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) depth if "sum mod p" gates with an unbounded number of inputs are allowed. Thus these CAs can be predicted by (idealized) parallel computers much faster than by explicit simulation, even though they are non-linear. This class includes any CA whose rule, when written as an algebra, is a solvable group. We also show that CAs based on nilpotent groups can be predicted in depth O(log t) or O(1) by circuits with binary or "sum mod p" gates respectively. We use these techniques to give an efficient algorithm for a CA rule which, like elementary CA rule 18, has diffusing defects that annihilate in pairs. This can be used to predict the motion of defects in rule 18 in O(log 2 t) parallel time. PACS Keywords: 02.10, 02.70, 05.45, 46.10 1 Introduction The...

Abstract. We present a new stream cipher, Rabbit, based on iterating a set of coupled nonlinear functions. Rabbit is characterized by a high performance in software with a measured encryption/decryption speed of 3.7 clock cycles per byte on a Pentium III processor. We have performed detailed security analysis, in particular, correlation analysis and algebraic investigations. The cryptanalysis of Rabbit did not reveal an attack better than exhaustive key search.

Simulating a cellular automaton (CA) for t time-steps into the future requires t 2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed linear because they obey a principle of superposition. This allows them to be predicted efficiently, in serial timeO(t) orO(log t) in parallel. In this paper, we generalize this by looking at CAs with a variety of algebraic structures, including quasigroups, non-Abelian groups, Steiner systems, and others. We show that in many cases, an efficient algorithm exists even though these CAs are not linear in the previous sense; we term them quasilinear. We find examples which can be predicted in serial time proportional to t, t log t, t log 2 t and t α for α < 2, and parallel time log t, log t log log t and log 2 t. We also discuss what algebraic properties are required or implied by the existence of scaling relations and principles of superposition, and exhibit several novel “vector-valued ” CAs. 1 Introduction: CAs

In the implementation of Radio Frequency Identification (RFID) systems concerns have been raised regarding information security and violations of end-user privacy. There is a large collection of literature available on efficient and inexpensive cryptographic engines, but they are still extravagant solutions for low cost RFID systems. Security and privacy provided by low cost RFID is both directly and indirectly limited by a number of factors that are unique to low cost RFID. This paper examines security and privacy issues regarding RFID and presents the challenges that arise in view of the unique environment presented by low cost RFID systems.

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Dynamical systems are often described as "unpredictable" or "complex " as aspects of their behavior may bear a cryptic relationship with the simple evolution laws which define them. Some theorists work to quantify this complexity in various ways. Others try to turn the cryptic nature of dynamical systems to a practical end: encryption of messages to preserve their secrecy. Here some previous efforts to engineer cryptosystems based on dynamical systems are reviewed, leading up to a detailed proposal for a cellular automaton cryptosystem. Cryptosystems constructed from cellular automaton primitives can be implemented in simply constructed massively parallel hardware. They can be counted on to deliver high encryption/decryption rates at low cost. In addition to these practical features, cellular automaton cryptosystems may help illuminate some foundational issues in both dynamical systems theory and cryptology, since each of these disciplines rests heavily on the meanings given to the int...

We propose the use of reversible cellular automata (RCA) as efficient encryption and decryption devices. The efficiency is due to their inherent parallelism. They can be used both as classical secret-key cryptosystems and as public-key systems. 1 Introduction The low speed of encryption and/or decryption causes often big problems when practical implementations of cryptosystems are built. This is true especially in connection with public-key cryptosystems, but in some contexts higher speed of secret-key systems would be necessary as well. Normally, the first solution to this problem is to replace software implementations with specialized hardware. If this is not enough, a usual approach is to make parallel implementation of encryption/decryption algorithms. In practice this can be difficult. If the cryptosystem is not especially constructed parallelism in mind it might be impossible to find efficient parallel algorithms for it. And even if parallelization is possible, in order to g...

Abstract — In this work, we present a general scheme for the design of block ciphers by means of Genetic Programming. In this vein, we try to evolve highly nonlinear and efficient functions to be used for the key expansion and the F-function of a Feistel network. Following this scheme, we propose a new block cipher design called Wheedham, that operates on 512 bit blocks and keys of 256 bits, of which we offer its C code (directly translated from the GP Trees) and some preliminary security results. I.

Abstract- The paper presents a new encryption algorithm based on one dimensional, uniform and reversible cellular automata (CA). A class of CA with ruler specifically constructed to be reversible is used. The quality of encryption depends en the type of ruler used, and randomness of the numbers used in the process of encryption. 1.

We have developed statistical techniques to study the structure the state-transition graphs of cellular automata with periodic boundary conditions, in the limit of large system size. We organize our results around the concept of a topological skeleton. The topological skeleton is the set of physically relevant states. Covering this skeleton is a surface, typically thin and dense, which contains the bulk of the set of states. States in the skeleton have some long histories. States on the surface, by contrast, have only short histories; they are reached only near the beginning of cellular automaton evolution. We study in detail a sequence of rules which exhibit mostly skeletal to mostly surface structure. 1 Introduction Consider a cellular automaton operating on a periodic lattice of cells. If the number of cells in the lattice is s, and the number of cell states is k, then there are k s possible lattice configurations. Each configuration maps to a new configuration under the action...