László Mérai

Construction of pseudorandom binary lattices based on multiplicative characters

In this paper a large family of pseudorandom binary lattices is constructed by using the multiplicative characters of finite fields. This construction generalizes several one-dimensional constructions to arbitrary dimensions.

Expansion complexity and linear complexity of sequences over finite fields

The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. We study the relationship between linear complexity and expansion complexity. In particular, we show that for purely periodic sequences both figures of merit provide essentially the same quality test for a sufficiently long part of the sequence. However, if we study shorter parts of the period or nonperiodic sequences, then we can show, roughly speaking, that the expansion complexity provides a stronger test. We demonstrate this by analyzing a sequence of binomial coefficients modulo p. Finally, we establish a probabilistic result on the behavior of the expansion complexity of random sequences over a finite field.

Remarks on Pseudorandom Binary Sequences Over Elliptic Curves

In the paper the pseudorandomness of binary sequences defined over elliptic curves is studied and both the well-distribution and correlation measures are estimated. The paper is based on the Kohel-Shparlinski bound and the Erdos-Turan-Koksma inequality.

Construction of pseudorandom binary lattices using elliptic curves

In an earlier paper, Hubert, Mauduit and Sarkozy introduced and studied the notion of pseudorandomness of binary lattices. Later constructions were given by using characters and the notion of a multiplicative inverse over finite fields. In this paper a further large family of pseudorandom binary lattices is constructed by using elliptic curves.

On Pseudorandom Properties of Certain Sequences of Points on Elliptic Curve

In this paper we study the pseudorandom properties of sequences of points on elliptic curves. These sequences are constructed by taking linear combinations with small coefficients (e.g. \(-1,0,+1\)) of the orbit elements of a point with respect to a given endomorphism of the curve. We investigate the linear complexity and the distribution of these sequences. The result on the linear complexity answers a question of Igor Shparlinski.

On the typical values of the cross-correlation measure

Gyarmati, Mauduit and Sárközy introduced the cross-correlation measure

Anonymous sealed bid auction protocol based on a variant of the dining cryptographers’ protocol

\Phi _k(\mathcal {F})

The Measures of Pseudorandomness and the NIST Tests

Φk(F) to measure the randomness of families of binary sequences