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

ecp.cpp
1 // ecp.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 "ecp.h"
8 #include "asn.h"
9 #include "integer.h"
10 #include "nbtheory.h"
11 #include "modarith.h"
12 #include "filters.h"
13 #include "algebra.cpp"
14
15 ANONYMOUS_NAMESPACE_BEGIN
16
17 using CryptoPP::ECP;
18 using CryptoPP::ModularArithmetic;
19
20 #if defined(HAVE_GCC_INIT_PRIORITY)
21 const ECP::Point g_identity __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 51))) = ECP::Point();
22 #elif defined(HAVE_MSC_INIT_PRIORITY)
23 #pragma warning(disable: 4075)
24 #pragma init_seg(".CRT$XCU")
25 const ECP::Point g_identity;
26 #pragma warning(default: 4075)
27 #elif defined(HAVE_XLC_INIT_PRIORITY)
28 #pragma priority(290)
29 const ECP::Point g_identity;
30 #endif
31
32 inline ECP::Point ToMontgomery(const ModularArithmetic &mr, const ECP::Point &P)
33 {
34 return P.identity ? P : ECP::Point(mr.ConvertIn(P.x), mr.ConvertIn(P.y));
35 }
36
37 inline ECP::Point FromMontgomery(const ModularArithmetic &mr, const ECP::Point &P)
38 {
39 return P.identity ? P : ECP::Point(mr.ConvertOut(P.x), mr.ConvertOut(P.y));
40 }
41
42 ANONYMOUS_NAMESPACE_END
43
44 NAMESPACE_BEGIN(CryptoPP)
45
46 ECP::ECP(const ECP &ecp, bool convertToMontgomeryRepresentation)
47 {
48 if (convertToMontgomeryRepresentation && !ecp.GetField().IsMontgomeryRepresentation())
49 {
50 m_fieldPtr.reset(new MontgomeryRepresentation(ecp.GetField().GetModulus()));
51 m_a = GetField().ConvertIn(ecp.m_a);
52 m_b = GetField().ConvertIn(ecp.m_b);
53 }
54 else
55 operator=(ecp);
56 }
57
58 ECP::ECP(BufferedTransformation &bt)
59 : m_fieldPtr(new Field(bt))
60 {
61 BERSequenceDecoder seq(bt);
62 GetField().BERDecodeElement(seq, m_a);
63 GetField().BERDecodeElement(seq, m_b);
64 // skip optional seed
65 if (!seq.EndReached())
66 {
67 SecByteBlock seed;
68 unsigned int unused;
69 BERDecodeBitString(seq, seed, unused);
70 }
71 seq.MessageEnd();
72 }
73
74 void ECP::DEREncode(BufferedTransformation &bt) const
75 {
76 GetField().DEREncode(bt);
77 DERSequenceEncoder seq(bt);
78 GetField().DEREncodeElement(seq, m_a);
79 GetField().DEREncodeElement(seq, m_b);
80 seq.MessageEnd();
81 }
82
83 bool ECP::DecodePoint(ECP::Point &P, const byte *encodedPoint, size_t encodedPointLen) const
84 {
85 StringStore store(encodedPoint, encodedPointLen);
86 return DecodePoint(P, store, encodedPointLen);
87 }
88
89 bool ECP::DecodePoint(ECP::Point &P, BufferedTransformation &bt, size_t encodedPointLen) const
90 {
91 byte type;
92 if (encodedPointLen < 1 || !bt.Get(type))
93 return false;
94
95 switch (type)
96 {
97 case 0:
98 P.identity = true;
99 return true;
100 case 2:
101 case 3:
102 {
103 if (encodedPointLen != EncodedPointSize(true))
104 return false;
105
106 Integer p = FieldSize();
107
108 P.identity = false;
109 P.x.Decode(bt, GetField().MaxElementByteLength());
110 P.y = ((P.x*P.x+m_a)*P.x+m_b) % p;
111
112 if (Jacobi(P.y, p) !=1)
113 return false;
114
115 P.y = ModularSquareRoot(P.y, p);
116
117 if ((type & 1) != P.y.GetBit(0))
118 P.y = p-P.y;
119
120 return true;
121 }
122 case 4:
123 {
124 if (encodedPointLen != EncodedPointSize(false))
125 return false;
126
127 unsigned int len = GetField().MaxElementByteLength();
128 P.identity = false;
129 P.x.Decode(bt, len);
130 P.y.Decode(bt, len);
131 return true;
132 }
133 default:
134 return false;
135 }
