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  • Cryptography
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  • 1
    Language: English
    In: IEEE Transactions on Circuits and Systems-I-Regular Papers, August, 2011, Vol.58(8), p.1897(12)
    Description: This paper presents a compression method that exploits pseudo-chaotic systems, to be applied to True Random Bit Generators (TRBGs). The theoretical explanation of the proposed compression scheme required the projection of some results achieved within the Ergodic Theory for chaotic systems on the world of digital pseudo-chaos. To this aim, a weaker and more general interpretation of the Shadowing Theory has been proposed, focusing on probability measures, rather than on single chaotic trajectories. The design of the compression scheme has been theoretically discussed in order to assure the final entropy of the compressed TRBG to be arbitrarily close to the maximum limit of 1 bit/time-step. The proposed solution requires extremely low-complex hardware circuits for being implemented, assures a constant throughput and is based on theoretical results of general validity.
    Keywords: Cryptography -- Technology Application ; Electric Generators -- Innovations ; Ergodic Theory -- Usage ; Stochastic Processes -- Usage
    ISSN: 1549-8328
    E-ISSN: 15580806
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  • 2
    Language: English
    In: IEEE Transactions on Circuits and Systems II: Express Briefs, October 2013, Vol.60(10), pp.702-706
    Description: A method is described for the construction of parameters' subspaces where Markov partitions can be found. The method is illustrated on the three-region piecewise linear 1-D (3PL1D) map, which is a popular approach for the chaos-based random number generator (RNG). For Markov partitions, the 3PL1D chaotic maps behave as Markov sources, and analytical calculation of its information entropy is possible, as demonstrated in this brief. From the knowledge of the stochastic transition matrix of the Markov source, one can exactly measure the appropriateness of the RNG in a given area. For classical RNGs, one typically relies on statistical tests as a quality indicator. Mathematical calculation of the quality of an RNG based on the 3PL1D chaotic maps makes the statistical tests useful only in the postimplementation phase as a verification of the hardware implementation.
    Keywords: Markov Processes ; Entropy ; Chaos ; Generators ; Cryptography ; Polynomials ; Information Entropy ; Chaos ; Information Entropy ; Markov Processes ; Random Number Generation (Rng) ; Engineering
    ISSN: 1549-7747
    E-ISSN: 1558-3791
    Source: IEEE Conference Publications
    Source: IEEE Journals & Magazines 
    Source: IEEE Xplore
    Source: IEEE Journals & Magazines
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  • 3
    Language: English
    In: IEEE Transactions on Circuits and Systems-I: Fundamental Theory..., Jan, 2003, Vol.50(1), p.123(4)
    Description: Different possibilities of using chaotic maps as pseudorandom number generators are discussed. A class of chaos-based pseudorandom bit generators is constructed. We give simple arguments to explain the unpredictability of the generators. Index Terms--Chaos, pseudorandom numbers.
    Keywords: Chaos Theory ; Random Numbers ; Chaotic Systems
    ISSN: 1057-7122
    E-ISSN: 15581268
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  • 4
    Language: English
    In: IEEE Transactions on Circuits and Systems-I-Regular Papers, June, 2006, Vol.53(6), p.1300(10)
    Description: We propose a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by proving that, for large classes of chaotic maps, the corresponding discrete Lyapunov exponent approaches the largest Lyapunov exponent of a chaotic map when M [right arrow] [infinity], where M is the cardinality of the discrete phase space. In analogy with continuous systems, we say the system has discrete chaos if its discrete Lyapunov exponent tends to a positive number, when M [right arrow] [infinity]. We present several examples to illustrate the concepts being introduced. Index Terms--Chaos, discrete chaos, Lyapunov components.
    Keywords: Chaos Theory -- Analysis ; Liapunov Functions -- Usage ; Discrete Time Systems -- Usage
    ISSN: 1549-8328
    E-ISSN: 15580806
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  • 5
    Language: English
    In: IEEE Transactions on Circuits and Systems-I: Fundamental Theory..., Jan, 2003, Vol.50(1), p.121(3)
    Description: We establish that the algorithm proposed recently by Jakimoski and Kocarev is secure against differential and linear attacks. Index Terms--Block-encryption cipher, chaos-based cryptography, differential and linear probabilities.
