Crypto++ 8.9 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::Integer;
19 using CryptoPP::ModularArithmetic;
20
21 #if defined(HAVE_GCC_INIT_PRIORITY)
22 #define INIT_ATTRIBUTE __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 50)))
23 const ECP::Point g_identity INIT_ATTRIBUTE = ECP::Point();
24 #elif defined(HAVE_MSC_INIT_PRIORITY)
25 #pragma warning(disable: 4075)
26 #pragma init_seg(".CRT$XCU")
27 const ECP::Point g_identity;
28 #pragma warning(default: 4075)
29 #elif defined(HAVE_XLC_INIT_PRIORITY)
30 #pragma priority(290)
31 const ECP::Point g_identity;
32 #endif
33
34 inline ECP::Point ToMontgomery(const ModularArithmetic &mr, const ECP::Point &P)
35 {
36 return P.identity ? P : ECP::Point(mr.ConvertIn(P.x), mr.ConvertIn(P.y));
37 }
38
39 inline ECP::Point FromMontgomery(const ModularArithmetic &mr, const ECP::Point &P)
40 {
41 return P.identity ? P : ECP::Point(mr.ConvertOut(P.x), mr.ConvertOut(P.y));
42 }
43
44 inline Integer IdentityToInteger(bool val)
45 {
46 return val ? Integer::One() : Integer::Zero();
47 }
48
49 struct ProjectivePoint
50 {
51 ProjectivePoint() {}
52 ProjectivePoint(const Integer &x, const Integer &y, const Integer &z)
53 : x(x), y(y), z(z) {}
54
55 Integer x, y, z;
56 };
57
58 ANONYMOUS_NAMESPACE_END
59
60 NAMESPACE_BEGIN(CryptoPP)
61
62 ECP::ECP(const ECP &ecp, bool convertToMontgomeryRepresentation)
63 {
64 if (convertToMontgomeryRepresentation && !ecp.GetField().IsMontgomeryRepresentation())
65 {
66 m_fieldPtr.reset(new MontgomeryRepresentation(ecp.GetField().GetModulus()));
67 m_a = GetField().ConvertIn(ecp.m_a);
68 m_b = GetField().ConvertIn(ecp.m_b);
69 }
70 else
71 operator=(ecp);
72 }
73
74 ECP::ECP(BufferedTransformation &bt)
75 : m_fieldPtr(new Field(bt))
76 {
77 BERSequenceDecoder seq(bt);
78 GetField().BERDecodeElement(seq, m_a);
79 GetField().BERDecodeElement(seq, m_b);
80 // skip optional seed
81 if (!seq.EndReached())
82 {
83 SecByteBlock seed;
84 unsigned int unused;
85 BERDecodeBitString(seq, seed, unused);
86 }
87 seq.MessageEnd();
88 }
89
90 void ECP::DEREncode(BufferedTransformation &bt) const
91 {
92 GetField().DEREncode(bt);
93 DERSequenceEncoder seq(bt);
94 GetField().DEREncodeElement(seq, m_a);
95 GetField().DEREncodeElement(seq, m_b);
96 seq.MessageEnd();
97 }
98
99 bool ECP::DecodePoint(ECP::Point &P, const byte *encodedPoint, size_t encodedPointLen) const
100 {
101 StringStore store(encodedPoint, encodedPointLen);
102 return DecodePoint(P, store, encodedPointLen);
103 }
104
105 bool ECP::DecodePoint(ECP::Point &P, BufferedTransformation &bt, size_t encodedPointLen) const
106 {
107 byte type;
108 if (encodedPointLen < 1 || !bt.Get(type))
109 return false;
110
111 switch (type)
112 {
113 case 0:
114 P.identity = true;
115 return true;
116 case 2:
117 case 3:
118 {
119 if (encodedPointLen != EncodedPointSize(true))
120 return false;
121
122 // Check for p is prime due to GH #1249
123 const Integer p = FieldSize();
124 CRYPTOPP_ASSERT(IsPrime(p));
125 if (!IsPrime(p))
126 return false;
127
128 P.identity = false;
129 P.x.Decode(bt, GetField().MaxElementByteLength());
130 P.y = ((P.x*P.x+m_a)*P.x+m_b) % p;
131
132 if (Jacobi(P.y, p) !=1)
133 return false;
134
135 // Callers must ensure p is prime, GH #1249
136 P.y = ModularSquareRoot(P.y, p);
137
138 if ((type & 1) != P.y.GetBit(0))
139 P.y = p-P.y;
140
141 return true;
142 }
