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Diffstat (limited to 'CryptoPP/ecp.cpp')
| -rw-r--r-- | CryptoPP/ecp.cpp | 473 |
1 files changed, 0 insertions, 473 deletions
diff --git a/CryptoPP/ecp.cpp b/CryptoPP/ecp.cpp deleted file mode 100644 index 55a7cc15b..000000000 --- a/CryptoPP/ecp.cpp +++ /dev/null @@ -1,473 +0,0 @@ -// ecp.cpp - written and placed in the public domain by Wei Dai - -#include "pch.h" - -#ifndef CRYPTOPP_IMPORTS - -#include "ecp.h" -#include "asn.h" -#include "nbtheory.h" - -#include "algebra.cpp" - -NAMESPACE_BEGIN(CryptoPP) - -ANONYMOUS_NAMESPACE_BEGIN -static inline ECP::Point ToMontgomery(const ModularArithmetic &mr, const ECP::Point &P) -{ - return P.identity ? P : ECP::Point(mr.ConvertIn(P.x), mr.ConvertIn(P.y)); -} - -static inline ECP::Point FromMontgomery(const ModularArithmetic &mr, const ECP::Point &P) -{ - return P.identity ? P : ECP::Point(mr.ConvertOut(P.x), mr.ConvertOut(P.y)); -} -NAMESPACE_END - -ECP::ECP(const ECP &ecp, bool convertToMontgomeryRepresentation) -{ - if (convertToMontgomeryRepresentation && !ecp.GetField().IsMontgomeryRepresentation()) - { - m_fieldPtr.reset(new MontgomeryRepresentation(ecp.GetField().GetModulus())); - m_a = GetField().ConvertIn(ecp.m_a); - m_b = GetField().ConvertIn(ecp.m_b); - } - else - operator=(ecp); -} - -ECP::ECP(BufferedTransformation &bt) - : m_fieldPtr(new Field(bt)) -{ - BERSequenceDecoder seq(bt); - GetField().BERDecodeElement(seq, m_a); - GetField().BERDecodeElement(seq, m_b); - // skip optional seed - if (!seq.EndReached()) - { - SecByteBlock seed; - unsigned int unused; - BERDecodeBitString(seq, seed, unused); - } - seq.MessageEnd(); -} - -void ECP::DEREncode(BufferedTransformation &bt) const -{ - GetField().DEREncode(bt); - DERSequenceEncoder seq(bt); - GetField().DEREncodeElement(seq, m_a); - GetField().DEREncodeElement(seq, m_b); - seq.MessageEnd(); -} - -bool ECP::DecodePoint(ECP::Point &P, const byte *encodedPoint, size_t encodedPointLen) const -{ - StringStore store(encodedPoint, encodedPointLen); - return DecodePoint(P, store, encodedPointLen); -} - -bool ECP::DecodePoint(ECP::Point &P, BufferedTransformation &bt, size_t encodedPointLen) const -{ - byte type; - if (encodedPointLen < 1 || !bt.Get(type)) - return false; - - switch (type) - { - case 0: - P.identity = true; - return true; - case 2: - case 3: - { - if (encodedPointLen != EncodedPointSize(true)) - return false; - - Integer p = FieldSize(); - - P.identity = false; - P.x.Decode(bt, GetField().MaxElementByteLength()); - P.y = ((P.x*P.x+m_a)*P.x+m_b) % p; - - if (Jacobi(P.y, p) !=1) - return false; - - P.y = ModularSquareRoot(P.y, p); - - if ((type & 1) != P.y.GetBit(0)) - P.y = p-P.y; - - return true; - } - case 4: - { - if (encodedPointLen != EncodedPointSize(false)) - return false; - - unsigned int len = GetField().MaxElementByteLength(); - P.identity = false; - P.x.Decode(bt, len); - P.y.Decode(bt, len); - return true; - } - default: - return false; - } -} - -void ECP::EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const -{ - if (P.identity) - NullStore().TransferTo(bt, EncodedPointSize(compressed)); - else if (compressed) - { - bt.Put(2 + P.y.GetBit(0)); - P.x.Encode(bt, GetField().MaxElementByteLength()); - } - else - { - unsigned int len = GetField().MaxElementByteLength(); - bt.Put(4); // uncompressed - P.x.Encode(bt, len); - P.y.Encode(bt, len); - } -} - -void ECP::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const -{ - ArraySink sink(encodedPoint, EncodedPointSize(compressed)); - EncodePoint(sink, P, compressed); - assert(sink.TotalPutLength() == EncodedPointSize(compressed)); -} - -ECP::Point ECP::BERDecodePoint(BufferedTransformation &bt) const -{ - SecByteBlock str; - BERDecodeOctetString(bt, str); - Point P; - if (!DecodePoint(P, str, str.size())) - BERDecodeError(); - return P; -} - -void ECP::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const -{ - SecByteBlock