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

xtr.h
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1 #ifndef CRYPTOPP_XTR_H
2 #define CRYPTOPP_XTR_H
3
4 /// \file xtr.h
5 /// \brief The XTR public key system
6 /// \details The XTR public key system by Arjen K. Lenstra and Eric R. Verheul
7
8 #include "cryptlib.h"
9 #include "modarith.h"
10 #include "integer.h"
11 #include "algebra.h"
12
13 NAMESPACE_BEGIN(CryptoPP)
14
15 /// \brief an element of GF(p^2)
16 class GFP2Element
17 {
18 public:
19 GFP2Element() {}
20 GFP2Element(const Integer &c1, const Integer &c2) : c1(c1), c2(c2) {}
21 GFP2Element(const byte *encodedElement, unsigned int size)
22 : c1(encodedElement, size/2), c2(encodedElement+size/2, size/2) {}
23
24 void Encode(byte *encodedElement, unsigned int size)
25 {
26 c1.Encode(encodedElement, size/2);
27 c2.Encode(encodedElement+size/2, size/2);
28 }
29
30 bool operator==(const GFP2Element &rhs) const {return c1 == rhs.c1 && c2 == rhs.c2;}
31 bool operator!=(const GFP2Element &rhs) const {return !operator==(rhs);}
32
33 void swap(GFP2Element &a)
34 {
35 c1.swap(a.c1);
36 c2.swap(a.c2);
37 }
38
39 static const GFP2Element & Zero();
40
41 Integer c1, c2;
42 };
43
44 /// \brief GF(p^2), optimal normal basis
45 template <class F>
46 class GFP2_ONB : public AbstractRing<GFP2Element>
47 {
48 public:
49 typedef F BaseField;
50
51 GFP2_ONB(const Integer &p) : modp(p)
52 {
53 if (p%3 != 2)
54 throw InvalidArgument("GFP2_ONB: modulus must be equivalent to 2 mod 3");
55 }
56
57 const Integer& GetModulus() const {return modp.GetModulus();}
58
59 GFP2Element ConvertIn(const Integer &a) const
60 {
61 t = modp.Inverse(modp.ConvertIn(a));
62 return GFP2Element(t, t);
63 }
64
65 GFP2Element ConvertIn(const GFP2Element &a) const
66 {return GFP2Element(modp.ConvertIn(a.c1), modp.ConvertIn(a.c2));}
67
68 GFP2Element ConvertOut(const GFP2Element &a) const
69 {return GFP2Element(modp.ConvertOut(a.c1), modp.ConvertOut(a.c2));}
70
71 bool Equal(const GFP2Element &a, const GFP2Element &b) const
72 {
73 return modp.Equal(a.c1, b.c1) && modp.Equal(a.c2, b.c2);
74 }
75
76 const Element& Identity() const
77 {
78 return GFP2Element::Zero();
79 }
80
81 const Element& Add(const Element &a, const Element &b) const
82 {
83 result.c1 = modp.Add(a.c1, b.c1);
84 result.c2 = modp.Add(a.c2, b.c2);
85 return result;
86 }
87
88 const Element& Inverse(const Element &a) const
89 {
90 result.c1 = modp.Inverse(a.c1);
91 result.c2 = modp.Inverse(a.c2);
92 return result;
93 }
94
95 const Element& Double(const Element &a) const
96 {
97 result.c1 = modp.Double(a.c1);
98 result.c2 = modp.Double(a.c2);
99 return result;
100 }
101
102 const Element& Subtract(const Element &a, const Element &b) const
103 {
104 result.c1 = modp.Subtract(a.c1, b.c1);
105 result.c2 = modp.Subtract(a.c2, b.c2);
106 return result;
107 }
108
109 Element& Accumulate(Element &a, const Element &b) const
110 {
111 modp.Accumulate(a.c1, b.c1);
112 modp.Accumulate(a.c2, b.c2);
113 return a;
114 }
115
116 Element& Reduce(Element &a, const Element &b) const
117 {
118 modp.Reduce(a.c1, b.c1);
119 modp.Reduce(a.c2, b.c2);
120 return a;
121 }
122
123 bool IsUnit(const Element &a) const
124 {
125 return a.c1.NotZero() || a.c2.NotZero();
126 }
127
128 const Element& MultiplicativeIdentity() const
129 {
130 result.c1 = result.c2 = modp.Inverse(modp.MultiplicativeIdentity());
131 return result;
132 }
133
134 const Element& Multiply(const Element &a, const Element &b) const
135 {
136 t = modp.Add(a.c1, a.c2);
137 t = modp.Multiply(t, modp.Add(b.c1, b.c2));
138 result.c1 = modp.Multiply(a.c1, b.c1);
139 result.c2 = modp.Multiply(a.c2, b.c2);
140 result.c1.swap(result.c2);
141 modp.Reduce(t, result.c1);
142 modp.Reduce(t, result.c2);
143 modp.Reduce(result.c1, t);
144 modp.Reduce(result.c2, t);
145 return result;
146 }
147
148 const Element& MultiplicativeInverse(const Element &a) const
149 {
150 return result = Exponentiate(a, modp.GetModulus()-2);
151 }
152
153 const Element& Square(const Element &a) const
154 {
155 const Integer &ac1 = (&a == &result) ? (t = a.c1) : a.c1;
156 result.c1 = modp.Multiply(modp.Subtract(modp.Subtract(a.c2, a.c1), a.c1), a.c2);
157 result.c2 = modp.Multiply(modp.Subtract(modp.Subtract(ac1, a.c2), a.c2), ac1);
158 return result;
159 }
160
161 Element Exponentiate(const Element &a, const Integer &e) const
162 {
163 Integer edivp, emodp;
164 Integer::Divide(emodp, edivp, e, modp.GetModulus());
165 Element b = PthPower(a);
166 return AbstractRing<GFP2Element>::CascadeExponentiate(a, emodp, b, edivp);
167 }
168
169 const Element & PthPower(const Element &a) const
170 {
171 result = a;
172 result.c1.swap(result.c2);
173 return result;
174 }
175