143 case 4:
144 {
145 if (encodedPointLen != EncodedPointSize(false))
146 return false;
147
148 unsigned int len = GetField().MaxElementByteLength();
149 P.identity = false;
150 P.x.Decode(bt, len);
151 P.y.Decode(bt, len);
152 return true;
153 }
154 default:
155 return false;
156 }
157 }
158
159 void ECP::EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
160 {
161 if (P.identity)
162 NullStore().TransferTo(bt, EncodedPointSize(compressed));
163 else if (compressed)
164 {
165 bt.Put((byte)(2U + P.y.GetBit(0)));
166 P.x.Encode(bt, GetField().MaxElementByteLength());
167 }
168 else
169 {
170 unsigned int len = GetField().MaxElementByteLength();
171 bt.Put(4U); // uncompressed
172 P.x.Encode(bt, len);
173 P.y.Encode(bt, len);
174 }
175 }
176
177 void ECP::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
178 {
179 ArraySink sink(encodedPoint, EncodedPointSize(compressed));
180 EncodePoint(sink, P, compressed);
181 CRYPTOPP_ASSERT(sink.TotalPutLength() == EncodedPointSize(compressed));
182 }
183
184 ECP::Point ECP::BERDecodePoint(BufferedTransformation &bt) const
185 {
186 SecByteBlock str;
187 BERDecodeOctetString(bt, str);
188 Point P;
189 if (!DecodePoint(P, str, str.size()))
190 BERDecodeError();
191 return P;
192 }
193
194 void ECP::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
195 {
196 SecByteBlock str(EncodedPointSize(compressed));
197 EncodePoint(str, P, compressed);
198 DEREncodeOctetString(bt, str);
199 }
200
201 bool ECP::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const
202 {
203 Integer p = FieldSize();
204
205 bool pass = p.IsOdd();
206 pass = pass && !m_a.IsNegative() && m_a<p && !m_b.IsNegative() && m_b<p;
207
208 if (level >= 1)
209 pass = pass && ((4*m_a*m_a*m_a+27*m_b*m_b)%p).IsPositive();
210
211 if (level >= 2)
212 pass = pass && VerifyPrime(rng, p);
213
214 return pass;
215 }
216
217 bool ECP::VerifyPoint(const Point &P) const
218 {
219 const FieldElement &x = P.x, &y = P.y;
220 Integer p = FieldSize();
221 return P.identity ||
222 (!x.IsNegative() && x<p && !y.IsNegative() && y<p
223 && !(((x*x+m_a)*x+m_b-y*y)%p));
224 }
225
226 bool ECP::Equal(const Point &P, const Point &Q) const
227 {
228 if (P.identity && Q.identity)
229 return true;
230
231 if (P.identity && !Q.identity)
232 return false;
233
234 if (!P.identity && Q.identity)
235 return false;
236
237 return (GetField().Equal(P.x,Q.x) && GetField().Equal(P.y,Q.y));
238 }
239
240 const ECP::Point& ECP::Identity() const
241 {
242 #if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
243 return g_identity;
244 #elif defined(CRYPTOPP_CXX11_STATIC_INIT)
245 static const ECP::Point g_identity;
246 return g_identity;
247 #else
248 return Singleton<Point>().Ref();
249 #endif
250 }
251
252 const ECP::Point& ECP::Inverse(const Point &P) const
253 {
254 if (P.identity)
255 return P;
256 else
257 {
258 m_R.identity = false;
259 m_R.x = P.x;
260 m_R.y = GetField().Inverse(P.y);
261 return m_R;
262 }
263 }
264
265 const ECP::Point& ECP::Add(const Point &P, const Point &Q) const
266 {
267 if (P.identity) return Q;
268 if (Q.identity) return P;
269 if (GetField().Equal(P.x, Q.x))
270 return GetField().Equal(P.y, Q.y) ? Double(P) : Identity();
271
272 FieldElement t = GetField().Subtract(Q.y, P.y);
273 t = GetField().Divide(t, GetField().Subtract(Q.x, P.x));
274 FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), Q.x);
