IEICE TRANSACTIONS on Fundamentals
New Binary Sequences Derived from Euler Quotients Modulo pq and Their Generalizations
Summary :
Pseudorandom sequences with large linear complexity can resist the linear attack. The trace representation plays an important role in analysis and design of pseudorandom sequences. In this letter, we present the construction of a family of new binary sequences derived from Euler quotients modulo pq, where pq is a product of two primes and p divides q-1. Firstly, the linear complexity of the sequences are investigated. It is proved that the sequences have larger linear complexity and can resist the attack of Berlekamp-Massey algorithm. Then, we give the trace representation of the proposed sequences by determining the corresponding defining pair. Moreover, we generalize the result to the Euler quotients modulo pmqn with m≤n. Results indicate that the generalized sequences still have high linear complexity. We also give the trace representation of the generalized sequences by determining the corresponding defining pair. The result will be helpful for the implementation and the pseudorandom properties analysis of the sequences.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.4 pp.657-664
- Publication Date
- 2023/04/01
- Publicized
- 2022/09/30
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022EAP1069
- Type of Manuscript
- PAPER
- Category
- Coding Theory
Authors
Jiang MA
Yanshan University
Jun ZHANG
Tangshan Administration for Market Regulation
Yanguo JIA
Yanshan University
Xiumin SHEN
Yanshan University
Keyword
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Jiang MA, Jun ZHANG, Yanguo JIA, Xiumin SHEN, "New Binary Sequences Derived from Euler Quotients Modulo pq and Their Generalizations" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 4, pp. 657-664, April 2023, doi: 10.1587/transfun.2022EAP1069.
Abstract: Pseudorandom sequences with large linear complexity can resist the linear attack. The trace representation plays an important role in analysis and design of pseudorandom sequences. In this letter, we present the construction of a family of new binary sequences derived from Euler quotients modulo pq, where pq is a product of two primes and p divides q-1. Firstly, the linear complexity of the sequences are investigated. It is proved that the sequences have larger linear complexity and can resist the attack of Berlekamp-Massey algorithm. Then, we give the trace representation of the proposed sequences by determining the corresponding defining pair. Moreover, we generalize the result to the Euler quotients modulo pmqn with m≤n. Results indicate that the generalized sequences still have high linear complexity. We also give the trace representation of the generalized sequences by determining the corresponding defining pair. The result will be helpful for the implementation and the pseudorandom properties analysis of the sequences.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAP1069/_p
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@ARTICLE{e106-a_4_657,
author={Jiang MA, Jun ZHANG, Yanguo JIA, Xiumin SHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Binary Sequences Derived from Euler Quotients Modulo pq and Their Generalizations},
year={2023},
volume={E106-A},
number={4},
pages={657-664},
abstract={Pseudorandom sequences with large linear complexity can resist the linear attack. The trace representation plays an important role in analysis and design of pseudorandom sequences. In this letter, we present the construction of a family of new binary sequences derived from Euler quotients modulo pq, where pq is a product of two primes and p divides q-1. Firstly, the linear complexity of the sequences are investigated. It is proved that the sequences have larger linear complexity and can resist the attack of Berlekamp-Massey algorithm. Then, we give the trace representation of the proposed sequences by determining the corresponding defining pair. Moreover, we generalize the result to the Euler quotients modulo pmqn with m≤n. Results indicate that the generalized sequences still have high linear complexity. We also give the trace representation of the generalized sequences by determining the corresponding defining pair. The result will be helpful for the implementation and the pseudorandom properties analysis of the sequences.},
keywords={},
doi={10.1587/transfun.2022EAP1069},
ISSN={1745-1337},
month={April},}
Copy
TY - JOUR
TI - New Binary Sequences Derived from Euler Quotients Modulo pq and Their Generalizations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 657
EP - 664
AU - Jiang MA
AU - Jun ZHANG
AU - Yanguo JIA
AU - Xiumin SHEN
PY - 2023
DO - 10.1587/transfun.2022EAP1069
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2023
AB - Pseudorandom sequences with large linear complexity can resist the linear attack. The trace representation plays an important role in analysis and design of pseudorandom sequences. In this letter, we present the construction of a family of new binary sequences derived from Euler quotients modulo pq, where pq is a product of two primes and p divides q-1. Firstly, the linear complexity of the sequences are investigated. It is proved that the sequences have larger linear complexity and can resist the attack of Berlekamp-Massey algorithm. Then, we give the trace representation of the proposed sequences by determining the corresponding defining pair. Moreover, we generalize the result to the Euler quotients modulo pmqn with m≤n. Results indicate that the generalized sequences still have high linear complexity. We also give the trace representation of the generalized sequences by determining the corresponding defining pair. The result will be helpful for the implementation and the pseudorandom properties analysis of the sequences.
ER -
English
