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955 lines
25 KiB
C++
955 lines
25 KiB
C++
// ecp.cpp - originally 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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ANONYMOUS_NAMESPACE_BEGIN
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using CryptoPP::ECP;
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using CryptoPP::Integer;
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using CryptoPP::ModularArithmetic;
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#if defined(HAVE_GCC_INIT_PRIORITY)
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#define INIT_ATTRIBUTE __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 50)))
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const ECP::Point g_identity INIT_ATTRIBUTE = ECP::Point();
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#elif defined(HAVE_MSC_INIT_PRIORITY)
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#pragma warning(disable: 4075)
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#pragma init_seg(".CRT$XCU")
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const ECP::Point g_identity;
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#pragma warning(default: 4075)
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#elif defined(HAVE_XLC_INIT_PRIORITY)
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#pragma priority(290)
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const ECP::Point g_identity;
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#endif
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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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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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inline Integer IdentityToInteger(bool val)
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{
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return val ? Integer::One() : Integer::Zero();
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}
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ANONYMOUS_NAMESPACE_END
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NAMESPACE_BEGIN(CryptoPP)
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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((byte)(2U + 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(4U); // 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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CRYPTOPP_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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#if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
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return g_identity;
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#elif defined(CRYPTOPP_CXX11_DYNAMIC_INIT)
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static const ECP::Point g_identity;
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return g_identity;
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#else
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return Singleton<Point>().Ref();
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#endif
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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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AdditionFunction add(*this);
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return (m_R = add(P, Q));
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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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AdditionFunction add(*this);
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return (m_R = add(P));
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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 &m_mr, const Integer &m_a, const Integer &m_b, const ECPPoint &Q)
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: mr(m_mr)
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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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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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CRYPTOPP_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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#define X p.x
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#define Y p.y
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#define Z p.z
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#define X1 p.x
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#define Y1 p.y
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#define Z1 p.z
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#define X2 q.x
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#define Y2 q.y
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#define Z2 q.z
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#define X3 r.x
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#define Y3 r.y