275 m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y);
276
277 m_R.x.swap(x);
278 m_R.identity = false;
279 return m_R;
280 }
281
282 const ECP::Point& ECP::Double(const Point &P) const
283 {
284 if (P.identity || P.y==GetField().Identity()) return Identity();
285
286 FieldElement t = GetField().Square(P.x);
287 t = GetField().Add(GetField().Add(GetField().Double(t), t), m_a);
288 t = GetField().Divide(t, GetField().Double(P.y));
289 FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), P.x);
290 m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y);
291
292 m_R.x.swap(x);
293 m_R.identity = false;
294 return m_R;
295 }
296
297 template <class T, class Iterator> void ParallelInvert(const AbstractRing<T> &ring, Iterator begin, Iterator end)
298 {
299 size_t n = end-begin;
300 if (n == 1)
301 *begin = ring.MultiplicativeInverse(*begin);
302 else if (n > 1)
303 {
304 std::vector<T> vec((n+1)/2);
305 unsigned int i;
306 Iterator it;
307
308 for (i=0, it=begin; i<n/2; i++, it+=2)
309 vec[i] = ring.Multiply(*it, *(it+1));
310 if (n%2 == 1)
311 vec[n/2] = *it;
312
313 ParallelInvert(ring, vec.begin(), vec.end());
314
315 for (i=0, it=begin; i<n/2; i++, it+=2)
316 {
317 if (!vec[i])
318 {
319 *it = ring.MultiplicativeInverse(*it);
320 *(it+1) = ring.MultiplicativeInverse(*(it+1));
321 }
322 else
323 {
324 std::swap(*it, *(it+1));
325 *it = ring.Multiply(*it, vec[i]);
326 *(it+1) = ring.Multiply(*(it+1), vec[i]);
327 }
328 }
329 if (n%2 == 1)
330 *it = vec[n/2];
331 }
332 }
333
334 class ProjectiveDoubling
335 {
336 public:
337 ProjectiveDoubling(const ModularArithmetic &m_mr, const Integer &m_a, const Integer &m_b, const ECPPoint &Q)
338 : mr(m_mr)
339 {
340 CRYPTOPP_UNUSED(m_b);
341 if (Q.identity)
342 {
343 sixteenY4 = P.x = P.y = mr.MultiplicativeIdentity();
344 aZ4 = P.z = mr.Identity();
345 }
346 else
347 {
348 P.x = Q.x;
349 P.y = Q.y;
350 sixteenY4 = P.z = mr.MultiplicativeIdentity();
351 aZ4 = m_a;
352 }
353 }
354
355 void Double()
356 {
357 twoY = mr.Double(P.y);
358 P.z = mr.Multiply(P.z, twoY);
359 fourY2 = mr.Square(twoY);
360 S = mr.Multiply(fourY2, P.x);
361 aZ4 = mr.Multiply(aZ4, sixteenY4);
362 M = mr.Square(P.x);
363 M = mr.Add(mr.Add(mr.Double(M), M), aZ4);
364 P.x = mr.Square(M);
365 mr.Reduce(P.x, S);
366 mr.Reduce(P.x, S);
367 mr.Reduce(S, P.x);
368 P.y = mr.Multiply(M, S);
369 sixteenY4 = mr.Square(fourY2);
370 mr.Reduce(P.y, mr.Half(sixteenY4));
371 }
372
373 const ModularArithmetic &mr;
374 ProjectivePoint P;
375 Integer sixteenY4, aZ4, twoY, fourY2, S, M;
376 };
377
378 struct ZIterator
379 {
380 ZIterator() {}
381 ZIterator(std::vector<ProjectivePoint>::iterator it) : it(it) {}
382 Integer& operator*() {return it->z;}
383 int operator-(ZIterator it2) {return int(it-it2.it);}
384 ZIterator operator+(int i) {return ZIterator(it+i);}
385 ZIterator& operator+=(int i) {it+=i; return *this;}
386 std::vector<ProjectivePoint>::iterator it;
387 };
388
389 ECP::Point ECP::ScalarMultiply(const Point &P, const Integer &k) const
390 {
391 Element result;
392 if (k.BitCount() <= 5)
393 AbstractGroup<ECPPoint>::SimultaneousMultiply(&result, P, &k, 1);
394 else
395 ECP::SimultaneousMultiply(&result, P, &k, 1);
396 return result;
397 }
398
399 void ECP::SimultaneousMultiply(ECP::Point *results, const ECP::Point &P, const Integer *expBegin, unsigned int expCount) const
