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Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
Marsaglia proposed recently xorshift generators as a class of very fast, good-quality pseudorandom number generators. Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing several…
Many automatic sequences, such as the Thue-Morse sequence or the Rudin-Shapiro sequence, have some desirable features of pseudorandomness such as a large linear complexity and a small well-distribution measure. However, they also have some…
We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…
In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of…
Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable…
We have introduced in former work the concept of Deep Randomness and its interest to design Unconditionally Secure communication protocols. We have in particular given an example of such protocol and introduced how to design a Deep Random…
Recent advancements in graph representation learning have shifted attention towards dynamic graphs, which exhibit evolving topologies and features over time. The increased use of such graphs creates a paramount need for generative models…
Leap generators have been introduced in [Duchon et al.'04] for exact-size random generation of structures in a class of the form $\mathcal{C}=\mathrm{Seq}(\mathcal{B})$ (sequence construction), in the supercritical case. We extend these…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…
The linear complexity of a sequence has been used as an important measure of keystream strength, hence designing a sequence which possesses high linear complexity and $k$-error linear complexity is a hot topic in cryptography and…
Marsaglia recently introduced a class of xorshift random number generators (RNGs) with periods 2n-1 for n = 32, 64, etc. Here we give a generalisation of Marsaglia's xorshift generators in order to obtain fast and high-quality RNGs with…
The sequences produced by the cryptographic sequence generator known as the shrinking generator can be modelled as the output sequences of linear elementary cellular automata. These sequences are composed of interleaved m-sequences produced…
For discrete data, the likelihood $P(x)$ can be rewritten exactly and parametrized into $P(X = x) = P(X = x | H = f(x)) P(H = f(x))$ if $P(X | H)$ has enough capacity to put no probability mass on any $x'$ for which $f(x')\neq f(x)$, where…
The generation of pseudorandom elements over finite fields is fundamental to the time, space and randomness complexity of randomized algorithms and data structures. We consider the problem of generating $k$-independent random values over a…
We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We…
We propose a unified deep learning framework for the generation and analysis of driving scenario trajectories, and validate its effectiveness in a principled way. To model and generate scenarios of trajectories with different lengths, we…
A technique for controlling errors in the functioning of nodes for the formation of $q$-valued pseudo-random sequences (PRS) operating under both random errors and errors generated through intentional attack by an attacker is provided, in…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…