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  #define INIT_ATTRIBUTE __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 51)))
20  const EC2N::Point g_identity INIT_ATTRIBUTE = EC2N::Point();
21 #elif defined(HAVE_MSC_INIT_PRIORITY)
22  #pragma warning(disable: 4075)
23  #pragma init_seg(".CRT$XCU")
24  const EC2N::Point g_identity;
25  #pragma warning(default: 4075)
26 #elif defined(HAVE_XLC_INIT_PRIORITY)
27  #pragma priority(290)
28  const EC2N::Point g_identity;
29 #endif
30 
31 ANONYMOUS_NAMESPACE_END
32 
33 NAMESPACE_BEGIN(CryptoPP)
34 
36  : m_field(BERDecodeGF2NP(bt))
37 {
38  BERSequenceDecoder seq(bt);
39  m_field->BERDecodeElement(seq, m_a);
40  m_field->BERDecodeElement(seq, m_b);
41  // skip optional seed
42  if (!seq.EndReached())
43  {
44  SecByteBlock seed;
45  unsigned int unused;
46  BERDecodeBitString(seq, seed, unused);
47  }
48  seq.MessageEnd();
49 }
50 
52 {
53  m_field->DEREncode(bt);
54  DERSequenceEncoder seq(bt);
55  m_field->DEREncodeElement(seq, m_a);
56  m_field->DEREncodeElement(seq, m_b);
57  seq.MessageEnd();
58 }
59 
60 bool EC2N::DecodePoint(EC2N::Point &P, const byte *encodedPoint, size_t encodedPointLen) const
61 {
62  StringStore store(encodedPoint, encodedPointLen);
63  return DecodePoint(P, store, encodedPointLen);
64 }
65 
66 bool EC2N::DecodePoint(EC2N::Point &P, BufferedTransformation &bt, size_t encodedPointLen) const
67 {
68  byte type;
69  if (encodedPointLen < 1 || !bt.Get(type))
70  return false;
71 
72  switch (type)
73  {
74  case 0:
75  P.identity = true;
76  return true;
77  case 2:
78  case 3:
79  {
80  if (encodedPointLen != EncodedPointSize(true))
81  return false;
82 
83  P.identity = false;
84  P.x.Decode(bt, m_field->MaxElementByteLength());
85 
86  if (P.x.IsZero())
87  {
88  P.y = m_field->SquareRoot(m_b);
89  return true;
90  }
91 
92  FieldElement z = m_field->Square(P.x);
93  CRYPTOPP_ASSERT(P.x == m_field->SquareRoot(z));
94  P.y = m_field->Divide(m_field->Add(m_field->Multiply(z, m_field->Add(P.x, m_a)), m_b), z);
95  CRYPTOPP_ASSERT(P.x == m_field->Subtract(m_field->Divide(m_field->Subtract(m_field->Multiply(P.y, z), m_b), z), m_a));
96  z = m_field->SolveQuadraticEquation(P.y);
97  CRYPTOPP_ASSERT(m_field->Add(m_field->Square(z), z) == P.y);
98  z.SetCoefficient(0, type & 1);
99 
100  P.y = m_field->Multiply(z, P.x);
101  return true;
102  }
103  case 4:
104  {
105  if (encodedPointLen != EncodedPointSize(false))
106  return false;
107 
108  unsigned int len = m_field->MaxElementByteLength();
109  P.identity = false;
110  P.x.Decode(bt, len);
111  P.y.Decode(bt, len);
112  return true;
113  }
114  default:
115  return false;
116  }
117 }
118 
119 void EC2N::EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
120 {
121  if (P.identity)
122  NullStore().TransferTo(bt, EncodedPointSize(compressed));
123  else if (compressed)
124  {
125  bt.Put((byte)(2U + (!P.x ? 0U : m_field->Divide(P.y, P.x).GetBit(0))));
126  P.x.Encode(bt, m_field->MaxElementByteLength());
127  }
128  else
129  {
130  unsigned int len = m_field->MaxElementByteLength();
131  bt.Put(4); // uncompressed
132  P.x.Encode(bt, len);
133  P.y.Encode(bt, len);
134  }
135 }
136 
137 void EC2N::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
138 {
139  ArraySink sink(encodedPoint, EncodedPointSize(compressed));
140  EncodePoint(sink, P, compressed);
141  CRYPTOPP_ASSERT(sink.TotalPutLength() == EncodedPointSize(compressed));
142 }
143 
145 {
146  SecByteBlock str;
147  BERDecodeOctetString(bt, str);
148  Point P;
149  if (!DecodePoint(P, str, str.size()))
150  BERDecodeError();
151  return P;
152 }
153 
154 void EC2N::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
155 {
156  SecByteBlock str(EncodedPointSize(compressed));
157  EncodePoint(str, P, compressed);
158  DEREncodeOctetString(bt, str);
159 }
160 
161 bool EC2N::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const
162 {
163  CRYPTOPP_UNUSED(rng);
164  bool pass = !!m_b;
165  pass = pass && m_a.CoefficientCount() <= m_field->MaxElementBitLength();
