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KGC_TEST/KGC/miracl/source/findbase.cpp

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//
// cl /O2 /GX findbase.cpp gf2m.cpp big.cpp miracl.lib
//
// program to find "best" irreducible polynomial for GF(2^m)
// See http://eprint.iacr.org/2007/192
// cl /O2 /GX findbase.cpp gf2m.cpp big.cpp miracl.lib
// To generate the code for the reduction in a form for inclusion in
// mrgf2m.c, function reduce2(.) use the irp.cpp utility
//
#include <iostream>
#include "gf2m.h"
using namespace std;
Miracl precision=100;
/* Max word size to be supported with irreducible polynomial */
#define MAX_WORD_SIZE MIRACL
/* define bit length of machine word - this can be changed here to 16 or whatever */
#define WORDLENGTH MAX_WORD_SIZE
/* insert costs of each operation in clock cycles */
#define XOR 1
/* cost of shifts (left and right) per shift size */
/* MSP430 Costs MIRACL = 16 */
//int ls[16]={0,1,2,3,4,5,6,5,2,3,4,5,6,5,4,3};
//int rs[16]={0,2,3,4,5,6,7,5,2,3,4,5,6,5,4,3};
/* Atmeg128 Costs MIRACL = 8 */
//int ls[8]={0,1,2,3,2,3,4,3};
//int rs[8]={0,1,2,3,2,3,4,3};
/* Pentium Costs MIRACL = 32 */
//int ls[32]={0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
//int rs[32]={0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
/* x86-64 Costs MIRACL=64 */
int ls[64]={0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
int rs[64]={0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
/* ARM Costs MIRACL = 32 */
//int ls[32]={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
//int rs[32]={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
int priceit(int *s,int *d)
{ /* given the shifts and the cost per shift - put a price on it */
int i,j,k,price,best;
if (s[0]==0) return 0;
price=d[s[1]];
for (i=2;i<=s[0];i++)
{
best=s[i]-s[i-1]; /* a number of one-bit shifts is always an option */
if (d[s[i]]< best) best=d[s[i]];
for (j=1;j<=i-1;j++)
{ /* see is there a cheaper way */
k=s[i]-s[j];
if (d[k]<best) best=d[k];
}
price+=best;
}
return price;
}
void insert(int sh,int *sharray)
{ /* insert into sorted array */
int i,j;
if (sharray[0]==0)
{ /* first element */
sharray[1]=sh;
sharray[0]=1;
return;
}
if (sh>=sharray[sharray[0]])
{ /* shift greatest so far - put it on the end */
sharray[0]++;
sharray[sharray[0]]=sh;
return;
}
/* insert */
i=1;
while (sh>sharray[i]) i++;
for (j=sharray[0];j>=i;j--)
sharray[j+1]=sharray[j];
sharray[0]++;
sharray[i]=sh;
return;
}
int cost(int W,int M,int A,int B,int C,int *shifts)
{
int i,j,len,rsh[4],lsh[4],ii;
int xors,lshifts[5],rshifts[5];
lshifts[0]=rshifts[0]=0;
rsh[0]=M%W;
lsh[0]=W-rsh[0];
rsh[1]=(M-A)%W;
lsh[1]=W-rsh[1];
len=2;
if (B)
{
len=4;
rsh[2]=(M-B)%W;
lsh[2]=W-rsh[2];
rsh[3]=(M-C)%W;
lsh[3]=W-rsh[3];
}
xors=0;
for (i=0;i<len;i++)
{
if (rsh[i]==0 || rsh[i]==W) xors++;
else
{
xors+=2;
insert(rsh[i],rshifts);
insert(lsh[i],lshifts);
}
}
*shifts=priceit(lshifts,ls)+priceit(rshifts,rs);
return xors;
}
BOOL irreducible(int m,int a,int b,int c)
{
GF2m w4,w5,modulo;
Big modulus;
get_mip()->M=m;
get_mip()->AA=a;
get_mip()->BB=b;
get_mip()->CC=c;
if (b==0) modulus=pow((Big)2,m)+pow((Big)2,a)+1;
else modulus=pow((Big)2,m)+pow((Big)2,a)+pow((Big)2,b)+pow((Big)2,c)+1;
copy(modulus.getbig(),get_mip()->modulus);
copy(modulus.getbig(),getbig(modulo));
w4=2;
for (int i=1;i<=m/2;i++)
{
w4*=w4;
w5=w4+2;
if (gcd(w5,modulo)!=1) return FALSE;
}
return TRUE;
}
int main(int argc,char **argv)
{
int i,M,A,B,C,L,xors,shifts,price,bestprice;
long cheapest,wcost;
int CA,CB,CC;
argc--; argv++;
if (argc!=1 && argc!=2)
{
cout << "Bad Parameters" << endl;
cout << "findbase <M>" << endl;
cout << "finds irreducible polynomials for field F(2^M)" << endl;
cout << "findbase <M> <L>" << endl;
cout << "finds irreducible polynomials with cost less than or equal to L" << endl;
exit(0);
}
get_mip()->IOBASE=16;
M=atoi(argv[0]);
if (argc==2) L=atoi(argv[1]);
else L=0;
cheapest=1000000L;
cout << "Looking for suitable trinomial basis x^M+x^A+1" << endl;
for (A=M-MAX_WORD_SIZE;A>=1;A--)
{
if (A%2==0) continue; // odds only
if (irreducible(M,A,0,0))
{
xors=cost(WORDLENGTH,M,A,0,0,&shifts);
price=xors+shifts;
wcost=1000*price-A;
if (wcost<cheapest)
{
cheapest=wcost;
bestprice=price;
CA=A;
CB=CC=0;
}
if (L==0 || price<=L)
{
cout << "A= " << A;
cout << " ";
if ((M-A)%WORDLENGTH==0) cout << "*";
if (((A+1)/2)%WORDLENGTH==0) cout << "+";
cout << " cost= " << xors << "+" << shifts << " = " << price << endl;
}
}
}
cout << "Looking for suitable pentanomial basis x^M+x^A+x^B+x^C+1" << endl;
for (A=M-MAX_WORD_SIZE;A>=1;A--)
{
if (A%2==0) continue; // odds only
for (B=A-1;B>=1;B--)
{
if (B%2==0) continue; // odds only
for (C=B-1;C>=1;C--)
{
if (C%2==0) continue; // odds only
if (irreducible(M,A,B,C))
{
xors=cost(WORDLENGTH,M,A,B,C,&shifts);
price=xors+shifts;
wcost=1000*price-C;
if (wcost<cheapest)
{
cheapest=wcost;
bestprice=price;
CA=A;
CB=B;
CC=C;
}
if (L==0 || price<=L)
{
cout << "A= " << A << " B= " << B << " C= " << C;
cout << " ";
if ((M-A)%WORDLENGTH==0) cout << "*";
if ((M-B)%WORDLENGTH==0) cout << "*";
if ((M-C)%WORDLENGTH==0) cout << "*";
if (((A+1)/2)%WORDLENGTH==0) cout << "+";
if (((B+1)/2)%WORDLENGTH==0) cout << "+";
if (((C+1)/2)%WORDLENGTH==0) cout << "+";
cout << " cost= " << xors << "+" << shifts << "=" << price << endl;
}
}
}
}
}
if (cheapest==1000000L) return 0;
cout << "cheapest= " << bestprice << endl;
cout << "A= " << CA;
if (CB)
cout << " B= " << CB << " C= " << CC;
cout << endl;
return 0;
}
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