400 {
401 if (!GetField().IsMontgomeryRepresentation())
402 {
403 ECP ecpmr(*this, true);
404 const ModularArithmetic &mr = ecpmr.GetField();
405 ecpmr.SimultaneousMultiply(results, ToMontgomery(mr, P), expBegin, expCount);
406 for (unsigned int i=0; i<expCount; i++)
407 results[i] = FromMontgomery(mr, results[i]);
408 return;
409 }
410
411 ProjectiveDoubling rd(GetField(), m_a, m_b, P);
412 std::vector<ProjectivePoint> bases;
413 std::vector<WindowSlider> exponents;
414 exponents.reserve(expCount);
415 std::vector<std::vector<word32> > baseIndices(expCount);
416 std::vector<std::vector<bool> > negateBase(expCount);
417 std::vector<std::vector<word32> > exponentWindows(expCount);
418 unsigned int i;
419
420 for (i=0; i<expCount; i++)
421 {
422 CRYPTOPP_ASSERT(expBegin->NotNegative());
423 exponents.push_back(WindowSlider(*expBegin++, InversionIsFast(), 5));
424 exponents[i].FindNextWindow();
425 }
426
427 unsigned int expBitPosition = 0;
428 bool notDone = true;
429
430 while (notDone)
431 {
432 notDone = false;
433 bool baseAdded = false;
434 for (i=0; i<expCount; i++)
435 {
436 if (!exponents[i].finished && expBitPosition == exponents[i].windowBegin)
437 {
438 if (!baseAdded)
439 {
440 bases.push_back(rd.P);
441 baseAdded =true;
442 }
443
444 exponentWindows[i].push_back(exponents[i].expWindow);
445 baseIndices[i].push_back((word32)bases.size()-1);
446 negateBase[i].push_back(exponents[i].negateNext);
447
448 exponents[i].FindNextWindow();
449 }
450 notDone = notDone || !exponents[i].finished;
451 }
452
453 if (notDone)
454 {
455 rd.Double();
456 expBitPosition++;
457 }
458 }
459
460 // convert from projective to affine coordinates
461 ParallelInvert(GetField(), ZIterator(bases.begin()), ZIterator(bases.end()));
462 for (i=0; i<bases.size(); i++)
463 {
464 if (bases[i].z.NotZero())
465 {
466 bases[i].y = GetField().Multiply(bases[i].y, bases[i].z);
467 bases[i].z = GetField().Square(bases[i].z);
468 bases[i].x = GetField().Multiply(bases[i].x, bases[i].z);
469 bases[i].y = GetField().Multiply(bases[i].y, bases[i].z);
470 }
471 }
472
473 std::vector<BaseAndExponent<Point, Integer> > finalCascade;
474 for (i=0; i<expCount; i++)
475 {
476 finalCascade.resize(baseIndices[i].size());
477 for (unsigned int j=0; j<baseIndices[i].size(); j++)
478 {
479 ProjectivePoint &base = bases[baseIndices[i][j]];
480 if (base.z.IsZero())
481 finalCascade[j].base.identity = true;
482 else
483 {
484 finalCascade[j].base.identity = false;
485 finalCascade[j].base.x = base.x;
486 if (negateBase[i][j])
487 finalCascade[j].base.y = GetField().Inverse(base.y);
488 else
489 finalCascade[j].base.y = base.y;
490 }
491 finalCascade[j].exponent = Integer(Integer::POSITIVE, 0, exponentWindows[i][j]);
492 }
493 results[i] = GeneralCascadeMultiplication(*this, finalCascade.begin(), finalCascade.end());
494 }
495 }
496
497 ECP::Point ECP::CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const
498 {
499 if (!GetField().IsMontgomeryRepresentation())
500 {
501 ECP ecpmr(*this, true);
502 const ModularArithmetic &mr = ecpmr.GetField();
503 return FromMontgomery(mr, ecpmr.CascadeScalarMultiply(ToMontgomery(mr, P), k1, ToMontgomery(mr, Q), k2));
504 }
505 else
506 return AbstractGroup<Point>::CascadeScalarMultiply(P, k1, Q, k2);
507 }
508
509 NAMESPACE_END
510
511 #endif
asn.h
Classes and functions for working with ANS.1 objects.
