Guaranteeing the diversity of number generators

A major problem in using iterative number generators of the form x_i=f(x_{i-1}) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is used, and can have devastating cryptanalytic implications. In this paper we define a measure of security, called_sequence_diversity_, which generalizes the notion of cycle-length for non-iterative generators. We then introduce the class of counter assisted generators, and show how to turn any iterative generator (even a bad one designed or seeded by an adversary) into a counter assisted generator with a provably high diversity, without reducing the quality of generators which are already cryptographically strong.Comment: Small update

Maximum-order Complexity and Correlation Measures

We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order $k$ cannot have very small maximum-order complexity

On finite pseudorandom binary lattices

Pseudorandom binary sequences play a crucial role in cryptography. The classical approach to pseudorandomness of binary sequences is based on computational complexity. This approach has certain weak points thus in the last two decades years a new, more constructive and quantitative approach has been developed. Since multidimensional analogs of binary sequences (called binary lattices) also have important applications thus it is a natural idea to extend this new approach to the multidimensional case. This extension started with a paper published in 2006, and since that about 25 papers have been written on this subject. Here our goal is to present a survey of all these papers

The cross-correlation measure for families of binary sequences

Large families of binary sequences of the same length are considered and a new measure, the cross-correlation measure of order $k$ is introduced to study the connection between the sequences belonging to the family. It is shown that this new measure is related to certain other important properties of families of binary sequences. Then the size of the cross-correlation measure is studied. Finally, the cross-correlation measures of two important families of pseudorandom binary sequences are estimated

On the complexity of a family based on irreducible polynomials

Ahlswede, Khachatrian, Mauduit and Sárközyy introduced the f-complexity measure ("f" for family) in order to study pseudorandom properties of large families of binary sequences. So far several families have been studied by this measure. In the present paper I considerably improve on my earlier result in [7], where the f-complexity measure of a family based on the Legendre symbol and polynomials over Fp is studied. This paper also extends the earlier results to a family restricted on irreducible polynomials