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-rw-r--r--CryptoPP/ecp.cpp473
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diff --git a/CryptoPP/ecp.cpp b/CryptoPP/ecp.cpp
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+// 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
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