Random number generation using decimal cellular automata

Bhattacharjee, Kamalika; Das, Sukanta

doi:10.1016/j.cnsns.2019.104878

Cited by 8 publications

(4 citation statements)

References 21 publications

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“…In particular, past experience seems to indicate that the best way to employ CA in a symmetric cipher is as nonlinear transformations applied for a single time step, and combining their output with that of other non-CA components to improve diffusion. The best known example of this design pattern is the v transformation used in KECCAK (Bertoni et al 2011), which is now part of the SHA-3 standard for cryptographic hash functions.…”

Section: Cellular Automatamentioning

confidence: 99%

“…Cellular automata (CA) have been extensively investigated as a computational building block for designing several cryptographic primitives. The most famous examples include Wolfram's pseudorandom number generator for Vernam-like stream ciphers (Wolfram 1986), which was based on the chaotic dynamics of the elementary local rule 30 (later shown to be vulnerable to correlation and approximation attacks Meier and Staffelbach 1991;Koc and Apohan 1997), and the v nonlinear transformation by Daemen et al (1994), used as an S-box in KECCAK (Bertoni et al 2011) and other symmetric ciphers. As far as we know, most of these works focused on the study of certain local rules that, when plugged into a CA, would yield good cryptographic functions.…”

Section: Introductionmentioning

confidence: 99%

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Heuristic search of (semi-)bent functions based on cellular automata

et al. 2022

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An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter.

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Section: Cellular Automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Heuristic search of (semi-)bent functions based on cellular automata

et al. 2022

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“…Bhattacharjee et al [4] considered CA rules on a ternary alphabet with diameter d = 3, finding one rule that was able to pass several statistical and empirical tests for randomness. Later, Bhattacharjee et al [3] extended the scope of this investigation to CA with a decimal alphabet, finding a few rules whose randomness can compete with some of the best pseudorandom generators proposed in the literature, both based on CA and not.…”

Section: Related Workmentioning

confidence: 99%

Heuristic Search of (Semi-)Bent Functions based on Cellular Automata

Mariot¹,

Saletta²,

Leporati³

et al. 2021

Preprint

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An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata, focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter.

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“…Several works related to the PRNG design have been proposed; for example, there are strategies that implement PRNGs using linear feedback shift registers (LFSR) [1][2][3][4][5], while other strategies are based on block cipher [6], stream cipher [7], quantum walks [8], cellular automata [9,10], chaotic oscillators and artificial neural networks (ANN) [11], or chaotic maps [12][13][14][15]. There are also PRNG design approaches that combine several of the above strategies [16].…”

Section: Introductionmentioning

confidence: 99%

Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

et al. 2021

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In cryptography, the pseudorandom number sequences must have random appearance to be used in secure information systems. The skew tent map (STM) is an attractive map to produce pseudorandom sequences due to its easy implementation and the absence of stability islands when it is in chaotic behavior. Using the STM and sine function, we propose and analyze a function composition to propose a pseudorandom number generator (PRNG). In the analysis of the function composition, we use the bifurcation diagram and the Lyapunov exponent to perform a behavioral comparison against the STM. We show that the proposed function composition is more sensitive to initial conditions than the STM, and then it is a better option than the STM for cryptography applications. For the proposed function we determine and avoid the chaos annulling traps. The proposed PRNG can be configured to generate pseudorandom numbers of 8, 16 or 32 bits and it can be implemented on microcontrollers with different architectures. We evaluate the pseudorandomness of the proposed PRNG using the NIST SP 800-22 and TestU01 suites. Additionally, to evaluate its quality, we apply tests such as correlation coefficient, key sensitivity, statistical and entropy analysis, key space, linear complexity, and speed. Finally, we performed a comparison with similar PRNGs that produce pseudorandom sequences considering numbers of 8 and 32 bits. The results show that the proposed PRNG maintains its security regardless of the selected configuration. The proposed PRNG has five important features: easy implementation, configurable to produce number with 8, 16 or 32 bits, high processing speed, high linear complexity, and wide key space. These features are necessary for cryptographic systems.

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Random number generation using decimal cellular automata

Cited by 8 publications

References 21 publications

Heuristic search of (semi-)bent functions based on cellular automata

Heuristic search of (semi-)bent functions based on cellular automata

Heuristic Search of (Semi-)Bent Functions based on Cellular Automata

Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

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