Pseudorandom Binary Sequences: Quality Measures and Number-Theoretic Constructions
Summary :
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
Authors
Arne WINTERHOF
Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences
Keyword
Latest Issue
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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},}
Copy
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 -
English
