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A pseudorandom number generator is widely used in cryptography. A cryptographic pseudorandom number generator is required to generate pseudorandom numbers which have good statistical properties as well as unpredictability. An m-sequence is…
It is shown that pairs of maximal linear recursive sequences (m-sequences) typically have mean square aperiodic crosscorrelation on par with that of random sequences, but that if one takes a pair of m-sequences where one is the reverse of…
An $m$-sequence is the one of the largest period among those produced by a linear feedback shift register. It possesses several desirable features of pseudorandomness such as balance, uniform pattern distribution and ideal autocorrelation…
Pseudorandom number generators have been widely used in Monte Carlo methods, communication systems, cryptography and so on. For cryptographic applications, pseudorandom number generators are required to generate sequences which have good…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
Subgraph and homomorphism counting are fundamental algorithmic problems. Given a constant-sized pattern graph $H$ and a large input graph $G$, we wish to count the number of $H$-homomorphisms/subgraphs in $G$. Given the massive sizes of…
The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity…
Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional…
We introduce hypergeometric-type sequences. They are linear combinations of interlaced hypergeometric sequences (of arbitrary interlacements). We prove that they form a subring of the ring of holonomic sequences. An interesting family of…
A scheme for pseudo-random binary sequence generation based on the two-dimensional discrete-time Henon map is proposed. Properties of the proposed sequences pertaining to linear complexity, linear complexity profile, correlation and…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Binary $m$-sequences are ones with the largest period $n=2^m-1$ among the binary sequences produced by linear shift registers with length $m$. They have a wide range of applications in communication since they have several desirable…
A sequence is difference algebraic (or D-algebraic) if finitely many shifts of its general term satisfy a polynomial relationship; that is, they are the coordinates of a generic point on an affine hypersurface. The corresponding equations…
A Skolem sequence is a linear arrangement of the multiset, {1, 1, 2, 2, ..., n, n} such that if r in [n] appears in positions i and j, then |i-j| = r. We first translate the problem to a particular set of perfect matchings, then apply the…
During the last two decades, many kinds of periodic sequences with good pseudo-random properties have been constructed from classical and generalized cyclotomic classes, and used as keystreams for stream ciphers and secure communications.…
A linear graph is a graph whose vertices are totally ordered. Biological and linguistic sequences with interactions among symbols are naturally represented as linear graphs. Examples include protein contact maps, RNA secondary structures…
Sequences with high linear complexity have wide applications in cryptography. In this paper, a new class of quaternary sequences over $\mathbb{F}_4$ with period $2p^mq^n$ is constructed using generalized cyclotomic classes. Results show…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
In this paper, the linear complexity over $\mathbf{GF}(r)$ of generalized cyclotomic quaternary sequences with period $2pq$ is determined, where $ r $ is an odd prime such that $r \ge 5$ and $r\notin \lbrace p,q\rbrace$. The minimal value…