|Bill Allombert on Fri, 10 Jun 2005 20:50:20 +0200|
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|Re: Elliptic Curve over binary field|
On Fri, Jun 10, 2005 at 10:05:25AM -0700, Hauw Suwito wrote: > Greetings to PARI experts, > I'm new to PARI, and would like to know how > to use ellinit to create elliptic curve over a binary field (F_2^m). > Any pointer to a document would be also appreciated. Try the following: 1) Compute a polynomial (in w) defining your field: F=ffinit(2,m,w); 2) Set a to w mod F a=Mod(w,F); 3.a) Define your curve in term of a: E=ellinit([0,0,a,0,a+1]); 3.b) If your curve is defined of F_2, simply multiply it by a^0 instead: E=ellinit([0,0,1,0,1]*a^0); Now you can do operations on points of E as usual: ? elladd(E,[1,a],[0,1]) %4 = [Mod(w^2 - 2*w, Mod(1, 2)*w^3 + Mod(1, 2)*w^2 + Mod(1, 2)), Mod(Mod(1, 2), Mod(1, 2)*w^3 + Mod(1, 2)*w^2 + Mod(1, 2))] Cheers, Bill.