Pseudorandom sequences derived from automatic sequences

Mérai, László; Winterhof, Arne

doi:10.1007/s12095-022-00556-9

Cited by 3 publications

(1 citation statement)

References 76 publications

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“…A closely related measure of pseudorandomness, the well-distribution measure, that is, roughly speaking, the balance of the sequence along arithmetic progressions, was studied in the series of papers [1], [8], [33], [34], [37], [39], [46].…”

Section: Omega Sequence (For Integers and Polynomials)mentioning

confidence: 99%

Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions

Winterhof

2023

IEICE Trans. Fundamentals

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In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity, correlation measure of order k, expansion complexity and 2-adic complexity. The number-theoretic sequences are the Legendre sequence and the two-prime generator, the Thue-Morse sequence and its sub-sequence along squares, and the prime omega sequences for integers and polynomials.

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Section: Omega Sequence (For Integers and Polynomials)mentioning

confidence: 99%

Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions

Winterhof

2023

IEICE Trans. Fundamentals

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Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences

2021

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Automatic sequences are not suitable sequences for cryptographic applications since both their subword complexity and their expansion complexity are small, and their correlation measure of order 2 is large. These sequences are highly predictable despite having a large maximum order complexity. However, recent results show that polynomial subsequences of automatic sequences, such as the Thue–Morse sequence, are better candidates for pseudorandom sequences. A natural generalization of automatic sequences are morphic sequences, given by a fixed point of a prolongeable morphism that is not necessarily uniform. In this paper we prove a lower bound for the maximum order complexity of the sum of digits function in Zeckendorf base which is an example of a morphic sequence. We also prove that the polynomial subsequences of this sequence keep large maximum order complexity, such as the Thue–Morse sequence.

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Maximum-Order Complexity and 2-Adic Complexity

Chen,

Obrovsky

et al. 2024

IEEE Trans. Inform. Theory

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Pseudorandom sequences derived from automatic sequences

Cited by 3 publications

References 76 publications

Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions

Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions

Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences

Maximum-Order Complexity and 2-Adic Complexity

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