BERDecodeBitString
CRYPTOPP_DLL size_t BERDecodeBitString(BufferedTransformation &bt, SecByteBlock &str, unsigned int &unusedBits)
DER decode bit string.
operator+
OID operator+(const OID &lhs, unsigned long rhs)
Append a value to an OID.
DEREncodeOctetString
CRYPTOPP_DLL size_t DEREncodeOctetString(BufferedTransformation &bt, const byte *str, size_t strLen)
DER encode octet string.
BERDecodeOctetString
CRYPTOPP_DLL size_t BERDecodeOctetString(BufferedTransformation &bt, SecByteBlock &str)
BER decode octet string.
BERDecodeError
void BERDecodeError()
Raises a BERDecodeErr.
Definition: asn.h:104
AbstractGroup::CascadeScalarMultiply
virtual Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
TODO.
Definition: algebra.cpp:97
AbstractGroup::SimultaneousMultiply
virtual void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
Multiplies a base to multiple exponents in a group.
Definition: algebra.cpp:256
AbstractGroup< ECPPoint >::Subtract
virtual const Element & Subtract(const Element &a, const Element &b) const
Subtracts elements in the group.
Definition: algebra.cpp:20
AbstractRing
Abstract ring.
Definition: algebra.h:119
AbstractRing::Multiply
virtual const Element & Multiply(const Element &a, const Element &b) const =0
Multiplies elements in the group.
AbstractRing::MultiplicativeInverse
virtual const Element & MultiplicativeInverse(const Element &a) const =0
Calculate the multiplicative inverse of an element in the group.
ArraySink
Copy input to a memory buffer.
Definition: filters.h:1200
BERSequenceDecoder
BER Sequence Decoder.
Definition: asn.h:526
BufferedTransformation
Interface for buffered transformations.
Definition: cryptlib.h:1657
BufferedTransformation::Get
virtual size_t Get(byte &outByte)
Retrieve a 8-bit byte.
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:1996
BufferedTransformation::Put
size_t Put(byte inByte, bool blocking=true)
Input a byte for processing.
Definition: cryptlib.h:1678
DERSequenceEncoder
DER Sequence Encoder.
Definition: asn.h:558
ECP
Elliptic Curve over GF(p), where p is prime.
Definition: ecp.h:27
ECP::InversionIsFast
bool InversionIsFast() const
Determine if inversion is fast.
Definition: ecp.h:75
ECP::Inverse
const Point & Inverse(const Point &P) const
Inverts the element in the group.
ECP::EncodePoint
void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
Encodes an elliptic curve point.
ECP::ECP
ECP()
Construct an ECP.
Definition: ecp.h:36
ECP::Equal
bool Equal(const Point &P, const Point &Q) const
Compare two points.
ECP::DEREncodePoint
void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
DER Encodes an elliptic curve point.
ECP::VerifyPoint
bool VerifyPoint(const Point &P) const
Verifies points on elliptic curve.
ECP::Identity
const Point & Identity() const
Provides the Identity element.
ECP::BERDecodePoint
Point BERDecodePoint(BufferedTransformation &bt) const
BER Decodes an elliptic curve point.
ECP::EncodedPointSize
unsigned int EncodedPointSize(bool compressed=false) const
Determines encoded point size.
Definition: ecp.h:90
ECP::DecodePoint
bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const
Decodes an elliptic curve point.
ECP::DEREncode
void DEREncode(BufferedTransformation &bt) const
DER Encode.
ECP::Add
const Point & Add(const Point &P, const Point &Q) const
Adds elements in the group.
Integer
Multiple precision integer with arithmetic operations.
Definition: integer.h:50
Integer::One
static const Integer & One()
Integer representing 1.
Integer::BitCount
unsigned int BitCount() const
Determines the number of bits required to represent the Integer.
Integer::NotNegative
bool NotNegative() const
Determines if the Integer is non-negative.
Definition: integer.h:344
Integer::swap
void swap(Integer &a)
Swaps this Integer with another Integer.
Integer::IsNegative
bool IsNegative() const
Determines if the Integer is negative.
Definition: integer.h:341
Integer::POSITIVE
@ 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:356
ModularArithmetic
Ring of congruence classes modulo n.
Definition: modarith.h:44
ModularArithmetic::Add
const Integer & Add(const Integer &a, const Integer &b) const
Adds elements in the ring.