136 }
137
138 void ECP::EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
139 {
140 if (P.identity)
141 NullStore().TransferTo(bt, EncodedPointSize(compressed));
142 else if (compressed)
143 {
144 bt.Put((byte)(2U + P.y.GetBit(0)));
145 P.x.Encode(bt, GetField().MaxElementByteLength());
146 }
147 else
148 {
149 unsigned int len = GetField().MaxElementByteLength();
150 bt.Put(4U); // uncompressed
151 P.x.Encode(bt, len);
152 P.y.Encode(bt, len);
153 }
154 }
155
156 void ECP::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
157 {
158 ArraySink sink(encodedPoint, EncodedPointSize(compressed));
159 EncodePoint(sink, P, compressed);
160 CRYPTOPP_ASSERT(sink.TotalPutLength() == EncodedPointSize(compressed));
161 }
162
163 ECP::Point ECP::BERDecodePoint(BufferedTransformation &bt) const
164 {
165 SecByteBlock str;
166 BERDecodeOctetString(bt, str);
167 Point P;
168 if (!DecodePoint(P, str, str.size()))
169 BERDecodeError();
170 return P;
171 }
172
173 void ECP::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
174 {
175 SecByteBlock str(EncodedPointSize(compressed));
176 EncodePoint(str, P, compressed);
177 DEREncodeOctetString(bt, str);
178 }
179
180 bool ECP::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const
181 {
182 Integer p = FieldSize();
183
184 bool pass = p.IsOdd();
185 pass = pass && !m_a.IsNegative() && m_a<p && !m_b.IsNegative() && m_b<p;
186
187 if (level >= 1)
188 pass = pass && ((4*m_a*m_a*m_a+27*m_b*m_b)%p).IsPositive();
189
190 if (level >= 2)
191 pass = pass && VerifyPrime(rng, p);
192
193 return pass;
194 }
195
196 bool ECP::VerifyPoint(const Point &P) const
197 {
198 const FieldElement &x = P.x, &y = P.y;
199 Integer p = FieldSize();
200 return P.identity ||
201 (!x.IsNegative() && x<p && !y.IsNegative() && y<p
202 && !(((x*x+m_a)*x+m_b-y*y)%p));
203 }
204
205 bool ECP::Equal(const Point &P, const Point &Q) const
206 {
207 if (P.identity && Q.identity)
208 return true;
209
210 if (P.identity && !Q.identity)
211 return false;
212
213 if (!P.identity && Q.identity)
214 return false;
215
216 return (GetField().Equal(P.x,Q.x) && GetField().Equal(P.y,Q.y));
217 }
218
219 const ECP::Point& ECP::Identity() const
220 {
221 #if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
222 return g_identity;
223 #elif defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
224 static const ECP::Point g_identity;
225 return g_identity;
226 #else
227 return Singleton<Point>().Ref();
228 #endif
229 }
230
231 const ECP::Point& ECP::Inverse(const Point &P) const
232 {
233 if (P.identity)
234 return P;
235 else
236 {
237 m_R.identity = false;
238 m_R.x = P.x;
239 m_R.y = GetField().Inverse(P.y);
240 return m_R;
241 }
242 }
243
244 const ECP::Point& ECP::Add(const Point &P, const Point &Q) const
245 {
246 if (P.identity) return Q;
247 if (Q.identity) return P;
248 if (GetField().Equal(P.x, Q.x))
249 return GetField().Equal(P.y, Q.y) ? Double(P) : Identity();
250
251 FieldElement t = GetField().Subtract(Q.y, P.y);
252 t = GetField().Divide(t, GetField().Subtract(Q.x, P.x));
253 FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), Q.x);
254 m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y);
255
256 m_R.x.swap(x);
257 m_R.identity = false;
258 return m_R;
259 }
260
261 const ECP::Point& ECP::Double(const Point &P) const
262 {
263 if (P.identity || P.y==GetField().Identity()) return Identity();
