Collision and avalanche effect in pseudorandom sequences

Abstract. Pseudorandom binary sequences have many applications. In particular they play a crucial role in cryptography, for example as keystream in the well-known Vernam cipher. The notion of pseudorandomness can be defined in different ways. Recently a constructive theory of pseudorandomness of finite sequences has been developed and many constructions for binary sequences with strong pseudorandom properties have been given. Motivated by applications, Mauduit and Sárközy in [10] generalized and extended this theory from the binary case to \(k\)-ary sequences, i.e., to \(k\) symbols. They constructed large families of binary and \(k\)-ary sequences with strong pseudorandom properties. I adapted the notions of collision and avalanche effect in order to study these pseudorandom properties of two of the most important families in [12] and [13]. Later, the study of the pseudorandom properties mentioned above was extended to \(k\)-ary sequences in [14]. This is a survey of my results.