On Security of Superelliptic Curves Based Cryptosystems against GHS Weil Descent Attacks
نویسندگان
چکیده
The GHS Weil descent attack by Gaudry, Hess and Smart was originally proposed to elliptic curves over finite fields of characteristic two [11]. Among a number of extensions of this attack, Diem treated the cases of hyperelliptic curves over finite fields of arbitrary odd characteristics [4]. His results were partially extended to algebraic curves of which the function fields are cyclic Galois extensions [14]. In this paper, we first improve the results in [14] and show a lower bound of genera of curves obtained by the GHS Weil descent attack. Then based on these results, a detailed analysis on security of superelliptic curves based cryptosystems is provided against various attacks.
منابع مشابه
An Extension of GHS Weil Descent Attack
The Weil descent attack, suggested by Frey, has been implemented by Gaudry, Hess and Smart (the so-called GHS attack), on elliptic curves over finite fields of characteristic two of composite degrees. The GHS attack has been extended by Galbraith to hyperelliptic curves of characteristic two. Recently, Diem presented a general treatment of GHS attack to hyperelliptic curves over finite fields o...
متن کاملWeil Descent Attacks
This article is to appear as a chapter in Advances in Elliptic Curve Cryptography, edited by I. Blake, G. Seroussi and N. Smart, Cambridge University Press, 2004. It summarises the main aspects of the existing literature on Weil descent attacks and contains some new material on the GHS attack in even characteristic.
متن کاملWeil descent attack for Kummer extensions
In this paper, we show how the Weil descent attack of Gaudry, Hess and Smart can be adapted to work for some hyperelliptic curves defined over fields of odd characteristic. This attack applies to a family of hyperelliptic and superelliptic curves over quadratic field extensions, as well as two families of hyperelliptic curves defined over cubic extensions. We also show that those are the only f...
متن کاملGeneralising the GHS Attack on the Elliptic Curve Discrete Logarithm Problem
We generalise the Weil descent construction of the GHS attack on the elliptic curve discrete logarithm problem (ECDLP) to arbitrary Artin-Schreier extensions. We give a formula for the characteristic polynomial of Frobenius of the obtained curves and prove that the large cyclic factor of the input elliptic curve is not contained in the kernel of the composition of the conorm and norm maps. As a...
متن کاملExtending the GHS Weil Descent Attack
In this paper we extend the Weil descent attack due to Gaudry, Hess and Smart (GHS) to a much larger class of elliptic curves. This extended attack applies to fields of composite degree over F2. The principle behind the extended attack is to use isogenies to find an elliptic curve for which the GHS attack is effective. The discrete logarithm problem on the target curve can be transformed into a...
متن کامل