264
265 FieldElement t = GetField().Square(P.x);
266 t = GetField().Add(GetField().Add(GetField().Double(t), t), m_a);
267 t = GetField().Divide(t, GetField().Double(P.y));
268 FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), P.x);
269 m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y);
270
271 m_R.x.swap(x);
272 m_R.identity = false;
273 return m_R;
274 }
275
276 template <class T, class Iterator> void ParallelInvert(const AbstractRing<T> &ring, Iterator begin, Iterator end)
277 {
278 size_t n = end-begin;
279 if (n == 1)
280 *begin = ring.MultiplicativeInverse(*begin);
281 else if (n > 1)
282 {
283 std::vector<T> vec((n+1)/2);
284 unsigned int i;
285 Iterator it;
286
287 for (i=0, it=begin; i<n/2; i++, it+=2)
288 vec[i] = ring.Multiply(*it, *(it+1));
289 if (n%2 == 1)
290 vec[n/2] = *it;
291
292 ParallelInvert(ring, vec.begin(), vec.end());
293
294 for (i=0, it=begin; i<n/2; i++, it+=2)
295 {
296 if (!vec[i])
297 {
298 *it = ring.MultiplicativeInverse(*it);
299 *(it+1) = ring.MultiplicativeInverse(*(it+1));
300 }
301 else
302 {
303 std::swap(*it, *(it+1));
304 *it = ring.Multiply(*it, vec[i]);
305 *(it+1) = ring.Multiply(*(it+1), vec[i]);
306 }
307 }
308 if (n%2 == 1)
309 *it = vec[n/2];
310 }
311 }
312
313 struct ProjectivePoint
314 {
315 ProjectivePoint() {}
316 ProjectivePoint(const Integer &x, const Integer &y, const Integer &z)
317 : x(x), y(y), z(z) {}
318
319 Integer x,y,z;
320 };
321
322 class ProjectiveDoubling
323 {
324 public:
325 ProjectiveDoubling(const ModularArithmetic &m_mr, const Integer &m_a, const Integer &m_b, const ECPPoint &Q)
326 : mr(m_mr), firstDoubling(true), negated(false)
327 {
328 CRYPTOPP_UNUSED(m_b);
329 if (Q.identity)
330 {
331 sixteenY4 = P.x = P.y = mr.MultiplicativeIdentity();
332 aZ4 = P.z = mr.Identity();
333 }
334 else
335 {
336 P.x = Q.x;
337 P.y = Q.y;
338 sixteenY4 = P.z = mr.MultiplicativeIdentity();
339 aZ4 = m_a;
340 }
341 }
342
343 void Double()
344 {
345 twoY = mr.Double(P.y);
346 P.z = mr.Multiply(P.z, twoY);
347 fourY2 = mr.Square(twoY);
348 S = mr.Multiply(fourY2, P.x);
349 aZ4 = mr.Multiply(aZ4, sixteenY4);
350 M = mr.Square(P.x);
351 M = mr.Add(mr.Add(mr.Double(M), M), aZ4);
352 P.x = mr.Square(M);
353 mr.Reduce(P.x, S);
354 mr.Reduce(P.x, S);
355 mr.Reduce(S, P.x);
356 P.y = mr.Multiply(M, S);
357 sixteenY4 = mr.Square(fourY2);
358 mr.Reduce(P.y, mr.Half(sixteenY4));
359 }
360
361 const ModularArithmetic &mr;
362 ProjectivePoint P;
363 bool firstDoubling, negated;
364 Integer sixteenY4, aZ4, twoY, fourY2, S, M;
365 };
366
367 struct ZIterator
368 {
369 ZIterator() {}
370 ZIterator(std::vector<ProjectivePoint>::iterator it) : it(it) {}
371 Integer& operator*() {return it->z;}
372 int operator-(ZIterator it2) {return int(it-it2.it);}
373 ZIterator operator+(int i) {return ZIterator(it+i);}
374 ZIterator& operator+=(int i) {it+=i; return *this;}
375 std::vector<ProjectivePoint>::iterator it;
376 };
377
378 ECP::Point ECP::ScalarMultiply(const Point &P, const Integer &k) const
379 {
380 Element result;
381 if (k.BitCount() <= 5)
382 AbstractGroup<ECPPoint>::SimultaneousMultiply(&result, P, &k, 1);
383 else
384 ECP::SimultaneousMultiply(&result, P, &k, 1);
385 return result;
386 }
387
388 void ECP::SimultaneousMultiply(ECP::Point *results, const ECP::Point &P, const Integer *expBegin, unsigned int expCount) const
389 {
