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

ec2n.cpp
1 // ec2n.cpp - originally written and placed in the public domain by Wei Dai
2
3 #include "pch.h"
4
5 #ifndef CRYPTOPP_IMPORTS
6
7 #include "ec2n.h"
8 #include "asn.h"
9 #include "integer.h"
10 #include "filters.h"
11 #include "algebra.cpp"
12 #include "eprecomp.cpp"
13
14 ANONYMOUS_NAMESPACE_BEGIN
15
16 using CryptoPP::EC2N;
17
18 #if defined(HAVE_GCC_INIT_PRIORITY)
19 const EC2N::Point g_identity __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 50))) = EC2N::Point();
20 #elif defined(HAVE_MSC_INIT_PRIORITY)
21 #pragma warning(disable: 4075)
22 #pragma init_seg(".CRT$XCU")
23 const EC2N::Point g_identity;
24 #pragma warning(default: 4075)
25 #elif defined(HAVE_XLC_INIT_PRIORITY)
26 #pragma priority(290)
27 const EC2N::Point g_identity;
28 #endif
29
30 ANONYMOUS_NAMESPACE_END
31
32 NAMESPACE_BEGIN(CryptoPP)
33
34 EC2N::EC2N(BufferedTransformation &bt)
35 : m_field(BERDecodeGF2NP(bt))
36 {
37 BERSequenceDecoder seq(bt);
38 m_field->BERDecodeElement(seq, m_a);
39 m_field->BERDecodeElement(seq, m_b);
40 // skip optional seed
41 if (!seq.EndReached())
42 {
43 SecByteBlock seed;
44 unsigned int unused;
45 BERDecodeBitString(seq, seed, unused);
46 }
47 seq.MessageEnd();
48 }
49
50 void EC2N::DEREncode(BufferedTransformation &bt) const
51 {
52 m_field->DEREncode(bt);
53 DERSequenceEncoder seq(bt);
54 m_field->DEREncodeElement(seq, m_a);
55 m_field->DEREncodeElement(seq, m_b);
56 seq.MessageEnd();
57 }
58
59 bool EC2N::DecodePoint(EC2N::Point &P, const byte *encodedPoint, size_t encodedPointLen) const
60 {
61 StringStore store(encodedPoint, encodedPointLen);
62 return DecodePoint(P, store, encodedPointLen);
63 }
64
65 bool EC2N::DecodePoint(EC2N::Point &P, BufferedTransformation &bt, size_t encodedPointLen) const
66 {
67 byte type;
68 if (encodedPointLen < 1 || !bt.Get(type))
69 return false;
70
71 switch (type)
72 {
73 case 0:
74 P.identity = true;
75 return true;
76 case 2:
77 case 3:
78 {
79 if (encodedPointLen != EncodedPointSize(true))
80 return false;
81
82 P.identity = false;
83 P.x.Decode(bt, m_field->MaxElementByteLength());
84
85 if (P.x.IsZero())
86 {
87 P.y = m_field->SquareRoot(m_b);
88 return true;
89 }
90
91 FieldElement z = m_field->Square(P.x);
92 CRYPTOPP_ASSERT(P.x == m_field->SquareRoot(z));
93 P.y = m_field->Divide(m_field->Add(m_field->Multiply(z, m_field->Add(P.x, m_a)), m_b), z);
94 CRYPTOPP_ASSERT(P.x == m_field->Subtract(m_field->Divide(m_field->Subtract(m_field->Multiply(P.y, z), m_b), z), m_a));
95 z = m_field->SolveQuadraticEquation(P.y);
96 CRYPTOPP_ASSERT(m_field->Add(m_field->Square(z), z) == P.y);
97 z.SetCoefficient(0, type & 1);
98
99 P.y = m_field->Multiply(z, P.x);
100 return true;
101 }
102 case 4:
103 {
104 if (encodedPointLen != EncodedPointSize(false))
105 return false;
106
107 unsigned int len = m_field->MaxElementByteLength();
108 P.identity = false;
109 P.x.Decode(bt, len);
110 P.y.Decode(bt, len);
111 return true;
112 }
113 default:
114 return false;
115 }
116 }
117
118 void EC2N::EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
119 {
120 if (P.identity)
