Crypto++
8.2
Free C++ class library of cryptographic schemes
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5 #ifndef CRYPTOPP_IMPORTS
13 #include "algebra.cpp"
15 ANONYMOUS_NAMESPACE_BEGIN
18 using CryptoPP::ModularArithmetic;
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")
26 #pragma warning(default: 4075)
27 #elif defined(HAVE_XLC_INIT_PRIORITY)
42 ANONYMOUS_NAMESPACE_END
46 ECP::
ECP(const
ECP &ecp,
bool convertToMontgomeryRepresentation)
48 if (convertToMontgomeryRepresentation && !ecp.GetField().IsMontgomeryRepresentation())
51 m_a = GetField().ConvertIn(ecp.m_a);
52 m_b = GetField().ConvertIn(ecp.m_b);
59 : m_fieldPtr(new
Field(bt))
65 if (!seq.EndReached())
92 if (encodedPointLen < 1 || !bt.
Get(type))
109 P.x.Decode(bt, GetField().MaxElementByteLength());
110 P.y = ((P.x*P.x+m_a)*P.x+m_b) % p;
117 if ((type & 1) != P.y.GetBit(0))
144 bt.
Put((
byte)(2U + P.y.GetBit(0)));
145 P.x.Encode(bt, GetField().MaxElementByteLength());
184 bool pass = p.
IsOdd();
188 pass = pass && ((4*m_a*m_a*m_a+27*m_b*m_b)%p).IsPositive();
201 (!x.IsNegative() && x<p && !y.
IsNegative() && y<p
202 && !(((x*x+m_a)*x+m_b-y*y)%p));
207 if (P.identity && Q.identity)
210 if (P.identity && !Q.identity)
213 if (!P.identity && Q.identity)
216 return (GetField().
Equal(P.x,Q.x) && GetField().
Equal(P.y,Q.y));
221 #if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
223 #elif defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
237 m_R.identity =
false;
239 m_R.y = GetField().
Inverse(P.y);
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();
254 m_R.y = GetField().
Subtract(GetField().Multiply(t, GetField().
Subtract(P.x, x)), P.y);
257 m_R.identity =
false;
263 if (P.identity || P.y==GetField().Identity())
return Identity();
266 t = GetField().
Add(GetField().
Add(GetField().
Double(t), t), m_a);
269 m_R.y = GetField().
Subtract(GetField().Multiply(t, GetField().
Subtract(P.x, x)), P.y);
272 m_R.identity =
false;
276 template <
class T,
class Iterator>
void ParallelInvert(
const AbstractRing<T> &ring, Iterator begin, Iterator end)
278 size_t n = end-begin;
283 std::vector<T> vec((n+1)/2);
287 for (i=0, it=begin; i<n/2; i++, it+=2)
288 vec[i] = ring.
Multiply(*it, *(it+1));
292 ParallelInvert(ring, vec.begin(), vec.end());
294 for (i=0, it=begin; i<n/2; i++, it+=2)
303 std::swap(*it, *(it+1));
305 *(it+1) = ring.
Multiply(*(it+1), vec[i]);
317 : x(x), y(y), z(z) {}
326 : mr(m_mr), firstDoubling(
true), negated(
false)
328 CRYPTOPP_UNUSED(m_b);
357 sixteenY4 = mr.
Square(fourY2);
363 bool firstDoubling, negated;
364 Integer sixteenY4, aZ4, twoY, fourY2, S, M;
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);}
374 ZIterator& operator+=(
int i) {it+=i;
return *
this;}
375 std::vector<ProjectivePoint>::iterator it;
390 if (!GetField().IsMontgomeryRepresentation())
392 ECP ecpmr(*
this,
true);
395 for (
unsigned int i=0; i<expCount; i++)
396 results[i] = FromMontgomery(mr, results[i]);
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);
409 for (i=0; i<expCount; i++)
412 exponents.push_back(
WindowSlider(*expBegin++, InversionIsFast(), 5));
413 exponents[i].FindNextWindow();
416 unsigned int expBitPosition = 0;
422 bool baseAdded =
false;
423 for (i=0; i<expCount; i++)
425 if (!exponents[i].finished && expBitPosition == exponents[i].windowBegin)
429 bases.push_back(rd.P);
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);
437 exponents[i].FindNextWindow();
439 notDone = notDone || !exponents[i].finished;
451 for (i=0; i<bases.size(); i++)
453 if (bases[i].z.NotZero())
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);
462 std::vector<BaseAndExponent<Point, Integer> > finalCascade;
463 for (i=0; i<expCount; i++)
465 finalCascade.resize(baseIndices[i].size());
466 for (
unsigned int j=0; j<baseIndices[i].size(); j++)
470 finalCascade[j].base.identity =
true;
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);
478 finalCascade[j].base.y = base.y;
482 results[i] = GeneralCascadeMultiplication(*
this, finalCascade.begin(), finalCascade.end());
488 if (!GetField().IsMontgomeryRepresentation())
490 ECP ecpmr(*
this,
true);
492 return FromMontgomery(mr, ecpmr.