390 if (!GetField().IsMontgomeryRepresentation())
391 {
392 ECP ecpmr(*this, true);
393 const ModularArithmetic &mr = ecpmr.GetField();
394 ecpmr.SimultaneousMultiply(results, ToMontgomery(mr, P), expBegin, expCount);
395 for (unsigned int i=0; i<expCount; i++)
396 results[i] = FromMontgomery(mr, results[i]);
397 return;
398 }
399
400 ProjectiveDoubling rd(GetField(), m_a, m_b, P);
401 std::vector<ProjectivePoint> bases;
402 std::vector<WindowSlider> exponents;
403 exponents.reserve(expCount);
404 std::vector<std::vector<word32> > baseIndices(expCount);
405 std::vector<std::vector<bool> > negateBase(expCount);
406 std::vector<std::vector<word32> > exponentWindows(expCount);
407 unsigned int i;
408
409 for (i=0; i<expCount; i++)
410 {
411 CRYPTOPP_ASSERT(expBegin->NotNegative());
412 exponents.push_back(WindowSlider(*expBegin++, InversionIsFast(), 5));
413 exponents[i].FindNextWindow();
414 }
415
416 unsigned int expBitPosition = 0;
417 bool notDone = true;
418
419 while (notDone)
420 {
421 notDone = false;
422 bool baseAdded = false;
423 for (i=0; i<expCount; i++)
424 {
425 if (!exponents[i].finished && expBitPosition == exponents[i].windowBegin)
426 {
427 if (!baseAdded)
428 {
429 bases.push_back(rd.P);
430 baseAdded =true;
431 }
432
433 exponentWindows[i].push_back(exponents[i].expWindow);
434 baseIndices[i].push_back((word32)bases.size()-1);
435 negateBase[i].push_back(exponents[i].negateNext);
436
437 exponents[i].FindNextWindow();
438 }
439 notDone = notDone || !exponents[i].finished;
440 }
441
442 if (notDone)
443 {
444 rd.Double();
445 expBitPosition++;
446 }
447 }
448
449 // convert from projective to affine coordinates
450 ParallelInvert(GetField(), ZIterator(bases.begin()), ZIterator(bases.end()));
451 for (i=0; i<bases.size(); i++)
452 {
453 if (bases[i].z.NotZero())
454 {
455 bases[i].y = GetField().Multiply(bases[i].y, bases[i].z);
456 bases[i].z = GetField().Square(bases[i].z);
457 bases[i].x = GetField().Multiply(bases[i].x, bases[i].z);
458 bases[i].y = GetField().Multiply(bases[i].y, bases[i].z);
459 }
460 }
461
462 std::vector<BaseAndExponent<Point, Integer> > finalCascade;
463 for (i=0; i<expCount; i++)
464 {
465 finalCascade.resize(baseIndices[i].size());
466 for (unsigned int j=0; j<baseIndices[i].size(); j++)
467 {
468 ProjectivePoint &base = bases[baseIndices[i][j]];
469 if (base.z.IsZero())
470 finalCascade[j].base.identity = true;
471 else
472 {
473 finalCascade[j].base.identity = false;
474 finalCascade[j].base.x = base.x;
475 if (negateBase[i][j])
476 finalCascade[j].base.y = GetField().Inverse(base.y);
477 else
478 finalCascade[j].base.y = base.y;
479 }
480 finalCascade[j].exponent = Integer(Integer::POSITIVE, 0, exponentWindows[i][j]);
481 }
482 results[i] = GeneralCascadeMultiplication(*this, finalCascade.begin(), finalCascade.end());
483 }
484 }
485
486 ECP::Point ECP::CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const
487 {
488 if (!GetField().IsMontgomeryRepresentation())
489 {
490 ECP ecpmr(*this, true);
491 const ModularArithmetic &mr = ecpmr.GetField();
492 return FromMontgomery(mr, ecpmr.CascadeScalarMultiply(ToMontgomery(mr, P), k1, ToMontgomery(mr, Q), k2));
493 }
494 else
495 return AbstractGroup<Point>::CascadeScalarMultiply(P, k1, Q, k2);
496 }
497
498 NAMESPACE_END
499
500 #endif
ModularArithmetic::Double
const Integer & Double(const Integer &a) const
Doubles an element in the ring.
