Decomposing Approach for Error Vectors of k-Error Linear Complexity of Certain Periodic Sequences
Summary :
The k-error linear complexity of periodic sequences is an important security index of stream cipher systems. By using an interesting decomposing approach, we investigate the intrinsic structure for the set of 2n-periodic binary sequences with fixed complexity measures. For k ≤ 4, we construct the complete set of error vectors that give the k-error linear complexity. As auxiliary results we obtain the counting functions of the k-error linear complexity of 2n-periodic binary sequences for k ≤ 4, as well as the expectations of the k-error linear complexity of a random sequence for k ≤ 3. Moreover, we study the 2t-error linear complexity of the set of 2n-periodic binary sequences with some fixed linear complexity L, where t < n-1 and the Hamming weight of the binary representation of 2n-L is t. Also, we extend some results to pn-periodic sequences over Fp. Finally, we discuss some potential applications.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.7 pp.1542-1555
- Publication Date
- 2014/07/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.1542
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Ming SU
Nankai University
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Ming SU, "Decomposing Approach for Error Vectors of k-Error Linear Complexity of Certain Periodic Sequences" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 7, pp. 1542-1555, July 2014, doi: 10.1587/transfun.E97.A.1542.
Abstract: The k-error linear complexity of periodic sequences is an important security index of stream cipher systems. By using an interesting decomposing approach, we investigate the intrinsic structure for the set of 2n-periodic binary sequences with fixed complexity measures. For k ≤ 4, we construct the complete set of error vectors that give the k-error linear complexity. As auxiliary results we obtain the counting functions of the k-error linear complexity of 2n-periodic binary sequences for k ≤ 4, as well as the expectations of the k-error linear complexity of a random sequence for k ≤ 3. Moreover, we study the 2t-error linear complexity of the set of 2n-periodic binary sequences with some fixed linear complexity L, where t < n-1 and the Hamming weight of the binary representation of 2n-L is t. Also, we extend some results to pn-periodic sequences over Fp. Finally, we discuss some potential applications.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.1542/_p
Copy
@ARTICLE{e97-a_7_1542,
author={Ming SU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Decomposing Approach for Error Vectors of k-Error Linear Complexity of Certain Periodic Sequences},
year={2014},
volume={E97-A},
number={7},
pages={1542-1555},
abstract={The k-error linear complexity of periodic sequences is an important security index of stream cipher systems. By using an interesting decomposing approach, we investigate the intrinsic structure for the set of 2n-periodic binary sequences with fixed complexity measures. For k ≤ 4, we construct the complete set of error vectors that give the k-error linear complexity. As auxiliary results we obtain the counting functions of the k-error linear complexity of 2n-periodic binary sequences for k ≤ 4, as well as the expectations of the k-error linear complexity of a random sequence for k ≤ 3. Moreover, we study the 2t-error linear complexity of the set of 2n-periodic binary sequences with some fixed linear complexity L, where t < n-1 and the Hamming weight of the binary representation of 2n-L is t. Also, we extend some results to pn-periodic sequences over Fp. Finally, we discuss some potential applications.},
keywords={},
doi={10.1587/transfun.E97.A.1542},
ISSN={1745-1337},
month={July},}
Copy
TY - JOUR
TI - Decomposing Approach for Error Vectors of k-Error Linear Complexity of Certain Periodic Sequences
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1542
EP - 1555
AU - Ming SU
PY - 2014
DO - 10.1587/transfun.E97.A.1542
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2014
AB - The k-error linear complexity of periodic sequences is an important security index of stream cipher systems. By using an interesting decomposing approach, we investigate the intrinsic structure for the set of 2n-periodic binary sequences with fixed complexity measures. For k ≤ 4, we construct the complete set of error vectors that give the k-error linear complexity. As auxiliary results we obtain the counting functions of the k-error linear complexity of 2n-periodic binary sequences for k ≤ 4, as well as the expectations of the k-error linear complexity of a random sequence for k ≤ 3. Moreover, we study the 2t-error linear complexity of the set of 2n-periodic binary sequences with some fixed linear complexity L, where t < n-1 and the Hamming weight of the binary representation of 2n-L is t. Also, we extend some results to pn-periodic sequences over Fp. Finally, we discuss some potential applications.
ER -
English
