Initial revision

1 files changed, 287 insertions, 0 deletions

diff --git a/ec2n.cpp b/ec2n.cpp
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+++ b/ec2n.cpp
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+// ec2n.cpp - written and placed in the public domain by Wei Dai
+
+#include "pch.h"
+#include "ec2n.h"
+#include "asn.h"
+
+#include "algebra.cpp"
+#include "eprecomp.cpp"
+
+NAMESPACE_BEGIN(CryptoPP)
+
+EC2N::EC2N(BufferedTransformation &bt)
+	: m_field(BERDecodeGF2NP(bt))
+{
+	BERSequenceDecoder seq(bt);
+	m_field->BERDecodeElement(seq, m_a);
+	m_field->BERDecodeElement(seq, m_b);
+	// skip optional seed
+	if (!seq.EndReached())
+		BERDecodeOctetString(seq, TheBitBucket());
+	seq.MessageEnd();
+}
+
+void EC2N::DEREncode(BufferedTransformation &bt) const
+{
+	m_field->DEREncode(bt);
+	DERSequenceEncoder seq(bt);
+	m_field->DEREncodeElement(seq, m_a);
+	m_field->DEREncodeElement(seq, m_b);
+	seq.MessageEnd();
+}
+
+bool EC2N::DecodePoint(EC2N::Point &P, const byte *encodedPoint, unsigned int encodedPointLen) const
+{
+	StringStore store(encodedPoint, encodedPointLen);
+	return DecodePoint(P, store, encodedPointLen);
+}
+
+bool EC2N::DecodePoint(EC2N::Point &P, BufferedTransformation &bt, unsigned int 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;
+
+		P.identity = false;
+		P.x.Decode(bt, m_field->MaxElementByteLength()); 
+
+		if (P.x.IsZero())
+		{
+			P.y = m_field->SquareRoot(m_b);
+			return true;
+		}
+
+		FieldElement z = m_field->Square(P.x);
+		assert(P.x == m_field->SquareRoot(z));
+		P.y = m_field->Divide(m_field->Add(m_field->Multiply(z, m_field->Add(P.x, m_a)), m_b), z);
+		assert(P.x == m_field->Subtract(m_field->Divide(m_field->Subtract(m_field->Multiply(P.y, z), m_b), z), m_a));
+		z = m_field->SolveQuadraticEquation(P.y);
+		assert(m_field->Add(m_field->Square(z), z) == P.y);
+		z.SetCoefficient(0, type & 1);
+
+		P.y = m_field->Multiply(z, P.x);
+		return true;
+	}
+	case 4:
+	{
+		if (encodedPointLen != EncodedPointSize(false))
+			return false;
+
+		unsigned int len = m_field->MaxElementByteLength();
+		P.identity = false;
+		P.x.Decode(bt, len);
+		P.y.Decode(bt, len);
+		return true;
+	}
+	default:
+		return false;
+	}
+}
+
+void EC2N::EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
+{
+	if (P.identity)
+		NullStore().TransferTo(bt, EncodedPointSize(compressed));
+	else if (compressed)
+	{
+		bt.Put(2 + (!P.x ? 0 : m_field->Divide(P.y, P.x).GetBit(0)));
+		P.x.Encode(bt, m_field->MaxElementByteLength());
+	}
+	else
+	{
+		unsigned int len = m_field->MaxElementByteLength();
+		bt.Put(4);	// uncompressed
+		P.x.Encode(bt, len);
+		P.y.Encode(bt, len);
+	}
+}
+
+void EC2N::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
+{
+	ArraySink sink(encodedPoint, EncodedPointSize(compressed));
+	EncodePoint(sink, P, compressed);
+	assert(sink.TotalPutLength() == EncodedPointSize(compressed));
+}
+
+EC2N::Point EC2N::BERDecodePoint(BufferedTransformation &bt) const
+{
+	SecByteBlock str;
+	BERDecodeOctetString(bt, str);
+	Point P;
+	if (!DecodePoint(P, str, str.size()))
+		BERDecodeError();
+	return P;
+}
+
+void EC2N::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
+{
+	SecByteBlock str(EncodedPointSize(compressed));
+	EncodePoint(str, P, compressed);
+	DEREncodeOctetString(bt, str);
+}
+
+bool EC2N::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const
+{
+	bool pass = !!m_b;
+	pass = pass && m_a.CoefficientCount() <= m_field->MaxElementBitLength();
+	pass = pass && m_b.CoefficientCount() <= m_field->MaxElementBitLength();
+
+	if (level >= 1)
+		pass = pass && m_field->GetModulus().IsIrreducible();
+		
+	return pass;
+}
+
