m_q;
166 }
167
168 if (jp==-1)
169 {
170 cp = cp*EuclideanMultiplicativeInverse(m_s, m_p)%m_p;
171 cq = cq*EuclideanMultiplicativeInverse(m_s, m_q)%m_q;
172 }
173
174 cp = ModularSquareRoot(cp, m_p);
175 cq = ModularSquareRoot(cq, m_q);
176
177 if (jp==-1)
178 cp = m_p-cp;
179
180 Integer out = CRT(cq, m_q, cp, m_p, m_u);
181
182 out = modn.Divide(out, r); // unblind
183
184 if ((jq==-1 && out.IsEven()) || (jq==1 && out.IsOdd()))
185 out = m_n-out;
186
187 return out;
188 }
189
190 bool InvertibleRabinFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
191 {
192 bool pass = RabinFunction::Validate(rng, level);
193 CRYPTOPP_ASSERT(pass);
194 pass = pass && m_p > Integer::One() && m_p%4 == 3 && m_p < m_n;
195 CRYPTOPP_ASSERT(pass);
196 pass = pass && m_q > Integer::One() && m_q%4 == 3 && m_q < m_n;
197 CRYPTOPP_ASSERT(pass);
198 pass = pass && m_u.IsPositive() && m_u < m_p;
199 CRYPTOPP_ASSERT(pass);
200 if (level >= 1)
201 {
202 pass = pass && m_p * m_q == m_n;
203 CRYPTOPP_ASSERT(pass);
204 pass = pass && m_u * m_q % m_p == 1;
205 CRYPTOPP_ASSERT(pass);
206 pass = pass && Jacobi(m_r, m_p) == 1;
207 CRYPTOPP_ASSERT(pass);
208 pass = pass && Jacobi(m_r, m_q) == -1;
209 CRYPTOPP_ASSERT(pass);
210 pass = pass && Jacobi(m_s, m_p) == -1;
211 CRYPTOPP_ASSERT(pass);
212 pass = pass && Jacobi(m_s, m_q) == 1;
213 CRYPTOPP_ASSERT(pass);
214 }
215 if (level >= 2)
216 {
217 pass = pass && VerifyPrime(rng, m_p, level-2) && VerifyPrime(rng, m_q, level-2);
218 CRYPTOPP_ASSERT(pass);
219 }
220 return pass;
221 }
222
223 bool InvertibleRabinFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
224 {
225 return GetValueHelper<RabinFunction>(this, name, valueType, pValue).Assignable()
226 CRYPTOPP_GET_FUNCTION_ENTRY(Prime1)
227 CRYPTOPP_GET_FUNCTION_ENTRY(Prime2)
228 CRYPTOPP_GET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
229 ;
230 }
231
232 void InvertibleRabinFunction::AssignFrom(const NameValuePairs &source)
233 {
234 AssignFromHelper<RabinFunction>(this, source)
235 CRYPTOPP_SET_FUNCTION_ENTRY(Prime1)
236 CRYPTOPP_SET_FUNCTION_ENTRY(Prime2)
237 CRYPTOPP_SET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
238 ;
239 }
240
241 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
Name::MultiplicativeInverseOfPrime2ModPrime1
const char * MultiplicativeInverseOfPrime2ModPrime1()
Integer.
Definition: argnames.h:47
InvalidArgument
An invalid argument was detected.
Definition: cryptlib.h:202
rabin.h
Classes for Rabin encryption and signature schemes.
ModularArithmetic::Square
const Integer & Square(const Integer &a) const
Square an element in the ring.
Definition: modarith.h:181
ModularArithmetic::Divide
const Integer & Divide(const Integer &a, const Integer &b) const
Divides elements in the ring.
Definition: modarith.h:202
Name::Prime2
const char * Prime2()
Integer.
Definition: argnames.h:44
Integer::DEREncode
void DEREncode(BufferedTransformation &bt) const
Encode in DER format.
Definition: integer.cpp:3432
Name::QuadraticResidueModPrime1
const char * QuadraticResidueModPrime1()
Integer.
Definition: argnames.h:48
InvertibleRabinFunction::CalculateInverse
Integer CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const
Calculates the inverse of an element.
