Constructing non-supersingular elliptic curves for pairing-based cryptosystems have attracted much attention in recent years. The best previous technique builds curves with ρ = lg(q) / lg(r) ≈ 1 (k = 12) and ρ = lg(q) / lg(r) ≈ 1.25 (k = 24). When k > 12, most of the previous works address the question by representing r(x) as a cyclotomic polynomial. In this paper, we propose a method to find m...

Recently the bilinear pairing such as Weil pairing or Tate pairing on elliptic curves and hyperelliptic curves have been found various applications in cryptography. Several identity-based (simply ID-based) cryptosystems using bilinear pairings of elliptic curves or hyperelliptic curves were presented. Blind signature and ring signature are very useful to provide the user’s anonymity and the sig...

Recent attacks show how an unskilled implementation of elliptic curve cryptosystems may reveal the involved secrets from a single execution of the algorithm. Most attacks exploit the property that addition and doubling on elliptic curves are different operations and so can be distinguished from side-channel analysis. Known countermeasures suggest to add dummy operations or to use specific param...

Recently, several research groups in cryptography have presented new elliptic curve model based on Edwards curves. These new curves were selected for their good performance and security perspectives. Cryptosystems based on elliptic curves in embedded devices can be vulnerable to Side-Channel Attacks (SCA), such as the Simple Power Analysis (SPA) or the Differential Power Analysis (DPA). In this...

Elliptic curve cryptosystems are usually implemented over fields of characteristic two or over (large) prime fields. For large prime fields, projective coordinates are more suitable as they reduce the computational workload in a point multiplication. In this case, choosing for parameter a the value −3 further reduces the workload. Over Fp, not all elliptic curves can be rescaled through isomorp...

finite fields, elliptic curves, cryptography A method is described to represent points on elliptic curves over F2n‚ in the context of elliptic curve cryptosystems‚ using n bits. The method allows for full recovery of the x and y components of the point. This improves on the naive representation using 2n bits and on a previously known compressed representation using n + 1 bits. Since n bits are ...

finite fields, elliptic curves, cryptography A method is described to represent points on elliptic curves over F2n‚ in the context of elliptic curve cryptosystems‚ using n bits. The method allows for full recovery of the x and y components of the point. This improves on the naive representation using 2n bits and on a previously known compressed representation using n + 1 bits. Since n bits are ...

Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in public-key cryptography. In this article, we aim to give the reader an introduction to elliptic curve cryptosystems, and to demo...

In this paper, we introduce a new approach to the generation of binary sequences by applying trace functions to elliptic curves over GF (2). We call these sequences elliptic curve pseudorandom sequences (EC-sequence). We determine their periods, distribution of zeros and ones, and linear spans for a class of EC-sequences generated from supersingular curves. We exhibit a class of EC-sequences wh...