166  pass = pass && m_b.CoefficientCount() <= m_field->MaxElementBitLength();
167 
168  if (level >= 1)
169  pass = pass && m_field->GetModulus().IsIrreducible();
170 
171  return pass;
172 }
173 
174 bool EC2N::VerifyPoint(const Point &P) const
175 {
176  const FieldElement &x = P.x, &y = P.y;
177  return P.identity ||
178  (x.CoefficientCount() <= m_field->MaxElementBitLength()
179  && y.CoefficientCount() <= m_field->MaxElementBitLength()
180  && !(((x+m_a)*x*x+m_b-(x+y)*y)%m_field->GetModulus()));
181 }
182 
183 bool EC2N::Equal(const Point &P, const Point &Q) const
184 {
185  if (P.identity && Q.identity)
186  return true;
187 
188  if (P.identity && !Q.identity)
189  return false;
190 
191  if (!P.identity && Q.identity)
192  return false;
193 
194  return (m_field->Equal(P.x,Q.x) && m_field->Equal(P.y,Q.y));
195 }
196 
198 {
199 #if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
200  return g_identity;
201 #elif defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
202  static const EC2N::Point g_identity;
203  return g_identity;
204 #else
205  return Singleton<Point>().Ref();
206 #endif
207 }
208 
209 const EC2N::Point& EC2N::Inverse(const Point &P) const
210 {
211  if (P.identity)
212  return P;
213  else
214  {
215  m_R.identity = false;
216  m_R.y = m_field->Add(P.x, P.y);
217  m_R.x = P.x;
218  return m_R;
219  }
220 }
221 
222 const EC2N::Point& EC2N::Add(const Point &P, const Point &Q) const
223 {
224  if (P.identity) return Q;
225  if (Q.identity) return P;
226  if (Equal(P, Q)) return Double(P);
227  if (m_field->Equal(P.x, Q.x) && m_field->Equal(P.y, m_field->Add(Q.x, Q.y))) return Identity();
228 
229  FieldElement t = m_field->Add(P.y, Q.y);
230  t = m_field->Divide(t, m_field->Add(P.x, Q.x));
231  FieldElement x = m_field->Square(t);
232  m_field->Accumulate(x, t);
233  m_field->Accumulate(x, Q.x);
234  m_field->Accumulate(x, m_a);
235  m_R.y = m_field->Add(P.y, m_field->Multiply(t, x));
236  m_field->Accumulate(x, P.x);
237  m_field->Accumulate(m_R.y, x);
238 
239  m_R.x.swap(x);
240  m_R.identity = false;
241  return m_R;
242 }
243 
244 const EC2N::Point& EC2N::Double(const Point &P) const
245 {
246  if (P.identity) return P;
247  if (!m_field->IsUnit(P.x)) return Identity();
248 
249  FieldElement t = m_field->Divide(P.y, P.x);
250  m_field->Accumulate(t, P.x);
251  m_R.y = m_field->Square(P.x);
252  m_R.x = m_field->Square(t);
253  m_field->Accumulate(m_R.x, t);
254  m_field->Accumulate(m_R.x, m_a);
255  m_field->Accumulate(m_R.y, m_field->Multiply(t, m_R.x));
256  m_field->Accumulate(m_R.y, m_R.x);
257 
258  m_R.identity = false;
259  return m_R;
260 }
261 
262 // ********************************************************
263 
264 #if 0
266 {
267  m_ec = rhs.m_ec;
268  m_ep = rhs.m_ep;
269  m_ep.m_group = m_ec.get();
270  return *this;
271 }
272 
273 void EcPrecomputation<EC2N>::SetCurveAndBase(const EC2N &ec, const EC2N::Point &base)
274 {
275  m_ec.reset(new EC2N(ec));
276  m_ep.SetGroupAndBase(*m_ec, base);
277 }
278 
279 void EcPrecomputation<EC2N>::Precompute(unsigned int maxExpBits, unsigned int storage)
280 {
281  m_ep.Precompute(maxExpBits, storage);
282 }
283 
285 {
286  BERSequenceDecoder seq(bt);
287  word32 version;
288  BERDecodeUnsigned<word32>(seq, version, INTEGER, 1, 1);
289  m_ep.m_exponentBase.BERDecode(seq);
290  m_ep.m_windowSize = m_ep.m_exponentBase.BitCount() - 1;
291  m_ep.m_bases.clear();
292  while (!seq.EndReached())
293  m_ep.m_bases.push_back(m_ec->BERDecodePoint(seq));
294  seq.MessageEnd();
295 }
296 
298 {
299  DERSequenceEncoder seq(bt);
300  DEREncodeUnsigned<word32>(seq, 1); // version
301  m_ep.m_exponentBase.DEREncode(seq);
302  for (unsigned i=0; i<m_ep.m_bases.size(); i++)
303  m_ec->DEREncodePoint(seq, m_ep.m_bases[i]);
304  seq.MessageEnd();
305 }
306 
308 {
309  return m_ep.Exponentiate(exponent);
310 }
311 
313 {
314  return m_ep.CascadeExponentiate(exponent, static_cast<const EcPrecomputation<EC2N> &>(pc2).m_ep, exponent2);
315 }
316 #endif
317 
318 NAMESPACE_END
319 
320 #endif
bool VerifyPoint(const Point &P) const
Verifies points on elliptic curve.