176 void RaiseToPthPower(Element &a) const
177 {
178 a.c1.swap(a.c2);
179 }
180
181 // a^2 - 2a^p
182 const Element & SpecialOperation1(const Element &a) const
183 {
184 CRYPTOPP_ASSERT(&a != &result);
185 result = Square(a);
186 modp.Reduce(result.c1, a.c2);
187 modp.Reduce(result.c1, a.c2);
188 modp.Reduce(result.c2, a.c1);
189 modp.Reduce(result.c2, a.c1);
190 return result;
191 }
192
193 // x * z - y * z^p
194 const Element & SpecialOperation2(const Element &x, const Element &y, const Element &z) const
195 {
196 CRYPTOPP_ASSERT(&x != &result && &y != &result && &z != &result);
197 t = modp.Add(x.c2, y.c2);
198 result.c1 = modp.Multiply(z.c1, modp.Subtract(y.c1, t));
199 modp.Accumulate(result.c1, modp.Multiply(z.c2, modp.Subtract(t, x.c1)));
200 t = modp.Add(x.c1, y.c1);
201 result.c2 = modp.Multiply(z.c2, modp.Subtract(y.c2, t));
202 modp.Accumulate(result.c2, modp.Multiply(z.c1, modp.Subtract(t, x.c2)));
203 return result;
204 }
205
206 protected:
207 BaseField modp;
208 mutable GFP2Element result;
209 mutable Integer t;
210 };
211
212 /// \brief Creates primes p,q and generator g for XTR
213 void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits);
214
215 GFP2Element XTR_Exponentiate(const GFP2Element &b, const Integer &e, const Integer &p);
216
217 NAMESPACE_END
218
219 #endif
InvalidArgument
An invalid argument was detected.
Definition: cryptlib.h:202
GFP2_ONB::Add
const Element & Add(const Element &a, const Element &b) const
Adds elements in the group.
Definition: xtr.h:81
GFP2_ONB::Reduce
Element & Reduce(Element &a, const Element &b) const
Reduces an element in the congruence class.
Definition: xtr.h:116
GFP2_ONB::Identity
const Element & Identity() const
Provides the Identity element.
Definition: xtr.h:76
AbstractRing::CascadeExponentiate
virtual Element CascadeExponentiate(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
TODO.
Definition: algebra.cpp:323
GFP2_ONB::Exponentiate
Element Exponentiate(const Element &a, const Integer &e) const
Raises a base to an exponent in the group.
Definition: xtr.h:161
cryptlib.h
Abstract base classes that provide a uniform interface to this library.
GFP2_ONB::Inverse
const Element & Inverse(const Element &a) const
Inverts the element in the group.
Definition: xtr.h:88
RandomNumberGenerator
Interface for random number generators.
Definition: cryptlib.h:1349
algebra.h
Classes for performing mathematics over different fields.
operator==
bool operator==(const OID &lhs, const OID &rhs)
Compare two OIDs for equality.
AbstractRing
Abstract ring.
Definition: algebra.h:118
operator!=
bool operator!=(const OID &lhs, const OID &rhs)
Compare two OIDs for inequality.
GFP2Element
an element of GF(p^2)
Definition: xtr.h:16
GFP2_ONB::Equal
bool Equal(const GFP2Element &a, const GFP2Element &b) const
Compare two elements for equality.
Definition: xtr.h:71
Integer::swap
void swap(Integer &a)
Swaps this Integer with another Integer.
Definition: integer.cpp:3164
GFP2_ONB::MultiplicativeIdentity
const Element & MultiplicativeIdentity() const
Retrieves the multiplicative identity.
Definition: xtr.h:128
Integer
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
CRYPTOPP_ASSERT
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
Definition: trap.h:60
Integer::Divide
static void Divide(Integer &r, Integer &q, const Integer &a, const Integer &d)
Extended Division.
Definition: integer.cpp:4173
Integer::Encode
void Encode(byte *output, size_t outputLen, Signedness sign=UNSIGNED) const
Encode in big-endian format.
Definition: integer.cpp:3404
GFP2_ONB::IsUnit
bool IsUnit(const Element &a) const
Determines whether an element is a unit in the group.
Definition: xtr.h:123
GFP2_ONB::Accumulate
Element & Accumulate(Element &a, const Element &b) const
TODO.
Definition: xtr.h:109
GFP2_ONB::Multiply
const Element & Multiply(const Element &a, const Element &b) const
Multiplies elements in the group.
Definition: xtr.h:134
GFP2_ONB::Subtract
const Element & Subtract(const Element &a, const Element &b) const
Subtracts elements in the group.
Definition: xtr.h:102
GFP2_ONB::MultiplicativeInverse
const Element & MultiplicativeInverse(const Element &a) const
Calculate the multiplicative inverse of an element in the group.
Definition: xtr.h:148
integer.h
Multiple precision integer with arithmetic operations.
GFP2_ONB::Double
const Element & Double(const Element &a) const
Doubles an element in the group.
Definition: xtr.h:95
modarith.h
Class file for performing modular arithmetic.
CryptoPP
Crypto++ library namespace.
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
GFP2_ONB::Square
const Element & Square(const Element &a) const
Square an element in the group.
Definition: xtr.h:153