474 lines
11 KiB
C++
474 lines
11 KiB
C++
// 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
|