Definition: modarith.h:160
ECP::VerifyPoint
bool VerifyPoint(const Point &P) const
Verifies points on elliptic curve.
Definition: ecp.cpp:196
ModularArithmetic::Reduce
Integer & Reduce(Integer &a, const Integer &b) const
TODO.
Definition: integer.cpp:4586
ModularArithmetic::Equal
bool Equal(const Integer &a, const Integer &b) const
Compare two elements for equality.
Definition: modarith.h:119
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
Singleton
Restricts the instantiation of a class to one static object without locks.
Definition: misc.h:263
ECPPoint
Elliptical Curve Point over GF(p), where p is prime.
Definition: ecpoint.h:20
AbstractGroup< ECPPoint >::Subtract
virtual const Element & Subtract(const Element &a, const Element &b) const
Subtracts elements in the group.
Definition: algebra.cpp:20
AbstractRing::Multiply
virtual const Element & Multiply(const Element &a, const Element &b) const =0
Multiplies elements in the group.
ecp.h
Classes for Elliptic Curves over prime fields.
ECP
Elliptic Curve over GF(p), where p is prime.
Definition: ecp.h:26
ModularArithmetic::ConvertOut
virtual Integer ConvertOut(const Integer &a) const
Reduces an element in the congruence class.
Definition: modarith.h:107
ProjectivePoint
Definition: ecp.cpp:313
ModularArithmetic::Inverse
const Integer & Inverse(const Integer &a) const
Inverts the element in the ring.
Definition: integer.cpp:4603
ECP::InversionIsFast
bool InversionIsFast() const
Determine if inversion is fast.
Definition: ecp.h:63
ModularArithmetic::Subtract
const Integer & Subtract(const Integer &a, const Integer &b) const
Subtracts elements in the ring.
Definition: integer.cpp:4569
ModularArithmetic::MaxElementByteLength
unsigned int MaxElementByteLength() const
Provides the maximum byte size of an element in the ring.
Definition: modarith.h:232
Square
Square block cipher.
Definition: square.h:24
Integer::IsNegative
bool IsNegative() const
Determines if the Integer is negative.
Definition: integer.h:336
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
ECP::DecodePoint
bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const
Decodes an elliptic curve point.
Definition: ecp.cpp:89
ModularSquareRoot
Integer ModularSquareRoot(const Integer &a, const Integer &p)
Extract a modular square root.
Definition: nbtheory.cpp:572
SecByteBlock
SecBlock<byte> typedef.
Definition: secblock.h:1058
BERSequenceDecoder
BER Sequence Decoder.
Definition: asn.h:309
BufferedTransformation
Interface for buffered transformations.
Definition: cryptlib.h:1598
Integer::NotNegative
bool NotNegative() const
Determines if the Integer is non-negative.
Definition: integer.h:339
AbstractGroup::CascadeScalarMultiply
virtual Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
TODO.
Definition: algebra.cpp:97
ModularArithmetic::Add
const Integer & Add(const Integer &a, const Integer &b) const
Adds elements in the ring.
Definition: integer.cpp:4529
AbstractRing
Abstract ring.
Definition: algebra.h:118
ModularArithmetic::Identity
const Integer & Identity() const
Provides the Identity element.
Definition: modarith.h:124
ECP::Identity
const Point & Identity() const
Provides the Identity element.
Definition: ecp.cpp:219
ModularArithmetic::DEREncodeElement
void DEREncodeElement(BufferedTransformation &out, const Element &a) const
Encodes element in DER format.
Definition: integer.cpp:4508
ECP::CascadeScalarMultiply
Point CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const
TODO.
Definition: ecp.cpp:486
ECP::Inverse
const Point & Inverse(const Point &P) const
Inverts the element in the group.
Definition: ecp.cpp:231
ArraySink
Copy input to a memory buffer.
Definition: filters.h:1136
ModularArithmetic::BERDecodeElement
void BERDecodeElement(BufferedTransformation &in, Element &a) const
Decodes element in DER format.
Definition: integer.cpp:4513
NullStore
Empty store.
Definition: filters.h:1257
ZIterator
Definition: ecp.cpp:367
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
ECP::ScalarMultiply
Point ScalarMultiply(const Point &P, const Integer &k) const
Performs a scalar multiplication.
