On the discrete logarithm problem for plane curves
نویسندگان
چکیده
منابع مشابه
On the discrete logarithm problem for plane curves
In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem in degree 0 class groups of non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of Õ(q), where q is the cardinality of the ground field. Moreover, it is proven...
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Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
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In recent years several papers have appeared investigating the classical discrete logarithm problem for elliptic curves by means of the multivariate polynomial approach based on the celebrated summation polynomials, introduced by Semaev in 2004. However, with a notable exception by Petit et al. in 2016, all numerous papers have investigated only the composite-field case, leaving apart the labor...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2012
ISSN: 1246-7405,2118-8572
DOI: 10.5802/jtnb.815