Hubert, Mauduit and Sárközy introduced the pseudorandom measure of order ℓ of binary lattices. This measure studies the pseudorandomness only on box lattices of very special type. In certain applications one may need measures covering a more general situation. In this paper the line measure and the convex measure are introduced.
Using the discrete logarithm in  and  a large family of pseudorandom binary sequences was constructed. Here we extend
this construction. An interesting feature of this extension is that in certain special cases we get sequences involving points
on elliptic curves.
In the applications it may occur that our initial pseudorandom binary sequence turns out to be not long enough, thus we have
to take the concatenation or merging of it with other pseudorandom binary sequences. Here our goal is study when we can form
the concatenation of several pseudorandom binary sequences belonging to a given family? We introduce and study new measures
which can be used for answering this question.
Ahlswede, Khachatrian, Mauduit and A. Sárközy introduced the notion of family-complexity of families of binary sequences.
They estimated the family-complexity of a large family related to Legendre symbol introduced by Goubin, Mauduit and Sárközy.
Here their result is improved, and apart from the constant factor the best lower bound is given for the family-complexity.
In recent papers ,  I studied collision and avalanche effect in families of finite pseudorandom binary sequences.
Motivated by applications, Mauduit and Sárközy in  generalized and extended this theory from the binary case to k-ary sequences, i.e., to k symbols. They constructed a large family of k-ary sequences with strong pseudorandom properties. In this paper our goal is to extend the study of the pseudorandom properties
mentioned above to k-ary sequences. The aim of this paper is twofold. First we will extend the definitions of collision and avalanche effect to
k-ary sequences, and then we will study these related properties in a large family of pseudorandom k-ary sequences with “small” pseudorandom measures.
In an earlier paper we studied collisions and avalanche effect in two of the most important constructions given for large
families of binary sequences possessing strong pseudorandom properties. It turned out that one of the two constructions (which
is based on the use of the Legendre symbol) is ideal from this point of view, while the other construction (which is based
on the size of the modulo p residue of f(n) for some polynomial f(x) ∈
[x]) is not satisfactory since there are “many” collisions in it. Here it is shown that this weakness of the second construction
can be corrected: one can take a subfamily of the given family which is just slightly smaller and collision free.
Recently a constructive theory of pseudorandomness of binary sequences has been developed and many constructions for binary
sequences with strong pseudorandom properties have been given. In the applications one usually needs large families of binary
sequences of this type. In this paper we adapt the notions of collision and avalanche effect to study these pseudorandom properties
of families of binary sequences. We test two of the most important constructions for these pseudorandom properties, and it
turns out that one of the two constructions is ideal from this point of view as well, while the other construction does not
possess these pseudorandom properties.
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.
The main aim of this paper is to present the concept of fault-injection backdoors in Random Number Generators. Backdoors can be activated by fault-injection techniques. Presented algorithms can be used in embedded systems like smart-cards and hardware security modules in order to implement subliminal channels in random number generators.
We prove a bound on sums of products of multiplicative characters of shifted Fermat quotients modulo p. From this bound we derive results on the pseudorandomness of sequences of modular discrete logarithms of Fermat quotients
modulo p: bounds on the well-distribution measure, the correlation measure of order ℓ, and the linear complexity.