Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two

English

Müller, Volker[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]

[en] Elliptic curve ; Frobenius expansion ; Finite field of characteristic 2

[en] The paper shows how Frobenius expansions can be used to speed up multiplication of points on elliptic curves that are defined over very small fields of characteristic two. The Frobenius expansion algorithm is analyzed in theory and in practice. It can gain significant improvements in practical applications. These curves are therefore especially interesting for implementations of elliptic curve cryptosystems.