str(EncodedPointSize(compressed)); - EncodePoint(str, P, compressed); - DEREncodeOctetString(bt, str); -} - -bool ECP::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const -{ - Integer p = FieldSize(); - - bool pass = p.IsOdd(); - pass = pass && !m_a.IsNegative() && m_a<p && !m_b.IsNegative() && m_b<p; - - if (level >= 1) - pass = pass && ((4*m_a*m_a*m_a+27*m_b*m_b)%p).IsPositive(); - - if (level >= 2) - pass = pass && VerifyPrime(rng, p); - - return pass; -} - -bool ECP::VerifyPoint(const Point &P) const -{ - const FieldElement &x = P.x, &y = P.y; - Integer p = FieldSize(); - return P.identity || - (!x.IsNegative() && x<p && !y.IsNegative() && y<p - && !(((x*x+m_a)*x+m_b-y*y)%p)); -} - -bool ECP::Equal(const Point &P, const Point &Q) const -{ - if (P.identity && Q.identity) - return true; - - if (P.identity && !Q.identity) - return false; - - if (!P.identity && Q.identity) - return false; - - return (GetField().Equal(P.x,Q.x) && GetField().Equal(P.y,Q.y)); -} - -const ECP::Point& ECP::Identity() const -{ - return Singleton<Point>().Ref(); -} - -const ECP::Point& ECP::Inverse(const Point &P) const -{ - if (P.identity) - return P; - else - { - m_R.identity = false; - m_R.x = P.x; - m_R.y = GetField().Inverse(P.y); - return m_R; - } -} - -const ECP::Point& ECP::Add(const Point &P, const Point &Q) const -{ - if (P.identity) return Q; - if (Q.identity) return P; - if (GetField().Equal(P.x, Q.x)) - return GetField().Equal(P.y, Q.y) ? Double(P) : Identity(); - - FieldElement t = GetField().Subtract(Q.y, P.y); - t = GetField().Divide(t, GetField().Subtract(Q.x, P.x)); - FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), Q.x); - m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y); - - m_R.x.swap(x); - m_R.identity = false; - return m_R; -} - -const ECP::Point& ECP::Double(const Point &P) const -{ - if (P.identity || P.y==GetField().Identity()) return Identity(); - - FieldElement t = GetField().Square(P.x); - t = GetField().Add(GetField().Add(GetField().Double(t), t), m_a); - t = GetField().Divide(t, GetField().Double(P.y)); - FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), P.x); - m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y); - - m_R.x.swap(x); - m_R.identity = false; - return m_R; -} - -template <class T, class Iterator> void ParallelInvert(const AbstractRing<T> &ring, Iterator begin, Iterator end) -{ - size_t n = end-begin; - if (n == 1) - *begin = ring.MultiplicativeInverse(*begin); - else if (n > 1) - { - std::vector<T> vec((n+1)/2); - unsigned int i; - Iterator it; - - for (i=0, it=begin; i<n/2; i++, it+=2) - vec[i] = ring.Multiply(*it, *(it+1)); - if (n%2 == 1) - vec[n/2] = *it; - - ParallelInvert(ring, vec.begin(), vec.end()); - - for (i=0, it=begin; i<n/2; i++, it+=2) - { - if (!vec[i]) - { - *it = ring.MultiplicativeInverse(*it); - *(it+1) = ring.MultiplicativeInverse(*(it+1)); - } - else - { - std::swap(*it, *(it+1)); - *it = ring.Multiply(*it, vec[i]); - *(it+1) = ring.Multiply(*(it+1), vec[i]); - } - } - if (n%2 == 1) - *it = vec[n/2]; - } -} - -struct ProjectivePoint -{ - ProjectivePoint() {} - ProjectivePoint(const Integer &x, const Integer &y, const Integer &z) - : x(x), y(y), z(z) {} - - Integer x,y,z; -}; - -class ProjectiveDoubling -{ -public: - ProjectiveDoubling(const ModularArithmetic &mr, const Integer &m_a, const Integer &m_b, const ECPPoint &Q) - : mr(mr), firstDoubling(true), negated(false) - { - if (Q.identity) - { - sixteenY4 = P.x = P.y = mr.MultiplicativeIdentity(); - aZ4 = P.z = mr.Identity(); - } - else - { - P.x = Q.x; - P.y = Q.y; - sixteenY4 = P.z = mr.MultiplicativeIdentity(); - aZ4 = m_a; - } - } - - void Double() - { - twoY = mr.Double(P.y); - P.z = mr.Multiply(P.z, twoY); - fourY2 = mr.Square(twoY); - S = mr.Multiply(fourY2, P.x); - aZ4 = mr.Multiply(aZ4, sixteenY4); - M = mr.Square(P.x); - M = mr.Add(mr.Add(mr.Double(M), M), aZ4); - P.x = mr.Square(M); - mr.Reduce(P.x, S); - mr.Reduce(P.x, S); - mr.Reduce(S, P.x); - P.y = mr.Multiply(M, S); - sixteenY4 = mr.Square(fourY2); - mr.Reduce(P.y, mr.Half(sixteenY4)); - } - - const ModularArithmetic &mr; - ProjectivePoint P; - bool firstDoubling, negated; - Integer sixteenY4, aZ4, twoY, fourY2, S, M; -}; - -struct ZIterator -{ - ZIterator() {} - ZIterator(std::vector<ProjectivePoint>::iterator it) : it(it) {} - Integer& operator*() {return it->z;} - int operator-(ZIterator it2) {return int(it-it2.it);} - ZIterator operator+(int i) {return ZIterator(it+i);} - ZIterator& operator+=(int i) {it+=i; return *this;} - std::vector<ProjectivePoint>::iterator it; -}; - -ECP::Point ECP::ScalarMultiply(const Point &P, const Integer &k) const -{ - Element result; - if (k.BitCount() <= 5) - AbstractGroup<ECPPoint>::SimultaneousMultiply(&result, P, &k, 1); - else - ECP::SimultaneousMultiply(&result, P, &k, 1); - return result; -} - -void ECP::SimultaneousMultiply(ECP::Point *results, const ECP::Point &P, const Integer *expBegin, unsigned int expCount) const -{ - if (!GetField().IsMontgomeryRepresentation()) - { - ECP ecpmr(*this, true); - const ModularArithmetic &mr = ecpmr.GetField(); - ecpmr.SimultaneousMultiply(results, ToMontgomery(mr, P), expBegin, expCount); - for (unsigned int i=0; i<expCount; i++) - results[i] = FromMontgomery(mr, results[i]); - return; - } - - ProjectiveDoubling rd(GetField(), m_a, m_b, P); - std::vector<ProjectivePoint> bases; - std::vector<WindowSlider> exponents; - exponents.reserve(expCount); - std::vector<std::vector<word32> > baseIndices(expCount); - std::vector<std::vector<bool> > negateBase(expCount); - std::vector<std::vector<word32> > exponentWindows(expCount); - unsigned int i; - - for (i=0; i<expCount; i++) - { - assert(expBegin->NotNegative()); - exponents.push_back(WindowSlider(*expBegin++, InversionIsFast(), 5)); - exponents[i].FindNextWindow(); - } - - unsigned int expBitPosition = 0; - bool notDone = true; - - while (notDone) - { - notDone = false; - bool baseAdded = false; - for (i=0; i<expCount; i++) - { - if (!exponents[i].finished && expBitPosition == exponents[i].windowBegin) - { - if (!baseAdded) - { - bases.push_back(rd.P); - baseAdded =true; - } - - exponentWindows[i].push_back(exponents[i].expWindow); - baseIndices[i].push_back((word32)bases.size()-1); - negateBase[i].push_back(exponents[i].negateNext); - - exponents[i].FindNextWindow(); - } - notDone = notDone || !exponents[i].finished; - } - - if (notDone) - { - rd.Double(); - expBitPosition++; - } - } - - // convert from projective to affine coordinates - ParallelInvert(GetField(), ZIterator(bases.begin()), ZIterator(bases.end())); - for (i=0; i<bases.size(); i++) - { - if (bases[i].z.NotZero()) - { - bases[i].y = GetField().Multiply(bases[i].y, bases[i].z); - bases[i].z = GetField().Square(bases[i].z); - bases[i].x = GetField().Multiply(bases[i].x, bases[i].z); - bases[i].y = GetField().Multiply(bases[i].y, bases[i].z); - } - } - - std::vector<BaseAndExponent<Point, Integer> > finalCascade; - for (i=0; i<expCount; i++) - { - finalCascade.resize(baseIndices[i].size()); - for (unsigned int j=0; j<baseIndices[i].size(); j++) - { - ProjectivePoint &base = bases[baseIndices[i][j]]; - if (base.z.IsZero()) - finalCascade[j].base.identity = true; - else - { - finalCascade[j].base.identity = false; - finalCascade[j].base.x = base.x; - if (negateBase[i][j]) - finalCascade[j].base.y = GetField().Inverse(base.y); - else - finalCascade[j].base.y = base.y; - } - finalCascade[j].exponent = Integer(Integer::POSITIVE, 0, exponentWindows[i][j]); - } - results[i] = GeneralCascadeMultiplication(*this, finalCascade.begin(), finalCascade.end()); - } -} - -ECP::Point ECP::CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const -{ - if (!GetField().IsMontgomeryRepresentation()) - { - ECP ecpmr(*this, true); - const ModularArithmetic &mr = ecpmr.GetField(); - return FromMontgomery(mr, ecpmr.CascadeScalarMultiply(ToMontgomery(mr, P), k1, ToMontgomery(mr, Q), k2)); - } - else - return AbstractGroup<Point>::CascadeScalarMultiply(P, k1, Q, k2); -} - -NAMESPACE_END - -#endif |