The GHS Attack Revisited
نویسنده
چکیده
We generalize the Weil descent construction of the GHS attack 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 an application we almost square the number of elliptic curves which succumb to the basic GHS attack, thereby weakening curves over F2155 further. We also discuss other possible extensions or variations of the GHS attack and conclude that they are not likely to yield further improvements.
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 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 کاملOn Security of Superelliptic Curves Based Cryptosystems against GHS Weil Descent Attacks
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 e...
متن کاملOn Implementation of GHS Attack against Elliptic Curve Cryptosystems over Cubic Extension Fields of Odd Characteristics
In this paper, we present algorithms for implementation of the GHS attack to Elliptic curve cryptosystems (ECC). In particular, we consider two large classes of elliptic curves over cubic extension fields of odd characteristics which have weak covering curves against GHS attack, whose existence have been shown recently [16][17][18]. We show an algorithm to find definition equation of the coveri...
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