Definition: ecp.cpp:378
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
ModularArithmetic::Multiply
const Integer & Multiply(const Integer &a, const Integer &b) const
Multiplies elements in the ring.
Definition: modarith.h:174
Integer::swap
void swap(Integer &a)
Swaps this Integer with another Integer.
Definition: integer.cpp:3169
ECP::Equal
bool Equal(const Point &P, const Point &Q) const
Compare two elements for equality.
Definition: ecp.cpp:205
Integer::IsZero
bool IsZero() const
Determines if the Integer is 0.
Definition: integer.h:330
VerifyPrime
bool VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level=1)
Verifies a number is probably prime.
Definition: nbtheory.cpp:247
AbstractRing::MultiplicativeInverse
virtual const Element & MultiplicativeInverse(const Element &a) const =0
Calculate the multiplicative inverse of an element in the group.
Integer
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
pch.h
Precompiled header file.
ModularArithmetic::Half
const Integer & Half(const Integer &a) const
Divides an element by 2.
Definition: integer.cpp:4518
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
AbstractGroup
Abstract group.
Definition: algebra.h:26
ModularArithmetic::ConvertIn
virtual Integer ConvertIn(const Integer &a) const
Reduces an element in the congruence class.
Definition: modarith.h:99
asn.h
Classes and functions for working with ANS.1 objects.
ECP::DEREncodePoint
void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
DER Encodes an elliptic curve point.
Definition: ecp.cpp:173
Integer::BitCount
unsigned int BitCount() const
Determines the number of bits required to represent the Integer.
Definition: integer.cpp:3345
filters.h
Implementation of BufferedTransformation&#39;s attachment interface.
nbtheory.h
Classes and functions for number theoretic operations.
DERSequenceEncoder
DER Sequence Encoder.
Definition: asn.h:319
ECP::Double
const Point & Double(const Point &P) const
Doubles an element in the group.
Definition: ecp.cpp:261
MontgomeryRepresentation
Performs modular arithmetic in Montgomery representation for increased speed.
Definition: modarith.h:274
ECP::EncodePoint
void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
Encodes an elliptic curve point.
Definition: ecp.cpp:156
ProjectiveDoubling
Definition: ecp.cpp:322
ECP::ECP
ECP()
Construct an ECP.
Definition: ecp.h:36
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.
ECP::EncodedPointSize
unsigned int EncodedPointSize(bool compressed=false) const
Determines encoded point size.
Definition: ecp.h:78
BERDecodeBitString
size_t BERDecodeBitString(BufferedTransformation &bt, SecByteBlock &str, unsigned int &unusedBits)
DER decode bit string.
Definition: asn.cpp:191
WindowSlider
Definition: algebra.cpp:206
BufferedTransformation::Get
virtual size_t Get(byte &outByte)
Retrieve a 8-bit byte.
Definition: cryptlib.cpp:527
modarith.h
Class file for performing modular arithmetic.
CryptoPP
Crypto++ library namespace.
ECP::DEREncode
void DEREncode(BufferedTransformation &bt) const
Encode the fields fieldID and curve of the sequence ECParameters.
Definition: ecp.cpp:74
ModularArithmetic::MultiplicativeIdentity
const Integer & MultiplicativeIdentity() const
Retrieves the multiplicative identity.
Definition: modarith.h:166
ECP::BERDecodePoint
Point BERDecodePoint(BufferedTransformation &bt) const
BER Decodes an elliptic curve point.
Definition: ecp.cpp:163
ECP::SimultaneousMultiply
void SimultaneousMultiply(Point *results, const Point &base, const Integer *exponents, unsigned int exponentsCount) const
Multiplies a base to multiple exponents in a group.
Definition: ecp.cpp:388
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
ModularArithmetic::DEREncode
void DEREncode(BufferedTransformation &bt) const
Encodes in DER format.
Definition: integer.cpp:4500
ECP::Add
const Point & Add(const Point &P, const Point &Q) const
Adds elements in the group.
Definition: ecp.cpp:244
Integer::POSITIVE
the value is positive or 0
Definition: integer.h:75
Integer::IsOdd
bool IsOdd() const
Determines if the Integer is odd parity.
Definition: integer.h:351