Institut de Mathématiques de Luminy

Abstract 2002-03

Louis Goubin, Christian Mauduit
Construction of large families of pseudo-random binary sequences.

In a series of papers Mauduit and Sarkozy (partly with coauthors) studied finite pseudorandom binary sequences. They showed that the Legendre symbol forms a "good" pseudorandom sequence, and they also tested other sequences for pseudorandomness, however, no large family of "good" pseudorandom sequences has been found yet.
In this paper, a large family of this type is constructed. Again, the construction is related to the Legendre symbol. Moreover, by using elliptic curves large families of binary sequences are constructed. It is expected that these sequences form "good" pseudorandom binary sequences.

1991 Mathematics Subject Classification : 11 K 45.

Key words : pseudorandom, binary sequence, Legendre symbol, elliptic curves.


Last update : february 6, 2002, EL.