Definition: rabin.cpp:147
RabinFunction::GetVoidValue
bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
Get a named value.
Definition: rabin.cpp:60
ModularArithmetic
Ring of congruence classes modulo n.
Definition: modarith.h:38
RandomNumberGenerator
Interface for random number generators.
Definition: cryptlib.h:1383
Jacobi
int Jacobi(const Integer &a, const Integer &b)
Calculate the Jacobi symbol.
Definition: nbtheory.cpp:785
Integer::InverseMod
Integer InverseMod(const Integer &n) const
Calculate multiplicative inverse.
Definition: integer.cpp:4421
ModularSquareRoot
Integer ModularSquareRoot(const Integer &a, const Integer &p)
Extract a modular square root.
Definition: nbtheory.cpp:572
BERSequenceDecoder
BER Sequence Decoder.
Definition: asn.h:309
Integer::GenerateRandom
void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params=g_nullNameValuePairs)
Generate a random number.
Definition: integer.h:484
BufferedTransformation
Interface for buffered transformations.
Definition: cryptlib.h:1598
Integer::IsPositive
bool IsPositive() const
Determines if the Integer is positive.
Definition: integer.h:342
Integer::One
static const Integer & One()
Integer representing 1.
Definition: integer.cpp:4868
RabinFunction::ApplyFunction
Integer ApplyFunction(const Integer &x) const
Applies the trapdoor.
Definition: rabin.cpp:31
Name::Prime1
const char * Prime1()
Integer.
Definition: argnames.h:43
CryptoMaterial::DoQuickSanityCheck
void DoQuickSanityCheck() const
Perform a quick sanity check.
Definition: cryptlib.h:2387
Name::QuadraticResidueModPrime2
const char * QuadraticResidueModPrime2()
Integer.
Definition: argnames.h:49
ModularArithmetic::Multiply
const Integer & Multiply(const Integer &a, const Integer &b) const
Multiplies elements in the ring.
Definition: modarith.h:174
VerifyPrime
bool VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level=1)
Verifies a number is probably prime.
Definition: nbtheory.cpp:247
Integer
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
pch.h
Precompiled header file.
Integer::IsEven
bool IsEven() const
Determines if the Integer is even parity.
Definition: integer.h:348
CRYPTOPP_ASSERT
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
Definition: trap.h:69
InvertibleRabinFunction::GenerateRandom
void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg)
Definition: rabin.cpp:82
asn.h
Classes and functions for working with ANS.1 objects.
sha.h
Classes for SHA-1 and SHA-2 family of message digests.
RabinFunction::Validate
bool Validate(RandomNumberGenerator &rng, unsigned int level) const
Check this object for errors.
Definition: rabin.cpp:43
nbtheory.h
Classes and functions for number theoretic operations.
InvertibleRabinFunction::Validate
bool Validate(RandomNumberGenerator &rng, unsigned int level) const
Check this object for errors.
Definition: rabin.cpp:190
DERSequenceEncoder
DER Sequence Encoder.
Definition: asn.h:319
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
InvertibleRabinFunction::AssignFrom
void AssignFrom(const NameValuePairs &source)
Assign values to this object.
Definition: rabin.cpp:232
AlgorithmParameters
An object that implements NameValuePairs.
Definition: algparam.h:419
Name::Modulus
const char * Modulus()
Integer.
Definition: argnames.h:33
integer.h
Multiple precision integer with arithmetic operations.
RabinFunction::AssignFrom
void AssignFrom(const NameValuePairs &source)
Assign values to this object.
Definition: rabin.cpp:69
Integer::BERDecode
void BERDecode(const byte *input, size_t inputLen)
Decode from BER format.
Definition: integer.cpp:3439
InvertibleRabinFunction::GetVoidValue
bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
Get a named value.
Definition: rabin.cpp:223
modarith.h
Class file for performing modular arithmetic.
CryptoPP
Crypto++ library namespace.
NameValuePairs::GetIntValue
bool GetIntValue(const char *name, int &value) const
Get a named value with type int.
Definition: cryptlib.h:386
Integer::IsOdd
bool IsOdd() const
Determines if the Integer is odd parity.
Definition: integer.h:351
NameValuePairs
Interface for retrieving values given their names.
Definition: cryptlib.h:293