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We discuss a class of cellular automata (CA) able to produce long random strings, starting from short "seed" strings. The approach uses two principles borrowed from cryptography: diffusion and confusion. We show numerically that the strings…
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…
Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two…
Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here we study the classic model of weakly activated cascades and obtain…
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…
Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in…
The autocorrelation and the linear complexity of a key stream sequence in a stream cipher are important cryptographic properties. Many sequences with these good properties have interleaved structure, three classes of binary sequences of…
We show that a wide variety of non-linear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depth O(log^2 t) using gates with binary inputs, or O(log t)…
The application of a nonlinear filtering function to a Linear Feedback Shift Register (LFSR) is a general technique for designing pseudorandom sequence generators with cryptographic application. In this paper, we investigate the equivalence…
The notion of branch numbers of a linear transformation is crucial for both linear and differential cryptanalysis. The number of non-zero elements in a state difference or linear mask directly correlates with the active S-Boxes. The…
Cryptographic algorithms and protocols often need unique random numbers as parameters (e.g. nonces). Failure to satisfy this requirement lead to vulnerable implementation and can result in security breach. We show how linear types and…
Many constraints restricting the result of some computations over an integer sequence can be compactly represented by register automata. We improve the propagation of the conjunction of such constraints on the same sequence by synthesising…
A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…
This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
Using non-linear difference equations, combined with symbolic computations, we make a detailed study of the running times of numerous variants of the celebrated Quicksort algorithms, where we consider the variants of single-pivot and…