Elliptic curve cryptosystems are usually implemented over fields of characteristic two or over (large) prime fields. For large prime fields, projective coordinates are more suitabl...
We present a new type of fault attacks on elliptic curve scalar multiplications: Sign Change Attacks. These attacks exploit different number representations as they are often emplo...
Abstract. Tabulating elliptic curves has been carried out since the earliest days of machine computation in number theory. After some historical remarks, we report on significant r...
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with ...
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between ellip...
In 1986, following the work of Schoof on counting points on elliptic curves over finite fields, new algorithms for primality proving emerged, due to Goldwasser and Kilian on the on...
Abstract. This paper addresses the discrete logarithm problem in elliptic curve cryptography. In particular, we generalize the Menezes, Okamoto, and Vanstone (MOV) reduction so tha...
Ryuichi Harasawa, Junji Shikata, Joe Suzuki, Hidek...
Abstract. Essentially all subexponential time algorithms for the discrete logarithm problem over nite elds are based on the index calculus idea. In proposing cryptosystems based on...
We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Comple...