Andreas Enge on Thu, 28 Jun 2012 09:29:02 +0200 |
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Re: Elliptic curves over GF(p)? |
On Thu, Jun 28, 2012 at 10:17:54AM +1000, Alasdair McAndrew wrote: > I want to do some simple computation on elliptic curves of the form y^2 = > x^3 + ax +b (mod p), where p is prime (of at least 32 bits) . My needs are > simple: define such a curve, find its cardinality, find a generator (if the > cardinality is prime) or a point of high order, and in general perform > arithmetic on the curve: addition, order, etc. Can libpari manage all of > this? The manual is fairly sparse on elliptic curves, and it's > not clear to me, as a beginner, whether Pari supports elliptic curves over > finite fields GF(p). All this is possible, try the following snippets: p = 53 E = ellinit ([Mod (-117, p), Mod (324, p)]) P = [0, 18] ellap (E, p) n = p + 1 - ellap (E, p) ellpow (E, P, 48) ellpow (E, P, 24) ellpow (E, P, 12) ellpow (E, P, 8) ellgroup (E) ?ellgroup ellgroup (E, , 1) If you are using the stable pari version 2.5.1 instead of the development version, ellinit takes 5 instead of (possibly) 2 arguments. Andreas