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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.12 pp.1452-1460

- Publication Date
- 2023/12/01

- Publicized
- 2023/05/31

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2023SDI0001

- Type of Manuscript
- Special Section INVITED PAPER (Special Section on Signal Design and Its Applications in Communications)

- Category
- Cryptography and Information Security

Arne WINTERHOF

Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences

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Arne WINTERHOF, "Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 12, pp. 1452-1460, December 2023, doi: 10.1587/transfun.2023SDI0001.

Abstract: 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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023SDI0001/_p

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@ARTICLE{e106-a_12_1452,

author={Arne WINTERHOF, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions},

year={2023},

volume={E106-A},

number={12},

pages={1452-1460},

abstract={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.},

keywords={},

doi={10.1587/transfun.2023SDI0001},

ISSN={1745-1337},

month={December},}

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TY - JOUR

TI - Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1452

EP - 1460

AU - Arne WINTERHOF

PY - 2023

DO - 10.1587/transfun.2023SDI0001

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E106-A

IS - 12

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - December 2023

AB - 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.

ER -