ModularArithmetic::Multiply
const Integer & Multiply(const Integer &a, const Integer &b) const
Multiplies elements in the ring.
Definition: modarith.h:190
ModularArithmetic::Inverse
const Integer & Inverse(const Integer &a) const
Inverts the element in the ring.
ModularArithmetic::Divide
const Integer & Divide(const Integer &a, const Integer &b) const
Divides elements in the ring.
Definition: modarith.h:218
ModularArithmetic::MaxElementByteLength
unsigned int MaxElementByteLength() const
Provides the maximum byte size of an element in the ring.
Definition: modarith.h:248
ModularArithmetic::DEREncodeElement
void DEREncodeElement(BufferedTransformation &out, const Element &a) const
Encodes element in DER format.
ModularArithmetic::GetModulus
const Integer & GetModulus() const
Retrieves the modulus.
Definition: modarith.h:99
ModularArithmetic::IsMontgomeryRepresentation
virtual bool IsMontgomeryRepresentation() const
Retrieves the representation.
Definition: modarith.h:108
ModularArithmetic::Square
const Integer & Square(const Integer &a) const
Square an element in the ring.
Definition: modarith.h:197
ModularArithmetic::Equal
bool Equal(const Integer &a, const Integer &b) const
Compare two elements for equality.
Definition: modarith.h:135
ModularArithmetic::Subtract
const Integer & Subtract(const Integer &a, const Integer &b) const
Subtracts elements in the ring.
ModularArithmetic::ConvertOut
virtual Integer ConvertOut(const Integer &a) const
Reduces an element in the congruence class.
Definition: modarith.h:123
ModularArithmetic::ConvertIn
virtual Integer ConvertIn(const Integer &a) const
Reduces an element in the congruence class.
Definition: modarith.h:115
ModularArithmetic::DEREncode
void DEREncode(BufferedTransformation &bt) const
Encodes in DER format.
MontgomeryRepresentation
Performs modular arithmetic in Montgomery representation for increased speed.
Definition: modarith.h:296
NullStore
Empty store.
Definition: filters.h:1321
RandomNumberGenerator
Interface for random number generators.
Definition: cryptlib.h:1440
SecBlock::size
size_type size() const
Provides the count of elements in the SecBlock.
Definition: secblock.h:867
SecByteBlock
SecBlock<byte> typedef.
Definition: secblock.h:1226
Singleton
Restricts the instantiation of a class to one static object without locks.
Definition: misc.h:309
Singleton::Ref
const T & Ref(...) const
Return a reference to the inner Singleton object.
Definition: misc.h:329
Square
Square block cipher.
Definition: square.h:25
StringStore
String-based implementation of Store interface.
Definition: filters.h:1259
word32
unsigned int word32
32-bit unsigned datatype
Definition: config_int.h:72
ecp.h
Classes for Elliptic Curves over prime fields.
filters.h
Implementation of BufferedTransformation's attachment interface.
integer.h
Multiple precision integer with arithmetic operations.
operator-
inline ::Integer operator-(const ::Integer &a, const ::Integer &b)
Subtraction.
Definition: integer.h:772
operator*
inline ::Integer operator*(const ::Integer &a, const ::Integer &b)
Multiplication.
Definition: integer.h:775
modarith.h
Class file for performing modular arithmetic.
CryptoPP
Crypto++ library namespace.
nbtheory.h
Classes and functions for number theoretic operations.
Jacobi
CRYPTOPP_DLL int Jacobi(const Integer &a, const Integer &b)
Calculate the Jacobi symbol.
IsPrime
CRYPTOPP_DLL bool IsPrime(const Integer &p)
Verifies a number is probably prime.
ModularSquareRoot
CRYPTOPP_DLL Integer ModularSquareRoot(const Integer &a, const Integer &p)
Extract a modular square root.
VerifyPrime
CRYPTOPP_DLL bool VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level=1)
Verifies a number is probably prime.
pch.h
Precompiled header file.
swap
void swap(::SecBlock< T, A > &a, ::SecBlock< T, A > &b)
Swap two SecBlocks.
Definition: secblock.h:1289
ECPPoint
Elliptical Curve Point over GF(p), where p is prime.
Definition: ecpoint.h:21
WindowSlider
Definition: algebra.cpp:207
CRYPTOPP_ASSERT
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
Definition: trap.h:68