Discrete Logarithms in Generalized Jacobians
نویسندگان
چکیده
Déchène has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect product of an elliptic curve and a multiplicative group of a finite field. We explain why her proposal has no advantages over simply taking the direct product of groups. We then argue that generalized Jacobians offer poorer security and efficiency than standard Jacobians.
منابع مشابه
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 کاملAn Efficient Threshold Verifiable Multi-Secret Sharing Scheme Using Generalized Jacobian of Elliptic Curves
In a (t,n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logar...
متن کاملSome experiments investigating a possible L(1/4) algorithm for the discrete logarithm problem in algebraic curves
The function field sieve, a subexponential algorithm of complexity L(1/3) that computes discrete logarithms in finite fields, has recently been improved to an algorithm of complexity L(1/4) and subsequently to a quasi-polynomial time algorithm. We investigate whether the new ideas also apply to index calculus algorithms for computing discrete logarithms in Jacobians of algebraic curves. While w...
متن کاملOn the security of generalized Jacobian cryptosystems
Generalized Jacobians are natural candidates to use in discrete logarithm (DL) based cryptography since they include the multiplicative group of nite elds, algebraic tori, elliptic curves as well as all Jacobians of curves. This observation therefore raised the possibility that other families of generalized Jacobians may be of cryptographic interest. This exploration began with the study of t...
متن کاملArithmetic of Generalized Jacobians
This paper aims at introducing generalized Jacobians as a new candidate for discrete logarithm (DL) based cryptography. The motivation for this work came from the observation that several practical DL-based cryptosystems, such as ElGamal, the Elliptic and Hyperelliptic Curve Cryptosystems, XTR, LUC as well as CEILIDH can all naturally be reinterpreted in terms of generalized Jacobians. However,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2006 شماره
صفحات -
تاریخ انتشار 2006