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#define Z3 r.z
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ECP::AdditionFunction::AdditionFunction(const ECP& ecp)
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: m_ecp(ecp), m_alpha(static_cast<Alpha>(0))
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{
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if (m_ecp.GetField().IsMontgomeryRepresentation())
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{
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m_alpha = A_Montgomery;
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}
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else
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{
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if (m_ecp.m_a == 0)
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{
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m_alpha = A_0;
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}
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else if (m_ecp.m_a == -3 || (m_ecp.m_a - m_ecp.GetField().GetModulus()) == -3)
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{
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m_alpha = A_3;
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}
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else
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{
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m_alpha = A_Star;
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}
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}
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}
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|
|
|
ECP::Point ECP::AdditionFunction::operator()(const Point& P) const
|
|
{
|
|
if (m_alpha == A_3)
|
|
{
|
|
const ECP::Field& field = m_ecp.GetField();
|
|
const FieldElement& b = m_ecp.m_b;
|
|
ECP::Point& R = m_ecp.m_R;
|
|
|
|
// Gyrations attempt to maintain constant-timeness
|
|
// We need either (P.x, P.y, 1) or (0, 1, 0).
|
|
const Integer x = P.x * IdentityToInteger(!P.identity);
|
|
const Integer y = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
|
|
const Integer z = 1 * IdentityToInteger(!P.identity);
|
|
|
|
ProjectivePoint p(x, y, z), r;
|
|
|
|
FieldElement t0 = field.Square(X);
|
|
FieldElement t1 = field.Square(Y);
|
|
FieldElement t2 = field.Square(Z);
|
|
FieldElement t3 = field.Multiply(X,Y);
|
|
t3 = field.Add(t3,t3);
|
|
Z3 = field.Multiply(X,Z);
|
|
Z3 = field.Add(Z3,Z3);
|
|
Y3 = field.Multiply(b,t2);
|
|
Y3 = field.Subtract(Y3,Z3);
|
|
X3 = field.Add(Y3,Y3);
|
|
Y3 = field.Add(X3,Y3);
|
|
X3 = field.Subtract(t1,Y3);
|
|
Y3 = field.Add(t1,Y3);
|
|
Y3 = field.Multiply(X3,Y3);
|
|
X3 = field.Multiply(X3,t3);
|
|
t3 = field.Add(t2,t2);
|
|
t2 = field.Add(t2,t3);
|
|
Z3 = field.Multiply(b,Z3);
|
|
Z3 = field.Subtract(Z3,t2);
|
|
Z3 = field.Subtract(Z3,t0);
|
|
t3 = field.Add(Z3,Z3);
|
|
Z3 = field.Add(Z3,t3);
|
|
t3 = field.Add(t0,t0);
|
|
t0 = field.Add(t3,t0);
|
|
t0 = field.Subtract(t0,t2);
|
|
t0 = field.Multiply(t0,Z3);
|
|
Y3 = field.Add(Y3,t0);
|
|
t0 = field.Multiply(Y,Z);
|
|
t0 = field.Add(t0,t0);
|
|
Z3 = field.Multiply(t0,Z3);
|
|
X3 = field.Subtract(X3,Z3);
|
|
Z3 = field.Multiply(t0,t1);
|
|
Z3 = field.Add(Z3,Z3);
|
|
Z3 = field.Add(Z3,Z3);
|
|
|
|
const FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
|
|
|
// More gyrations
|
|
R.x = X3*Z3.NotZero();
|
|
R.y = Y3*Z3.NotZero();
|
|
R.identity = Z3.IsZero();
|
|
|
|
return R;
|
|
}
|
|
else if (m_alpha == A_0)
|
|
{
|
|
const ECP::Field& field = m_ecp.GetField();
|
|
const FieldElement b3 = field.Multiply(m_ecp.m_b, 3);
|
|
ECP::Point& R = m_ecp.m_R;
|
|
|
|
// Gyrations attempt to maintain constant-timeness
|
|
// We need either (P.x, P.y, 1) or (0, 1, 0).
|
|
const Integer x = P.x * IdentityToInteger(!P.identity);
|
|
const Integer y = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
|
|
const Integer z = 1 * IdentityToInteger(!P.identity);
|
|
|
|
ProjectivePoint p(x, y, z), r;
|
|
|
|
FieldElement t0 = field.Square(Y);
|
|
Z3 = field.Add(t0,t0);
|
|
Z3 = field.Add(Z3,Z3);
|
|
Z3 = field.Add(Z3,Z3);
|
|
FieldElement t1 = field.Add(Y,Z);
|
|
FieldElement t2 = field.Square(Z);
|
|
t2 = field.Multiply(b3,t2);
|
|
X3 = field.Multiply(t2,Z3);
|
|
Y3 = field.Add(t0,t2);
|
|
Z3 = field.Multiply(t1,Z3);
|
|
t1 = field.Add(t2,t2);
|
|
t2 = field.Add(t1,t2);
|
|
t0 = field.Subtract(t0,t2);
|
|
Y3 = field.Multiply(t0,Y3);
|
|
Y3 = field.Add(X3,Y3);
|
|
t1 = field.Multiply(X,Y);
|
|
X3 = field.Multiply(t0,t1);
|
|
X3 = field.Add(X3,X3);
|
|
|
|
const FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
|
|
|
// More gyrations
|
|
R.x = X3*Z3.NotZero();
|
|
R.y = Y3*Z3.NotZero();
|
|
R.identity = Z3.IsZero();
|
|
|
|
return R;
|
|
}
|
|
else if (m_alpha == A_Star)
|
|
{
|
|
const ECP::Field& field = m_ecp.GetField();
|
|
const FieldElement b3 = field.Multiply(m_ecp.m_b, 3);
|
|
ECP::Point& R = m_ecp.m_R;
|
|
|
|
// Gyrations attempt to maintain constant-timeness
|
|
// We need either (P.x, P.y, 1) or (0, 1, 0).
