Computing the $\ell $-power torsion of an elliptic curve over a finite field
نویسندگان
چکیده
منابع مشابه
Computing the ℓ-power torsion of an elliptic curve over a finite field
The algorithm we develop outputs the order and the structure, including generators, of the -Sylow subgroup of the group of rational points of an elliptic curve defined over a finite field. To do this, we do not assume any knowledge of the group order. We are able to choose points in such a way that a linear number of successive -divisions leads to generators of the subgroup under consideration....
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We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field Fq . Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of log q , while our bound for the second algorithm depends primarily on log |DE |, where DE is the discriminant of the order isomorphic to En...
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We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here, we let both q and m vary; our estimate is explicit and does not depend on the elliptic curve.
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Public key cryptography systems are based on sound mathematical foundations that are designed to make the problem hard for an intruder to break into the system. Number theory and algebraic geometry, namely the theory of elliptic curves defined over finite fields, has found applications in cryptology. The basic reason for this is that elliptic curves over finite fields provide an inexhaustible s...
متن کاملOn the Exponents of the Group of Points of an Elliptic Curve over a Finite Field
We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here we let both q and m vary and our estimate is explicit and does not depend on the elliptic curve.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2009
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-08-02201-1