Definition: ec2n.cpp:174
EC2N()
Construct an EC2N.
Definition: ec2n.h:36
Restricts the instantiation of a class to one static object without locks.
Definition: misc.h:304
ASN.1 Integer.
Definition: asn.h:34
void MessageEnd()
Signals the end of messages to the object.
Definition: asn.cpp:624
unsigned int EncodedPointSize(bool compressed=false) const
Determines encoded point size.
Definition: ec2n.h:69
void Encode(byte *output, size_t outputLen) const
encode in big-endian format
Definition: gf2n.cpp:195
CRYPTOPP_DLL size_t CRYPTOPP_API DEREncodeOctetString(BufferedTransformation &bt, const byte *str, size_t strLen)
DER encode octet string.
Definition: asn.cpp:107
void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
DER Encodes an elliptic curve point.
Definition: ec2n.cpp:154
Interface for random number generators.
Definition: cryptlib.h:1413
SecBlock<byte> typedef.
Definition: secblock.h:1091
void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
Encodes an elliptic curve point.
Definition: ec2n.cpp:137
BER Sequence Decoder.
Definition: asn.h:524
Interface for buffered transformations.
Definition: cryptlib.h:1630
Classes for Elliptic Curves over binary fields.
Copy input to a memory buffer.
Definition: filters.h:1199
Empty store.
Definition: filters.h:1320
bool EndReached() const
Determine end of stream.
Definition: asn.cpp:527
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:1966
size_t Put(byte inByte, bool blocking=true)
Input a byte for processing.
Definition: cryptlib.h:1652
const Point & Inverse(const Point &P) const
Inverts the element in the group.
Definition: ec2n.cpp:209
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
Elliptic Curve over GF(2^n)
Definition: ec2n.h:26
Precompiled header file.
CRYPTOPP_DLL size_t CRYPTOPP_API BERDecodeBitString(BufferedTransformation &bt, SecByteBlock &str, unsigned int &unusedBits)
DER decode bit string.
Definition: asn.cpp:246
Point BERDecodePoint(BufferedTransformation &bt) const
BER Decodes an elliptic curve point.
Definition: ec2n.cpp:144
const Point & Identity() const
Provides the Identity element.
Definition: ec2n.cpp:197
String-based implementation of Store interface.
Definition: filters.h:1258
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
Definition: trap.h:69
void BERDecodeError()
Raises a BERDecodeErr.
Definition: asn.h:104
Classes and functions for working with ANS.1 objects.
DL_FixedBasePrecomputation interface.
Definition: eprecomp.h:60
Implementation of BufferedTransformation&#39;s attachment interface.
void MessageEnd()
Signals the end of messages to the object.
Definition: asn.cpp:553
DER Sequence Encoder.
Definition: asn.h:556
CRYPTOPP_DLL size_t CRYPTOPP_API BERDecodeOctetString(BufferedTransformation &bt, SecByteBlock &str)
BER decode octet string.
Definition: asn.cpp:120
bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const
Decodes an elliptic curve point.
Definition: ec2n.cpp:66
Elliptic Curve precomputation.
Definition: ec2n.h:99
Multiple precision integer with arithmetic operations.
EC2N precomputation specialization.
Definition: ec2n.h:104
bool Equal(const Point &P, const Point &Q) const
Compare two elements for equality.
Definition: ec2n.cpp:183
void DEREncode(BufferedTransformation &bt) const
Encode the fields fieldID and curve of the sequence ECParameters.
Definition: ec2n.cpp:51
virtual size_t Get(byte &outByte)
Retrieve a 8-bit byte.
Definition: cryptlib.cpp:528
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:222
size_type size() const
Provides the count of elements in the SecBlock.
Definition: secblock.h:829
lword TotalPutLength()
Provides the number of bytes written to the Sink.
Definition: filters.h:1222
const Point & Double(const Point &P) const
Doubles an element in the group.
Definition: ec2n.cpp:244