|
|
const Integer x = P.x * IdentityToInteger(!P.identity);
|
|
const Integer y = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
|
|
const Integer z = 1 * IdentityToInteger(!P.identity);
|
|
|
|
ProjectivePoint p(x, y, z), r;
|
|
|
|
FieldElement t0 = field.Square(Y);
|
|
Z3 = field.Add(t0,t0);
|
|
Z3 = field.Add(Z3,Z3);
|
|
Z3 = field.Add(Z3,Z3);
|
|
FieldElement t1 = field.Add(Y,Z);
|
|
FieldElement t2 = field.Square(Z);
|
|
t2 = field.Multiply(b3,t2);
|
|
X3 = field.Multiply(t2,Z3);
|
|
Y3 = field.Add(t0,t2);
|
|
Z3 = field.Multiply(t1,Z3);
|
|
t1 = field.Add(t2,t2);
|
|
t2 = field.Add(t1,t2);
|
|
t0 = field.Subtract(t0,t2);
|
|
Y3 = field.Multiply(t0,Y3);
|
|
Y3 = field.Add(X3,Y3);
|
|
t1 = field.Multiply(X,Y);
|
|
X3 = field.Multiply(t0,t1);
|
|
X3 = field.Add(X3,X3);
|
|
|
|
const FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
|
|
|
// More gyrations
|
|
R.x = X3*Z3.NotZero();
|
|
R.y = Y3*Z3.NotZero();
|
|
R.identity = Z3.IsZero();
|
|
|
|
return R;
|
|
}
|
|
else // A_Montgomery
|
|
{
|
|
ECP::Point& R = m_ecp.m_R;
|
|
const ECP::Field& field = m_ecp.GetField();
|
|
const FieldElement& a = m_ecp.m_a;
|
|
|
|
// More gyrations
|
|
bool identity = (P.identity | (P.y==field.Identity()));
|
|
|
|
FieldElement t = field.Square(P.x);
|
|
t = field.Add(field.Add(field.Double(t), t), a);
|
|
t = field.Divide(t, field.Double(P.y));
|
|
FieldElement x = field.Subtract(field.Subtract(field.Square(t), P.x), P.x);
|
|
R.y = field.Subtract(field.Multiply(t, field.Subtract(P.x, x)), P.y);
|
|
R.x.swap(x);
|
|
|
|
// More gyrations
|
|
R.x *= IdentityToInteger(!identity);
|
|
R.y *= IdentityToInteger(!identity);
|
|
R.identity = identity;
|
|
|
|
return R;
|
|
}
|
|
}
|
|
|
|
ECP::Point ECP::AdditionFunction::operator()(const Point& P, const Point& Q) const
|
|
{
|
|
if (m_alpha == A_3)
|
|
{
|
|
const ECP::Field& field = m_ecp.GetField();
|
|
const FieldElement& b = m_ecp.m_b;
|
|
ECP::Point& R = m_ecp.m_R;
|
|
|
|
// Gyrations attempt to maintain constant-timeness
|
|
// We need either (P.x, P.y, 1) or (0, 1, 0).
|
|
const Integer x1 = P.x * IdentityToInteger(!P.identity);
|
|
const Integer y1 = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
|
|
const Integer z1 = 1 * IdentityToInteger(!P.identity);
|
|
|
|
const Integer x2 = Q.x * IdentityToInteger(!Q.identity);
|
|
const Integer y2 = Q.y * IdentityToInteger(!Q.identity) + 1 * IdentityToInteger(Q.identity);
|
|
const Integer z2 = 1 * IdentityToInteger(!Q.identity);
|
|
|
|
ProjectivePoint p(x1, y1, z1), q(x2, y2, z2), r;
|
|
|
|
FieldElement t0 = field.Multiply(X1,X2);
|
|
FieldElement t1 = field.Multiply(Y1,Y2);
|
|
FieldElement t2 = field.Multiply(Z1,Z2);
|
|
FieldElement t3 = field.Add(X1,Y1);
|
|
FieldElement t4 = field.Add(X2,Y2);
|
|
t3 = field.Multiply(t3,t4);
|
|
t4 = field.Add(t0,t1);
|
|
t3 = field.Subtract(t3,t4);
|
|
t4 = field.Add(Y1,Z1);
|
|
X3 = field.Add(Y2,Z2);
|
|
t4 = field.Multiply(t4,X3);
|
|
X3 = field.Add(t1,t2);
|
|
t4 = field.Subtract(t4,X3);
|
|
X3 = field.Add(X1,Z1);
|
|
Y3 = field.Add(X2,Z2);
|
|
X3 = field.Multiply(X3,Y3);
|
|
Y3 = field.Add(t0,t2);
|
|
Y3 = field.Subtract(X3,Y3);
|
|
Z3 = field.Multiply(b,t2);
|
|
X3 = field.Subtract(Y3,Z3);
|
|
Z3 = field.Add(X3,X3);
|
|
X3 = field.Add(X3,Z3);
|
|
Z3 = field.Subtract(t1,X3);
|
|
X3 = field.Add(t1,X3);
|
|
Y3 = field.Multiply(b,Y3);
|
|
t1 = field.Add(t2,t2);
|
|
t2 = field.Add(t1,t2);
|
|
Y3 = field.Subtract(Y3,t2);
|
|
Y3 = field.Subtract(Y3,t0);
|
|
t1 = field.Add(Y3,Y3);
|
|
Y3 = field.Add(t1,Y3);
|
|
t1 = field.Add(t0,t0);
|
|
t0 = field.Add(t1,t0);
|
|
t0 = field.Subtract(t0,t2);
|
|
t1 = field.Multiply(t4,Y3);
|
|
t2 = field.Multiply(t0,Y3);
|
|
Y3 = field.Multiply(X3,Z3);
|
|
Y3 = field.Add(Y3,t2);
|
|
X3 = field.Multiply(t3,X3);
|
|
X3 = field.Subtract(X3,t1);
|
|
Z3 = field.Multiply(t4,Z3);
|
|
t1 = field.Multiply(t3,t0);
|
|
Z3 = field.Add(Z3,t1);
|
|
|
|
const FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
|
|
|
// More gyrations
|
|
R.x = X3*Z3.NotZero();
|
|
R.y = Y3*Z3.NotZero();
|
|
R.identity = Z3.IsZero();
|
|
|
|
return R;
|
|
}
|
|
else if (m_alpha == A_0)
|
|
{
|
|
const ECP::Field& field = m_ecp.GetField();
|
|
const FieldElement b3 = field.Multiply(m_ecp.m_b, 3);
|
|
ECP::Point& R = m_ecp.m_R;
|
|
|
|
// Gyrations attempt to maintain constant-timeness
|
|
// We need either (P.x, P.y, 1) or (0, 1, 0).
