Bill Allombert on Sat, 02 Apr 2011 16:30:59 +0200 |
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Re: ECC modelling |
On Sat, Apr 02, 2011 at 04:41:43PM +0300, Eugene N wrote: > Hello Sirs > > I am a student and i recently decided to use this renound tool for the > purpose of ECC modelling. > I browsed through the manuals & did some web searcehes ( > http://orion.math.iastate.edu/cbergman/crypto/pari/parihelp.html) > and i am very happy to discover this great tool. > > However, i stumbled upon some problems, wich made me turn for advice to > expirienced users like you. I hope you will clear som things for me. > > I am looking for a way to generate n-nomials (generators of m.gr. inGF(2^m) > ), especially tri-and pentanomials. I have read about ffinit(p,n) - but it > produces > long polies. There are no functions in PARI to generate irreducible trinomials or pentanomials. but you can program it in GP easily: trino(N)=for(i=1,N-1,P=x^N+x^i+1;if(polisirreducible(P*Mod(1,2)),return(P))) penta(N)=forvec(v=vector(3,i,[1,N-1]),P=x^N+1+sum(i=1,3,x^v[i]);if(polisirreducible(P*Mod(1,2)),return(P))) ffinit is much faster, though. > I would like also to find some examples of binary elliptic curves and > base-point generation. If you mean elliptic curve of GF(2^m), you need to get an irreducible polynomial P and do g=ffgen(P*Mod(1,2),'g) g is now a field generator for GF(2^m). You can define the elliptic curve Y^2+Y=X^3+X over GF(2^m) as follow: E=ellinit([0,0,1,1,0]*g^0); Cheers, Bill.