121 NullStore().TransferTo(bt, EncodedPointSize(compressed));
122 else if (compressed)
123 {
124 bt.Put((byte)(2U + (!P.x ? 0U : m_field->Divide(P.y, P.x).GetBit(0))));
125 P.x.Encode(bt, m_field->MaxElementByteLength());
126 }
127 else
128 {
129 unsigned int len = m_field->MaxElementByteLength();
130 bt.Put(4); // uncompressed
131 P.x.Encode(bt, len);
132 P.y.Encode(bt, len);
133 }
134 }
135
136 void EC2N::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
137 {
138 ArraySink sink(encodedPoint, EncodedPointSize(compressed));
139 EncodePoint(sink, P, compressed);
140 CRYPTOPP_ASSERT(sink.TotalPutLength() == EncodedPointSize(compressed));
141 }
142
143 EC2N::Point EC2N::BERDecodePoint(BufferedTransformation &bt) const
144 {
145 SecByteBlock str;
146 BERDecodeOctetString(bt, str);
147 Point P;
148 if (!DecodePoint(P, str, str.size()))
149 BERDecodeError();
150 return P;
151 }
152
153 void EC2N::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
154 {
155 SecByteBlock str(EncodedPointSize(compressed));
156 EncodePoint(str, P, compressed);
157 DEREncodeOctetString(bt, str);
158 }
159
160 bool EC2N::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const
161 {
162 CRYPTOPP_UNUSED(rng);
163 bool pass = !!m_b;
164 pass = pass && m_a.CoefficientCount() <= m_field->MaxElementBitLength();
165 pass = pass && m_b.CoefficientCount() <= m_field->MaxElementBitLength();
166
167 if (level >= 1)
168 pass = pass && m_field->GetModulus().IsIrreducible();
169
170 return pass;
171 }
172
173 bool EC2N::VerifyPoint(const Point &P) const
174 {
175 const FieldElement &x = P.x, &y = P.y;
176 return P.identity ||
177 (x.CoefficientCount() <= m_field->MaxElementBitLength()
178 && y.CoefficientCount() <= m_field->MaxElementBitLength()
179 && !(((x+m_a)*x*x+m_b-(x+y)*y)%m_field->GetModulus()));
180 }
181
182 bool EC2N::Equal(const Point &P, const Point &Q) const
183 {
184 if (P.identity && Q.identity)
185 return true;
186
187 if (P.identity && !Q.identity)
188 return false;
189
190 if (!P.identity && Q.identity)
191 return false;
192
193 return (m_field->Equal(P.x,Q.x) && m_field->Equal(P.y,Q.y));
194 }
195
196 const EC2N::Point& EC2N::Identity() const
197 {
198 #if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
199 return g_identity;
200 #elif defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
201 static const EC2N::Point g_identity;
202 return g_identity;
203 #else
204 return Singleton<Point>().Ref();
205 #endif
206 }
207
208 const EC2N::Point& EC2N::Inverse(const Point &P) const
209 {
210 if (P.identity)
211 return P;
212 else
213 {
214 m_R.identity = false;
215 m_R.y = m_field->Add(P.x, P.y);
216 m_R.x = P.x;
217 return m_R;
218 }
219 }
220
221 const EC2N::Point& EC2N::Add(const Point &P, const Point &Q) const
222 {
223 if (P.identity) return Q;
224 if (Q.identity) return P;
225 if (Equal(P, Q)) return Double(P);
226 if (m_field->Equal(P.x, Q.x) && m_field->Equal(P.y, m_field->Add(Q.x, Q.y))) return Identity();
227
228 FieldElement t = m_field->Add(P.y, Q.y);
229 t = m_field->Divide(t, m_field->Add(P.x, Q.x));
230 FieldElement x = m_field->Square(t);