    Keywords: Cryptography -- Research
    ISSN: 1057-7122
    E-ISSN: 15581268
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  • 6
    In: IEEE Transactions on Circuits and Systems-I: Fundamental Theory..., Feb, 2001, Vol.48(2), p.163
    Description: This paper is devoted to the analysis of the impact of chaos-based techniques on block encryption ciphers. We present several chaos based ciphers. Using the well-known principles in the cryptanalysis we show that these ciphers do not behave worse than the standard ones, opening in this way a novel approach to the design of block encryption ciphers. Index Terms--Block encryption ciphers, chaos, cryptography, S-boxes.
    Keywords: Data Encryption -- Research ; Cryptography -- Research
    ISSN: 1057-7122
    E-ISSN: 15581268
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  • 7
    In: IEEE Transactions on Circuits and Systems-I: Fundamental Theory..., March, 2001, Vol.48(3), p.281
    Description: This paper and its companion (Part II) are devoted to the analysis of the application of a chaotic piecewise-linear one-dimensional(PL1D) map as random number generator (RNG). Piecewise linearity of the map enables us to mathematically find parameter values for which a generating partition is Markov and the RNG behaves as a Markov information source, and then to mathematically analyze the information generation process and the RNG. In the companion paper we discuss practical aspects of our chaos-based RNGs. Index Terms--Chaos, random number generator, symbolic dynamics.
    Keywords: Random Number Generators (Software) -- Models ; Chaotic Systems -- Usage ; Markov Processes -- Analysis
    ISSN: 1057-7122
    E-ISSN: 15580806
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  • 8
    Language: English
    In: IEEE Transactions on Circuits and Systems-II-Express Briefs, Oct, 2007, Vol.54(10), p.882(5)
    Description: In a recent paper, Jakimoski and Subbalakshmi provided a nice connection between the so-called discrete Lyapunov exponent of a permutation F defined on a finite lattice and its maximal differential probability, a parameter that measures the complexity of a differential cryptanalysis attack on the substitution defined by F. In this brief, we take a second look at their result to find some practical shortcomings. We also discuss more general aspects. Index Terms--Differential cryptanalysis, discrete Lyapunov exponent (DLE), maximum differential probability (DP).
    Keywords: Liapunov Functions -- Evaluation ; Probability Theory -- Research ; Cryptography -- Research
    ISSN: 1549-7747
    E-ISSN: 15583791
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  • 9
    Language: English
    In: IEEE Transactions on Circuits and Systems-I-Regular Papers, June, 2006, Vol.53(6), p.1341(12)
    Description: Digital chaotic ciphers have been investigated for more than a decade. However, their overall performance in terms of the tradeoff between security and speed, as well as the connection between chaos and cryptography, has not been sufficiently addressed. We propose a chaotic Feistel cipher and a chaotic uniform cipher. Our plan is to examine crypto components from both dynamical-system and cryptographicai points of view, thus to explore connection between these two fields. In the due course, we also apply dynamical system theory to create cryptographically secure transformations and evaluate cryptographical security measures. Index Terms--Block cipher, chaos, cryptography, differential probability, linear probability.
    Keywords: Cryptography -- Analysis ; Chaos Theory -- Analysis ; Ciphers -- Analysis
    ISSN: 1549-8328
    E-ISSN: 15580806
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  • 10
    Language: English
    In: Physics Letters A, 2006, Vol.355(1), pp.27-31
    Description: Chaotic maps can mimic random behavior in a quite impressive way. In particular, those possessing a generating partition can produce any symbolic sequence by properly choosing the initial state. We study in this Letter the ability of chaotic maps to generate order patterns and come to the conclusion that their performance in this respect falls short of expectations. This result reveals some basic limitation of a deterministic dynamic as compared to a random one. This being the case, we propose a non-statistical test based on ‘forbidden’ order patterns to discriminate chaotic from truly random time series with, in principle, arbitrarily high probability. Some relations with discrete chaos and chaotic cryptography are also discussed.
    Keywords: Chaotic Maps ; Order Patterns ; Permutation Entropy ; Discrete Lyapunov Exponent ; Chaotic Cryptography ; Physics
    ISSN: 0375-9601
    E-ISSN: 1873-2429
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