|
|
const Integer x1 = P.x * IdentityToInteger(!P.identity);
|
|
const Integer y1 = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
|
|
const Integer z1 = 1 * IdentityToInteger(!P.identity);
|
|
|
|
const Integer x2 = Q.x * IdentityToInteger(!Q.identity);
|
|
const Integer y2 = Q.y * IdentityToInteger(!Q.identity) + 1 * IdentityToInteger(Q.identity);
|
|
const Integer z2 = 1 * IdentityToInteger(!Q.identity);
|
|
|
|
ProjectivePoint p(x1, y1, z1), q(x2, y2, z2), r;
|
|
|
|
FieldElement t0 = field.Square(Y);
|
|
Z3 = field.Add(t0,t0);
|
|
Z3 = field.Add(Z3,Z3);
|
|
Z3 = field.Add(Z3,Z3);
|
|
FieldElement t1 = field.Add(Y,Z);
|
|
FieldElement t2 = field.Square(Z);
|
|
t2 = field.Multiply(b3,t2);
|
|
X3 = field.Multiply(t2,Z3);
|
|
Y3 = field.Add(t0,t2);
|
|
Z3 = field.Multiply(t1,Z3);
|
|
t1 = field.Add(t2,t2);
|
|
t2 = field.Add(t1,t2);
|
|
t0 = field.Subtract(t0,t2);
|
|
Y3 = field.Multiply(t0,Y3);
|
|
Y3 = field.Add(X3,Y3);
|
|
t1 = field.Multiply(X,Y);
|
|
X3 = field.Multiply(t0,t1);
|
|
X3 = field.Add(X3,X3);
|
|
|
|
const FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
|
|
|
// More gyrations
|
|
R.x = X3*Z3.NotZero();
|
|
R.y = Y3*Z3.NotZero();
|
|
R.identity = Z3.IsZero();
|
|
|
|
return R;
|
|
}
|
|
else if (m_alpha == A_Star)
|
|
{
|
|
const ECP::Field& field = m_ecp.GetField();
|
|
const FieldElement &a = m_ecp.m_a;
|
|
const FieldElement b3 = field.Multiply(m_ecp.m_b, 3);
|
|
ECP::Point& R = m_ecp.m_R;
|
|
|
|
// Gyrations attempt to maintain constant-timeness
|
|
// We need either (P.x, P.y, 1) or (0, 1, 0).
