The 1984 article by Martin, Odlyzko and Wolfram on Wolfram’s Rule 90 heightened interest in the area of linear cellular automata defined on a vector space over a finite field [8]. In this article we find the closed form expression for the minimal polynomial of Rule 90, which is then used to completely characterize the dynamics of the map. In addition, we show that the standard basis vectors in ...

Quantum-dot cellular automata (QCA) are a promising nanotechnology to implement digital circuits at the nanoscale. Devices based on QCA have the advantages of faster speed, lower power consumption, and greatly reduced sizes. In this paper, we are presented the circuits, which generate random numbers in QCA.  Random numbers have many uses in science, art, statistics, cryptography, gaming, gambli...

Since Richard Feynman introduced the notion of quantum computation in 1982, various models of \quantum computers" have been proposed. These models include quantum Turing machines and quantum circuits. In this paper we deene another quantum computational model, one-dimensional quantum cellular automata, and demonstrate that any quantum Turing machine can be eeciently simulated by a one-dimension...

S-Box is the only non-linear component in Advanced Encryption Standard(AES) which determine its strength. The Look-Up Table based S-Box of conventional AES occupies large storage space, reduced throughput and consumes more power. This article presents the design of an S-Box based on Reversible Cellular Automata function that reduces the implementation cost. Further, Cellular Automata functions ...

The paper considers a family of formal grammars that extends linear context-free grammars with an operator for referring to the left context of a substring being defined, as well as with a conjunction operation (as in linear conjunctive grammars). These grammars are proved to be computationally equivalent to an extension of one-way real-time cellular automata with an extra data channel. The mai...

In this paper we study number-decreasing cellular automata. They form a super-class of standard number-conserving cellular automata. It is well-known that the property of being number-conserving is decidable in quasi-linear time. In this paper we prove that being number-decreasing is dimension sensitive i.e. it is decidable for one-dimensional cellular automata and undecidable for dimension 2 o...

This paper reports classification of CA (cellular automata) rules targeting efficient synthesis of reversible cellular automata. An analytical framework is developed to explore the properties of CA rules for 3-neighborhood 1-dimensional CA. It is found that in two-state 3neighborhood CA, the CA rules fall into 6 groups depending on their potential to form reversible CA. The proposed classificat...

This work proposes a known-plaintext attack on the Shrinking Generator through its characterization by means of Cellular Automata. It is based on the computation of the characteristic polynomials of sub-automata and on the generation of the Galois field associated to one of the Linear Feedback Shift Registers components of the generator. The proposed algorithm allows predicting a large number o...

In recent years, cellular automata eCA) have been found capable of producing complex behavior. Some examples of cellular automata show remarkably regular behavior on finite configurations. On simple initial configurations, the generated pattern might be fractal or selfsimilar. In this paper, regular evolution of totalistic linear CA is investigated. In particular, it is shown that additive CA w...

Cellular automata (CA) are considered to be a non-linear model of complex systems in which an infinite one-dimensional array of finite state machines (cells) updates itself in a synchronous manner according to a uniform local rule. We study a sequence generation problem on a special restricted class of cellular automata having 1-bit inter-cell communications (CA1−bit) and propose several state-...