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