231 m_field->Accumulate(x, t);
232 m_field->Accumulate(x, Q.x);
233 m_field->Accumulate(x, m_a);
234 m_R.y = m_field->Add(P.y, m_field->Multiply(t, x));
235 m_field->Accumulate(x, P.x);
236 m_field->Accumulate(m_R.y, x);
237
238 m_R.x.swap(x);
239 m_R.identity = false;
240 return m_R;
241 }
242
243 const EC2N::Point& EC2N::Double(const Point &P) const
244 {
245 if (P.identity) return P;
246 if (!m_field->IsUnit(P.x)) return Identity();
247
248 FieldElement t = m_field->Divide(P.y, P.x);
249 m_field->Accumulate(t, P.x);
250 m_R.y = m_field->Square(P.x);
251 m_R.x = m_field->Square(t);
252 m_field->Accumulate(m_R.x, t);
253 m_field->Accumulate(m_R.x, m_a);
254 m_field->Accumulate(m_R.y, m_field->Multiply(t, m_R.x));
255 m_field->Accumulate(m_R.y, m_R.x);
256
257 m_R.identity = false;
258 return m_R;
259 }
260
261 // ********************************************************
262
263 /*
264 EcPrecomputation<EC2N>& EcPrecomputation<EC2N>::operator=(const EcPrecomputation<EC2N> &rhs)
265 {
266 m_ec = rhs.m_ec;
267 m_ep = rhs.m_ep;
268 m_ep.m_group = m_ec.get();
269 return *this;
270 }
271
272 void EcPrecomputation<EC2N>::SetCurveAndBase(const EC2N &ec, const EC2N::Point &base)
273 {
274 m_ec.reset(new EC2N(ec));
275 m_ep.SetGroupAndBase(*m_ec, base);
276 }
277
278 void EcPrecomputation<EC2N>::Precompute(unsigned int maxExpBits, unsigned int storage)
279 {
280 m_ep.Precompute(maxExpBits, storage);
281 }
282
283 void EcPrecomputation<EC2N>::Load(BufferedTransformation &bt)
284 {
285 BERSequenceDecoder seq(bt);
286 word32 version;
287 BERDecodeUnsigned<word32>(seq, version, INTEGER, 1, 1);
288 m_ep.m_exponentBase.BERDecode(seq);
289 m_ep.m_windowSize = m_ep.m_exponentBase.BitCount() - 1;
290 m_ep.m_bases.clear();
291 while (!seq.EndReached())
292 m_ep.m_bases.push_back(m_ec->BERDecodePoint(seq));
293 seq.MessageEnd();
294 }
295
296 void EcPrecomputation<EC2N>::Save(BufferedTransformation &bt) const
297 {
298 DERSequenceEncoder seq(bt);
299 DEREncodeUnsigned<word32>(seq, 1); // version
300 m_ep.m_exponentBase.DEREncode(seq);
301 for (unsigned i=0; i<m_ep.m_bases.size(); i++)
302 m_ec->DEREncodePoint(seq, m_ep.m_bases[i]);
303 seq.MessageEnd();
304 }
305
306 EC2N::Point EcPrecomputation<EC2N>::Exponentiate(const Integer &exponent) const
307 {
308 return m_ep.Exponentiate(exponent);
309 }
310
311 EC2N::Point EcPrecomputation<EC2N>::CascadeExponentiate(const Integer &exponent, const DL_FixedBasePrecomputation<Element> &pc2, const Integer &exponent2) const
312 {
313 return m_ep.CascadeExponentiate(exponent, static_cast<const EcPrecomputation<EC2N> &>(pc2).m_ep, exponent2);
314 }
315 */
316
317 NAMESPACE_END
318
319 #endif
EC2N::VerifyPoint
bool VerifyPoint(const Point &P) const
Verifies points on elliptic curve.
Definition: ec2n.cpp:173
Singleton
Restricts the instantiation of a class to one static object without locks.
Definition: misc.h:263
EC2N::EncodedPointSize
unsigned int EncodedPointSize(bool compressed=false) const
Determines encoded point size.
Definition: ec2n.h:70
EC2N::DEREncodePoint
void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
DER Encodes an elliptic curve point.