|
|
const Integer x1 = P.x * IdentityToInteger(!P.identity);
|
|
const Integer y1 = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
|
|
const Integer z1 = 1 * IdentityToInteger(!P.identity);
|
|
|
|
const Integer x2 = Q.x * IdentityToInteger(!Q.identity);
|
|
const Integer y2 = Q.y * IdentityToInteger(!Q.identity) + 1 * IdentityToInteger(Q.identity);
|
|
const Integer z2 = 1 * IdentityToInteger(!Q.identity);
|
|
|
|
ProjectivePoint p(x1, y1, z1), q(x2, y2, z2), r;
|
|
|
|
FieldElement t0 = field.Multiply(X1,X2);
|
|
FieldElement t1 = field.Multiply(Y1,Y2);
|
|
FieldElement t2 = field.Multiply(Z1,Z2);
|
|
FieldElement t3 = field.Add(X1,Y1);
|
|
FieldElement t4 = field.Add(X2,Y2);
|
|
t3 = field.Multiply(t3,t4);
|
|
t4 = field.Add(t0,t1);
|
|
t3 = field.Subtract(t3,t4);
|
|
t4 = field.Add(X1,Z1);
|
|
FieldElement t5 = field.Add(X2,Z2);
|
|
t4 = field.Multiply(t4,t5);
|
|
t5 = field.Add(t0,t2);
|
|
t4 = field.Subtract(t4,t5);
|
|
t5 = field.Add(Y1,Z1);
|
|
X3 = field.Add(Y2,Z2);
|
|
t5 = field.Multiply(t5,X3);
|
|
X3 = field.Add(t1,t2);
|
|
t5 = field.Subtract(t5,X3);
|
|
Z3 = field.Multiply(a,t4);
|
|
X3 = field.Multiply(b3,t2);
|
|
Z3 = field.Add(X3,Z3);
|
|
X3 = field.Subtract(t1,Z3);
|
|
Z3 = field.Add(t1,Z3);
|
|
Y3 = field.Multiply(X3,Z3);
|
|
t1 = field.Add(t0,t0);
|
|
t1 = field.Add(t1,t0);
|
|
t2 = field.Multiply(a,t2);
|
|
t4 = field.Multiply(b3,t4);
|
|
t1 = field.Add(t1,t2);
|
|
t2 = field.Subtract(t0,t2);
|
|
t2 = field.Multiply(a,t2);
|
|
t4 = field.Add(t4,t2);
|
|
t0 = field.Multiply(t1,t4);
|
|
Y3 = field.Add(Y3,t0);
|
|
t0 = field.Multiply(t5,t4);
|
|
X3 = field.Multiply(t3,X3);
|
|
X3 = field.Subtract(X3,t0);
|
|
t0 = field.Multiply(t3,t1);
|
|
Z3 = field.Multiply(t5,Z3);
|
|
Z3 = field.Add(Z3,t0);
|
|
|
|
const FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
|
|
|
// More gyrations
|
|
R.x = X3*Z3.NotZero();
|
|
R.y = Y3*Z3.NotZero();
|
|
R.identity = Z3.IsZero();
|
|
|
|
return R;
|
|
}
|
|
else // A_Montgomery
|
|
{
|
|
const ECP::Field& field = m_ecp.GetField();
|
|
const FieldElement& a = m_ecp.m_a;
|
|
ECP::Point& R = m_ecp.m_R, S = m_ecp.m_R;
|
|
|
|
// More gyrations
|
|
bool return_Q = P.identity;
|
|
bool return_P = Q.identity;
|
|
bool double_P = field.Equal(P.x, Q.x) && field.Equal(P.y, Q.y);
|
|
bool identity = field.Equal(P.x, Q.x) && !field.Equal(P.y, Q.y);
|
|
|
|
// This code taken from Double(P)
|
|
identity |= (double_P * (P.identity | (P.y==field.Identity())));
|
|
|
|
if (double_P)
|
|
{
|
|
// This code taken from Double(P)
|
|
FieldElement t = field.Square(P.x);
|
|
t = field.Add(field.Add(field.Double(t), t), a);
|
|
t = field.Divide(t, field.Double(P.y));
|
|
FieldElement x = field.Subtract(field.Subtract(field.Square(t), P.x), P.x);
|
|
R.y = field.Subtract(field.Multiply(t, field.Subtract(P.x, x)), P.y);
|
|
R.x.swap(x);
|
|
}
|
|
else
|
|
{
|
|
// Original Double (P,Q) code
|
|
FieldElement t = field.Subtract(Q.y, P.y);
|
|
t = field.Divide(t, field.Subtract(Q.x, P.x));
|
|
FieldElement x = field.Subtract(field.Subtract(field.Square(t), P.x), Q.x);
|
|
R.y = field.Subtract(field.Multiply(t, field.Subtract(P.x, x)), P.y);
|
|
R.x.swap(x);
|
|
}
|
|
|
|
// More gyrations
|
|
R.x = R.x * IdentityToInteger(!identity);
|
|
R.y = R.y * IdentityToInteger(!identity);
|
|
R.identity = identity;
|
|
|
|
if (return_Q)
|
|
return (R = S), Q;
|
|
else if (return_P)
|
|
return (R = S), P;
|
|
else
|
|
return (S = R), R;
|
|
}
|
|
}
|
|
|
|
#undef X
|
|
#undef Y
|
|
#undef Z
|
|
|
|
#undef X1
|
|
#undef Y1
|
|
#undef Z1
|
|
|
|
#undef X2
|
|
#undef Y2
|
|
#undef Z2
|
|
|
|
#undef X3
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#undef Y3
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#undef Z3
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NAMESPACE_END
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#endif
|