Computing $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curves
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Publication:5246849
DOI10.1090/S0025-5718-2014-02899-8zbMath1315.11103MaRDI QIDQ5246849
Publication date: 22 April 2015
Published in: Mathematics of Computation (Search for Journal in Brave)
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Jacobians, Prym varieties (14H40) Algebraic number theory computations (11Y40) Isogeny (14K02)
Related Items (17)
Arithmetic on abelian and Kummer varieties ⋮ Computing functions on Jacobians and their quotients ⋮ Computing the endomorphism ring of an ordinary abelian surface over a finite field ⋮ Fast change of level and applications to isogenies ⋮ An efficient key recovery attack on SIDH ⋮ Efficient computation of \((3^n,3^n)\)-isogenies ⋮ Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem ⋮ Cyclic Isogenies for Abelian Varieties with Real Multiplication ⋮ On the computation of the endomorphism rings of abelian surfaces ⋮ Isogeny graphs of ordinary abelian varieties ⋮ Cover attacks for elliptic curves with cofactor two ⋮ Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with \((\ell ,\ell ,\ell)\)-isogenies ⋮ A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties ⋮ Computing isogenies between Jacobians of curves of genus 2 and 3 ⋮ Isogeny graphs with maximal real multiplication ⋮ Computing endomorphism rings of abelian varieties of dimension two ⋮ Spanning the isogeny class of a power of an elliptic curve
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