+bool EC2N::VerifyPoint(const Point &P) const
+{
+	const FieldElement &x = P.x, &y = P.y;
+	return P.identity || 
+		(x.CoefficientCount() <= m_field->MaxElementBitLength()
+		&& y.CoefficientCount() <= m_field->MaxElementBitLength()
+		&& !(((x+m_a)*x*x+m_b-(x+y)*y)%m_field->GetModulus()));
+}
+
+bool EC2N::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 (m_field->Equal(P.x,Q.x) && m_field->Equal(P.y,Q.y));
+}
+
+const EC2N::Point& EC2N::Identity() const
+{
+	static const Point zero;
+	return zero;
+}
+
+const EC2N::Point& EC2N::Inverse(const Point &P) const
+{
+	if (P.identity)
+		return P;
+	else
+	{
+		m_R.identity = false;
+		m_R.y = m_field->Add(P.x, P.y);
+		m_R.x = P.x;
+		return m_R;
+	}
+}
+
+const EC2N::Point& EC2N::Add(const Point &P, const Point &Q) const
+{
+	if (P.identity) return Q;
+	if (Q.identity) return P;
+	if (Equal(P, Q)) return Double(P);
+	if (m_field->Equal(P.x, Q.x) && m_field->Equal(P.y, m_field->Add(Q.x, Q.y))) return Identity();
+
+	FieldElement t = m_field->Add(P.y, Q.y);
+	t = m_field->Divide(t, m_field->Add(P.x, Q.x));
+	FieldElement x = m_field->Square(t);
+	m_field->Accumulate(x, t);
+	m_field->Accumulate(x, Q.x);
+	m_field->Accumulate(x, m_a);
+	m_R.y = m_field->Add(P.y, m_field->Multiply(t, x));
+	m_field->Accumulate(x, P.x);
+	m_field->Accumulate(m_R.y, x);
+
+	m_R.x.swap(x);
+	m_R.identity = false;
+	return m_R;
+}
+
+const EC2N::Point& EC2N::Double(const Point &P) const
+{
+	if (P.identity) return P;
+	if (!m_field->IsUnit(P.x)) return Identity();
+
+	FieldElement t = m_field->Divide(P.y, P.x);
+	m_field->Accumulate(t, P.x);
+	m_R.y = m_field->Square(P.x);
+	m_R.x = m_field->Square(t);
+	m_field->Accumulate(m_R.x, t);
+	m_field->Accumulate(m_R.x, m_a);
+	m_field->Accumulate(m_R.y, m_field->Multiply(t, m_R.x));
+	m_field->Accumulate(m_R.y, m_R.x);
+
+	m_R.identity = false;
+	return m_R;
+}
+
+// ********************************************************
+
+/*
+EcPrecomputation<EC2N>& EcPrecomputation<EC2N>::operator=(const EcPrecomputation<EC2N> &rhs)
+{
+	m_ec = rhs.m_ec;
+	m_ep = rhs.m_ep;
+	m_ep.m_group = m_ec.get();
+	return *this;
+}
+
+void EcPrecomputation<EC2N>::SetCurveAndBase(const EC2N &ec, const EC2N::Point &base)
+{
+	m_ec.reset(new EC2N(ec));
+	m_ep.SetGroupAndBase(*m_ec, base);
+}
+
+void EcPrecomputation<EC2N>::Precompute(unsigned int maxExpBits, unsigned int storage)
+{
+	m_ep.Precompute(maxExpBits, storage);
+}
+
+void EcPrecomputation<EC2N>::Load(BufferedTransformation &bt)
+{
+	BERSequenceDecoder seq(bt);
+	word32 version;
+	BERDecodeUnsigned<word32>(seq, version, INTEGER, 1, 1);
+	m_ep.m_exponentBase.BERDecode(seq);
+	m_ep.m_windowSize = m_ep.m_exponentBase.BitCount() - 1;
+	m_ep.m_bases.clear();
+	while (!seq.EndReached())
+		m_ep.m_bases.push_back(m_ec->BERDecodePoint(seq));
+	seq.MessageEnd();
+}
+
+void EcPrecomputation<EC2N>::Save(BufferedTransformation &bt) const
+{
+	DERSequenceEncoder seq(bt);
+	DEREncodeUnsigned<word32>(seq, 1);	// version
+	m_ep.m_exponentBase.DEREncode(seq);
+	for (unsigned i=0; i<m_ep.m_bases.size(); i++)
+		m_ec->DEREncodePoint(seq, m_ep.m_bases[i]);
+	seq.MessageEnd();
+}
+
+EC2N::Point EcPrecomputation<EC2N>::Exponentiate(const Integer &exponent) const
+{
+	return m_ep.Exponentiate(exponent);
+}
+
+EC2N::Point EcPrecomputation<EC2N>::CascadeExponentiate(const Integer &exponent, const DL_FixedBasePrecomputation<Element> &pc2, const Integer &exponent2) const
+{
+	return m_ep.CascadeExponentiate(exponent, static_cast<const EcPrecomputation<EC2N> &>(pc2).m_ep, exponent2);
+}
+*/
+
+template class AbstractGroup<EC2N::Point>;
+template class DL_FixedBasePrecomputationImpl<EC2N::Point>;
+
+NAMESPACE_END