Abstract

Elliptic curves play an important role in many areas of modern cryptology such as integer factorization and primality proving. Moreover, they can be used in cryptosystems based on discrete logarithms for building one-way permutations. For the latter purpose, it is required to have cyclic elliptic curves over finite fields. The aim of this note is to explain how to construct such curves over a finite field of large prime cardinality, using the ECPP primality proving test of Atkin and Morain. 1 Introduction Elliptic curves prove to be a powerful tool in modern cryptology. Following the original work of H. W. Lenstra, Jr. [18] concerning integer factorization, many researchers have used this new idea to work out primality proving algorithms [8, 14, 2, 4, 22] as well as cryptosystems [21, 16] generalizing those of [12, 1, 9]. Recent work on these topics can be found in [20, 19]. More recently, Kaliski [15] has used elliptic curves in the design of one-way permutations. For this, the autho...

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