Crypto++  8.2
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 
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 
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 
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 
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
bool VerifyPoint(const Point &P) const
Verifies points on elliptic curve.
Definition: ec2n.cpp:173
Restricts the instantiation of a class to one static object without locks.
Definition: misc.h:263
unsigned int EncodedPointSize(bool compressed=false) const
Determines encoded point size.
Definition: ec2n.h:70
void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
DER Encodes an elliptic curve point.
Definition: ec2n.cpp:153
Interface for random number generators.
Definition: cryptlib.h:1383
SecBlock<byte> typedef.
Definition: secblock.h:1058
void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
Encodes an elliptic curve point.
Definition: ec2n.cpp:136
BER Sequence Decoder.
Definition: asn.h:309
Interface for buffered transformations.
Definition: cryptlib.h:1598
Classes for Elliptic Curves over binary fields.
Copy input to a memory buffer.
Definition: filters.h:1136
Empty store.
Definition: filters.h:1257
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
size_t Put(byte inByte, bool blocking=true)
Input a byte for processing.
Definition: cryptlib.h:1620
size_t BERDecodeOctetString(BufferedTransformation &bt, SecByteBlock &str)
BER decode octet string.
Definition: asn.cpp:117
const Point & Inverse(const Point &P) const
Inverts the element in the group.
Definition: ec2n.cpp:208
Elliptic Curve over GF(2^n)
Definition: ec2n.h:27
Precompiled header file.
Point BERDecodePoint(BufferedTransformation &bt) const
BER Decodes an elliptic curve point.
Definition: ec2n.cpp:143
const Point & Identity() const
Provides the Identity element.
Definition: ec2n.cpp:196
String-based implementation of Store interface.
Definition: filters.h:1195
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
Definition: trap.h:69
void BERDecodeError()
Raises a BERDecodeErr.
Definition: asn.h:69
Classes and functions for working with ANS.1 objects.
Implementation of BufferedTransformation&#39;s attachment interface.
DER Sequence Encoder.
Definition: asn.h:319
bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const
Decodes an elliptic curve point.
Definition: ec2n.cpp:65
size_t DEREncodeOctetString(BufferedTransformation &bt, const byte *str, size_t strLen)
DER encode octet string.
Definition: asn.cpp:104
Multiple precision integer with arithmetic operations.
bool Equal(const Point &P, const Point &Q) const
Compare two elements for equality.
Definition: ec2n.cpp:182
size_t BERDecodeBitString(BufferedTransformation &bt, SecByteBlock &str, unsigned int &unusedBits)
DER decode bit string.
Definition: asn.cpp:191
void DEREncode(BufferedTransformation &bt) const
Encode the fields fieldID and curve of the sequence ECParameters.
Definition: ec2n.cpp:50
virtual size_t Get(byte &outByte)
Retrieve a 8-bit byte.
Definition: cryptlib.cpp:527
Crypto++ library namespace.
Elliptical Curve Point over GF(2^n)
Definition: ecpoint.h:53
const Point & Add(const Point &P, const Point &Q) const
Adds elements in the group.
Definition: ec2n.cpp:221
size_type size() const
Provides the count of elements in the SecBlock.
Definition: secblock.h:797
lword TotalPutLength()
Provides the number of bytes written to the Sink.
Definition: filters.h:1159
const Point & Double(const Point &P) const
Doubles an element in the group.
Definition: ec2n.cpp:243