Isogenies and the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves

نویسنده

  • Benjamin A. Smith
چکیده

We describe the use of explicit isogenies to reduce Discrete Logarithm Problems (DLPs) on Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, which are vulnerable to faster index calculus attacks. We provide algorithms which compute an isogeny with kernel isomorphic to (Z/2Z) for any hyperelliptic genus 3 curve. These algorithms provide a rational isogeny for a positive fraction of all hyperelliptic genus 3 curves defined over a finite field of characteristic p > 3. Subject to reasonable assumptions, our algorithms provide an explicit and efficient reduction from hyperelliptic DLPs to nonhyperelliptic DLPs for around 18.57% of all hyperelliptic genus 3 curves over a given finite field.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Applications des fonctions thêta à la cryptographie sur courbes hyperelliptiques. (Applications of theta functions for hyperelliptic curve cryptography)

Since the mid 1980’s, abelian varieties have been widely used in cryptography: the discrete logarithm problem and the protocols that rely on it allow asymmetric encryption, signatures, authentification... For cryptographic applications, one of the most interesting examples of principally polarized abelian varieties is given by the Jacobians of hyperelliptic curves. The theory of theta functions...

متن کامل

Families of Explicit Isogenies of Hyperelliptic Jacobians

We construct three-dimensional families of hyperelliptic curves of genus 6, 12, and 14, two-dimensional families of hyperelliptic curves of genus 3, 6, 7, 10, 20, and 30, and one-dimensional families of hyperelliptic curves of genus 5, 10 and 15, all of which are equipped with an an explicit isogeny from their Jacobian to another hyperelliptic Jacobian. We show that the Jacobians are genericall...

متن کامل

Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time

We provide a subexponential algorithm for solving the discrete logarithm problem in Jacobians of high-genus hyperelliptic curves over finite fields. Its expected running time for instances with genus g and underlying finite field Fq satisfying g ≥ θ log q for a positive constant θ is given by

متن کامل

Experiments Using an Analogue of the Number Field Sieve Algorithm to Solve the Discrete Logarithm Problem in the Jacobians of Hyperelliptic Curves

In this paper we report on an implementation of the algorithm of Aldeman, De Marrais and Huang for the solution of the discrete logarithm problem on jacobians of hyperelliptic curves. The method of Aldeman, De Marrais and Huang is closely related to the Number Field Sieve factoring method which leads us to consider a \lattice sieve" version of the original method. The supposed intractability of...

متن کامل

Computational Aspects of Jacobians of Hyperelliptic Curves

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest of which remains the Pollard rho algorithm with r-adding walks. For the first time, we rigorously analyze the Pollard rho method with r-addin...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • IACR Cryptology ePrint Archive

دوره 2007  شماره 

صفحات  -

تاریخ انتشار 2007