Definition: ec2n.cpp:153
RandomNumberGenerator
Interface for random number generators.
Definition: cryptlib.h:1383
SecByteBlock
SecBlock<byte> typedef.
Definition: secblock.h:1058
EC2N::EncodePoint
void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
Encodes an elliptic curve point.
Definition: ec2n.cpp:136
BERSequenceDecoder
BER Sequence Decoder.
Definition: asn.h:309
BufferedTransformation
Interface for buffered transformations.
Definition: cryptlib.h:1598
ec2n.h
Classes for Elliptic Curves over binary fields.
ArraySink
Copy input to a memory buffer.
Definition: filters.h:1136
NullStore
Empty store.
Definition: filters.h:1257
BufferedTransformation::TransferTo
lword TransferTo(BufferedTransformation &target, lword transferMax=LWORD_MAX, const std::string &channel=DEFAULT_CHANNEL)
move transferMax bytes of the buffered output to target as input
Definition: cryptlib.h:1901
BufferedTransformation::Put
size_t Put(byte inByte, bool blocking=true)
Input a byte for processing.
Definition: cryptlib.h:1620
BERDecodeOctetString
size_t BERDecodeOctetString(BufferedTransformation &bt, SecByteBlock &str)
BER decode octet string.
Definition: asn.cpp:117
EC2N::Inverse
const Point & Inverse(const Point &P) const
Inverts the element in the group.
Definition: ec2n.cpp:208
EC2N
Elliptic Curve over GF(2^n)
Definition: ec2n.h:27
pch.h
Precompiled header file.
EC2N::BERDecodePoint
Point BERDecodePoint(BufferedTransformation &bt) const
BER Decodes an elliptic curve point.
Definition: ec2n.cpp:143
EC2N::Identity
const Point & Identity() const
Provides the Identity element.
Definition: ec2n.cpp:196
StringStore
String-based implementation of Store interface.
Definition: filters.h:1195
CRYPTOPP_ASSERT
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
Definition: trap.h:69
BERDecodeError
void BERDecodeError()
Raises a BERDecodeErr.
Definition: asn.h:69
asn.h
Classes and functions for working with ANS.1 objects.
filters.h
Implementation of BufferedTransformation&#39;s attachment interface.
DERSequenceEncoder
DER Sequence Encoder.
Definition: asn.h:319
EC2N::DecodePoint
bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const
Decodes an elliptic curve point.
Definition: ec2n.cpp:65
DEREncodeOctetString
size_t DEREncodeOctetString(BufferedTransformation &bt, const byte *str, size_t strLen)
DER encode octet string.
Definition: asn.cpp:104
integer.h
Multiple precision integer with arithmetic operations.
EC2N::Equal
bool Equal(const Point &P, const Point &Q) const
Compare two elements for equality.
Definition: ec2n.cpp:182
BERDecodeBitString
size_t BERDecodeBitString(BufferedTransformation &bt, SecByteBlock &str, unsigned int &unusedBits)
DER decode bit string.
Definition: asn.cpp:191
EC2N::DEREncode
void DEREncode(BufferedTransformation &bt) const
Encode the fields fieldID and curve of the sequence ECParameters.
Definition: ec2n.cpp:50
BufferedTransformation::Get
virtual size_t Get(byte &outByte)
Retrieve a 8-bit byte.
Definition: cryptlib.cpp:527
CryptoPP
Crypto++ library namespace.
EC2NPoint
Elliptical Curve Point over GF(2^n)
Definition: ecpoint.h:53
EC2N::Add
const Point & Add(const Point &P, const Point &Q) const
Adds elements in the group.
Definition: ec2n.cpp:221
SecBlock::size
size_type size() const
Provides the count of elements in the SecBlock.
Definition: secblock.h:797
ArraySink::TotalPutLength
lword TotalPutLength()
Provides the number of bytes written to the Sink.
Definition: filters.h:1159
EC2N::Double
const Point & Double(const Point &P) const
Doubles an element in the group.
Definition: ec2n.cpp:243