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Predicting nonlinear cellular automata quickly by decomposing them into linear ones
 Physica D
, 1998
"... We show that a wide variety of nonlinear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depthO(log 2 t) using gates with binary inputs, orO(log t) depth if “sum mod p ” gates with an unbounded number of inputs ..."
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Cited by 18 (7 self)
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We show that a wide variety of nonlinear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depthO(log 2 t) using gates with binary inputs, orO(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 nonlinear. 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
Rabbit: A new highperformance stream cipher
 Proc. Fast Software Encryption 2003, volume 2887 of LNCS
, 2003
"... 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 securit ..."
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Cited by 16 (6 self)
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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.
Quasilinear Cellular Automata
 Physica D
, 1997
"... Simulating a cellular automaton (CA) for t timesteps 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 e ..."
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Cited by 14 (4 self)
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Simulating a cellular automaton (CA) for t timesteps 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, nonAbelian 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 “vectorvalued ” CAs. 1 Introduction: CAs
LowCost RFID Systems: Confronting Security and Privacy
 In: AutoID Labs Research Workshop
, 2005
"... In the implementation of Radio Frequency Identification (RFID) systems concerns have been raised regarding information security and violations of enduser privacy. There is a large collection of literature available on efficient and inexpensive cryptographic engines, but they are still extravagant s ..."
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Cited by 11 (0 self)
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In the implementation of Radio Frequency Identification (RFID) systems concerns have been raised regarding information security and violations of enduser 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.
Cryptography with Dynamical Systems
 In: Cellular Automata and Cooperative Phenomena, Eds: E. Goles and N. Boccara
, 1993
"... 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 sy ..."
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Cited by 9 (1 self)
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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...
Cryptosystems Based on Reversible Cellular Automata
, 1992
"... 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 secretkey cryptosystems and as publickey systems. 1 Introduction The low speed of encryption and/or ..."
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Cited by 8 (0 self)
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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 secretkey cryptosystems and as publickey 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 publickey cryptosystems, but in some contexts higher speed of secretkey 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...
A cellular automaton based fast oneway hash function suitable for hardware implementation
 In Public Key Cryptography, number 1431 in Lecture Notes in Computer Science
, 1998
"... Abstract. Oneway hash functions are an important toolinachieving authentication and data integrity. The aim of this paper is to propose anovel oneway hash function based on cellular automata whose cryptographic properties have been extensivelystudiedover the past decade or so. Furthermore, securit ..."
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Cited by 6 (0 self)
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Abstract. Oneway hash functions are an important toolinachieving authentication and data integrity. The aim of this paper is to propose anovel oneway hash function based on cellular automata whose cryptographic properties have been extensivelystudiedover the past decade or so. Furthermore, security of the proposed oneway hash function is analyzed by the use of very recently published results on applications of cellular automata in cryptography. The analysis indicates that the oneway hash function is secure against all known attacks. An important feature of the proposed oneway hash function is that it is especially suitable for compact and fast implementation in hardware, which is particularly attractive to emerging security applications that employ smart cards, such asdigital identi cation cards and electronic cash payment protocols, 1
Wheedham: An Automatically Designed Block Cipher by means of Genetic Programming
"... 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 Ffunction of a Feistel network. Following this scheme, we propose a ..."
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Cited by 5 (3 self)
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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 Ffunction 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.
Inversion of Cellular Automata Iterations
 IEE PROCEEDINGS: COMPUTERS AND DIGITAL TECHNIQUES, 144(5):279284, SEPTEMBER 1997.
, 1997
"... We describe an algorithm for inverting an iteration of the onedimensional cellular automaton. The algorithm is based on the linear approximation of the updating function, and requires less than exponential time for particular classes of updating functions and seed values. For example, an ncell ..."
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Cited by 5 (0 self)
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We describe an algorithm for inverting an iteration of the onedimensional cellular automaton. The algorithm is based on the linear approximation of the updating function, and requires less than exponential time for particular classes of updating functions and seed values. For example, an ncell cellular automaton based on the updating function CA30 can be inverted in O#n# time for certain seed values, and at most 2 n=2 trials are required for arbitrary seed values. The inversion algorithm requires at most 2 #q,1##1,##n trials for arbitrary nonlinear functions and seed values, where q is the number of variables of the updating function, and # is the probability of agreement between the function and its best affine approximation. The inversion algorithm coupled with the method of Meier and Staffelbach #6# becomes a powerful tool to cryptanalyze the random number generators based on onedimensional cellular automata, showing that these random number generators provide less amount...