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Constructing hyperelliptic curves of genus 2 suitable for cryptography
 Math. Comp
, 2003
"... Abstract. In this article we show how to generalize the CMmethod for elliptic curves to genus two. We describe the algorithm in detail and discuss the results of our implementation. 1. ..."
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Abstract. In this article we show how to generalize the CMmethod for elliptic curves to genus two. We describe the algorithm in detail and discuss the results of our implementation. 1.
Computational aspects of hyperelliptic curves
 Computer Mathematics (Beijing
, 2003
"... We introduce a new approach of computing the automorphism group and the field of moduli of points p = [C] in the moduli space of hyperelliptic curves Hg. Further, we show that for every moduli point p ∈ Hg(L) such that the reduced automorphism group of p has at least two involutions, there exists a ..."
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We introduce a new approach of computing the automorphism group and the field of moduli of points p = [C] in the moduli space of hyperelliptic curves Hg. Further, we show that for every moduli point p ∈ Hg(L) such that the reduced automorphism group of p has at least two involutions, there exists a representative C of the isomorphism class p which is defined over L. 1
PAPER Construction of Secure Cab Curves Using Modular Curves
"... SUMMARY This paper proposes a heuristic algorithm which, given a basis of a subspace of the space of cuspforms of weight 2 for Γ0(N) which is invariant for the action of the Hecke operators, tests whether the subspace corresponds to a quotient A of the jacobian of the modular curve X0(N) such that A ..."
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SUMMARY This paper proposes a heuristic algorithm which, given a basis of a subspace of the space of cuspforms of weight 2 for Γ0(N) which is invariant for the action of the Hecke operators, tests whether the subspace corresponds to a quotient A of the jacobian of the modular curve X0(N) such that A is the jacobian of a curve C. Moreover, equations for such a curve C are computed which make the quotient suitable for applications in cryptography. One advantage of using such quotients of modular jacobians is that fast methods are known for finding their number of points over finite fields. key words: discrete logarithm, modular curve, hyperelliptic curve, Cab curve