منابع مشابه
COUNTING POINTS ON ELLIPTIC CURVES OVER F2n,
In this paper we present an implementation of Schoofs algorithm for computing the number of i"2m-P°mts °f an elliptic curve that is defined over the finite field F2m . We have implemented some heuristic improvements, and give running times for various problem instances.
متن کاملPoint Counting on Reductions of Cm Elliptic Curves
We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM Q-curves in certain cases. This generalizes earlier results of Gross, Stark, and others.
متن کاملCounting points on elliptic curves over finite fields
-We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large; it is based on Shanks’s baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is ...
متن کاملCounting points on elliptic curves in medium characteristic
In this paper, we revisit the problem of computing the kernel of a separable isogeny of degree ` between two elliptic curves defined over a finite field Fq of characteristic p. We describe an algorithm the asymptotic time complexity of which is equal to e O(`(1 + `/p) log q) bit operations. This algorithm is particularly useful when ` > p and as a consequence, we obtain an improvement of the co...
متن کاملComputing the cardinality of CM elliptic curves using torsion points
Let E/Q be an elliptic curve having complex multiplication by a given quadratic order of an imaginary quadratic field K. The field of definition of E is the ring class field Ω of the order. If the prime p splits completely in Ω, then we can reduce E modulo one the factors of p and get a curve E defined over Fp. The trace of the Frobenius of E is known up to sign and we need a fast way to find t...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1996
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181072041