CascadeScalarMultiply(ToMontgomery(mr, P), k1, ToMontgomery(mr, Q), k2));
size_t BERDecodeOctetString(BufferedTransformation &bt, SecByteBlock &str)
BER decode octet string.
void BERDecodeElement(BufferedTransformation &in, Element &a) const
Decodes element in DER format.
const T & Ref(...) const
Return a reference to the inner Singleton object.
const Integer & Subtract(const Integer &a, const Integer &b) const
Subtracts elements in the ring.
Classes for Elliptic Curves over prime fields.
void DEREncode(BufferedTransformation &bt) const
Encode the fields fieldID and curve of the sequence ECParameters.
Point BERDecodePoint(BufferedTransformation &bt) const
BER Decodes an elliptic curve point.
Classes and functions for number theoretic operations.
virtual const Element & Multiply(const Element &a, const Element &b) const =0
Multiplies elements in the group.
void DEREncode(BufferedTransformation &bt) const
Encodes in DER format.
Elliptic Curve over GF(p), where p is prime.
const Integer & Inverse(const Integer &a) const
Inverts the element in the ring.
const Point & Double(const Point &P) const
Doubles an element in the group.
String-based implementation of Store interface.
@ POSITIVE
the value is positive or 0
lword TotalPutLength()
Provides the number of bytes written to the Sink.
Point CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const
TODO.
Ring of congruence classes modulo n.
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
bool IsZero() const
Determines if the Integer is 0.
virtual Integer ConvertOut(const Integer &a) const
Reduces an element in the congruence class.
Restricts the instantiation of a class to one static object without locks.
Class file for performing modular arithmetic.
const Integer & Multiply(const Integer &a, const Integer &b) const
Multiplies elements in the ring.
unsigned int MaxElementByteLength() const
Provides the maximum byte size of an element in the ring.
virtual const Element & Subtract(const Element &a, const Element &b) const
Subtracts elements in the group.
Implementation of BufferedTransformation's attachment interface.
Integer ModularSquareRoot(const Integer &a, const Integer &p)
Extract a modular square root.
const Integer & Square(const Integer &a) const
Square an element in the ring.
Interface for random number generators.
unsigned int EncodedPointSize(bool compressed=false) const
Determines encoded point size.
void BERDecodeError()
Raises a BERDecodeErr.
size_t BERDecodeBitString(BufferedTransformation &bt, SecByteBlock &str, unsigned int &unusedBits)
DER decode bit string.
int Jacobi(const Integer &a, const Integer &b)
Calculate the Jacobi symbol.
void SimultaneousMultiply(Point *results, const Point &base, const Integer *exponents, unsigned int exponentsCount) const
Multiplies a base to multiple exponents in a group.
const Integer & Identity() const
Provides the Identity element.
const Point & Add(const Point &P, const Point &Q) const
Adds elements in the group.
void DEREncodeElement(BufferedTransformation &out, const Element &a) const
Encodes element in DER format.
Copy input to a memory buffer.
virtual Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
TODO.
void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
DER Encodes an elliptic curve point.
bool IsOdd() const
Determines if the Integer is odd parity.
virtual const Element & MultiplicativeInverse(const Element &a) const =0
Calculate the multiplicative inverse of an element in the group.
bool VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level=1)
Verifies a number is probably prime.
Classes and functions for working with ANS.1 objects.
bool VerifyPoint(const Point &P) const
Verifies points on elliptic curve.
Elliptical Curve Point over GF(p), where p is prime.
bool Equal(const Point &P, const Point &Q) const
Compare two elements for equality.
void swap(Integer &a)
Swaps this Integer with another Integer.
size_t DEREncodeOctetString(BufferedTransformation &bt, const byte *str, size_t strLen)
DER encode octet string.
bool NotNegative() const
Determines if the Integer is non-negative.
unsigned int BitCount() const
Determines the number of bits required to represent the Integer.
bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const
Decodes an elliptic curve point.
size_type size() const
Provides the count of elements in the SecBlock.
const Integer & Half(const Integer &a) const
Divides an element by 2.
virtual Integer ConvertIn(const Integer &a) const
Reduces an element in the congruence class.
const Integer & MultiplicativeIdentity() const
Retrieves the multiplicative identity.
Crypto++ library namespace.
virtual void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
Multiplies a base to multiple exponents in a group.
bool IsNegative() const
Determines if the Integer is negative.
const Integer & Double(const Integer &a) const
Doubles an element in the ring.
Integer & Reduce(Integer &a, const Integer &b) const
TODO.
Performs modular arithmetic in Montgomery representation for increased speed.
bool Equal(const Integer &a, const Integer &b) const
Compare two elements for equality.
const Integer & Divide(const Integer &a, const Integer &b) const
Divides elements in the ring.
Point ScalarMultiply(const Point &P, const Integer &k) const
Performs a scalar multiplication.
const Point & Inverse(const Point &P) const
Inverts the element in the group.
void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
Encodes an elliptic curve point.
Multiple precision integer with arithmetic operations.
Multiple precision integer with arithmetic operations.
const Integer & Add(const Integer &a, const Integer &b) const
Adds elements in the ring.