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GF(2^n) arithmetics in bitvector

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Jiri Pittner
2023-12-31 19:48:07 +01:00
parent f0325ba6f5
commit 1e00570f66
3 changed files with 80 additions and 9 deletions
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65
bitvector.cc
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@@ -296,12 +296,13 @@ return n;
//NOTE: naive algorithm, just for testing
//does not perform modulo irreducible polynomial, is NOT GF(2^n) multiplication
bitvector bitvector::operator*(const bitvector &rhs) const
bitvector bitvector::multiply(const bitvector &rhs, bool autoresize) const
{
bitvector r(size()+rhs.size());
int maxsize=size(); if(rhs.size()>maxsize) maxsize=rhs.size();
bitvector r(autoresize?size()+rhs.size():maxsize);
r.clear();
bitvector tmp(rhs);
tmp.resize(size()+rhs.size(),true);
if(autoresize) tmp.resize(size()+rhs.size(),true);
for(int i=0; i<=degree(); ++i)
{
if((*this)[i]) r+= tmp;
@@ -310,6 +311,60 @@ for(int i=0; i<=degree(); ++i)
return r;
}
//this is GF(2^n) multiplication
bitvector bitvector::field_mult(const bitvector &rhs, const bitvector &irpolynom) const
{
int d=irpolynom.degree();
if(d>size()||d>rhs.size()) laerror("inconsistent dimensions in field_mult");
bitvector r(size());
r.clear();
bitvector tmp(*this);
tmp.resize(size()+1,true);
int rd=rhs.degree();
for(int i=0; i<=rd; ++i) //avoid making a working copy of rhs and shifting it
{
if(rhs[i]) r+= tmp;
tmp.leftshift(1,false);
if(tmp[d]) tmp -= irpolynom;
}
return r;
}
//this is GF(2^n) multiplicative inverseion
//cf. https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
bitvector bitvector::field_inv(const bitvector &irpolynom) const
{
int d=irpolynom.degree();
if(d>size()) laerror("inconsistent dimensions in field_inv");
bitvector t(size()); t.clear();
bitvector newt(size()); newt.clear(); newt.set(0);
bitvector r(irpolynom); r.copyonwrite();
bitvector newr(*this); if(r.size()>newr.size()) newr.resize(r.size(),true); newr.copyonwrite();
int rs=r.size();
while(!newr.is_zero())
{
//std::cout <<"r "<<r<<" newr "<<newr <<" "; std::cout <<"t "<<t<<" newt "<<newt; std::cout <<std::endl;
bitvector remainder(rs);
bitvector quotient = r.division(newr,remainder);
r=newr; newr=remainder;
remainder= t - quotient.multiply(newt,false); //avoid size growth
t=newt; newt=remainder;
}
if(r.degree()>0) laerror("field_inv: polynomial is not irreducible or input is its multiple");
if(!r[0]) laerror("zero in field_inv");
return t;
}
void bitvector::resize(const unsigned int n, bool preserve)
{
int old=size();
@@ -338,9 +393,9 @@ while((d=remainder.degree()) >= rhsd)
{
unsigned int pos = d-rhsd;
r.set(pos);
remainder -= (rhs<<pos);
remainder -= rhs<<pos;
}
remainder.resize(rhs.size(),true);
return r;
}