Studies on the distribution of the shortest linear recurring sequences

被引：0

作者：

Yin, Qian ^{[1
]}

Yuan, Zhi-Yong ^{[2
]}

Guo, Ping ^{[1
]}

机构：

[1] Beijing Normal Univ, Image Proc & Pattern Recognit Lab, Beijing 100875, Peoples R China

[2] Wuhan Univ, Sch Comp Sci, Wuhan 430079, Peoples R China

来源：

INFORMATION SCIENCES | 2009年 / 179卷 / 14期

基金：

中国国家自然科学基金;

关键词：

Stream cipher; Matrix-representation method; Berlekamp-Massey algorithm; Distribution regulation; Shortest linear recurring sequences; SHIFT-REGISTER SYNTHESIS; STREAM CIPHERS; ALGORITHM;

D O I：

10.1016/j.ins.2009.01.042

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The distribution of the shortest linear recurrence (SLR) sequences in the Z/(p) field and over the Z/(p(e)) ring is studied. It is found that the length of the shortest linear recurrent (SLRL) is always equal to n/2, if n is even and n/2 + 1 if n is odd in the Z/(p) field, respectively. On the other hand, over the Z/(p(e)) ring, the number of sequences with length n can also be calculated. The recurring distribution regulation of the shortest linear recurring sequences is also found. To solve the problem of calculating the SLRL, a new simple representation of the Berlekamp-Massey algorithm is developed as well. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2379 / 2389

页数：11

共 50 条

[1] Further studies on the distribution of the shortest linear recurring sequences for the stream cipher over the ring
Yin, Qian
Yuan, Zhi-Yong
Guo, Ping
ADVANCED INTELLIGENT COMPUTING THEORIES AND APPLICATIONS: WITH ASPECTS OF CONTEMPORARY INTELLIGENT COMPUTING TECHNIQUES, 2007, 2 : 680 - +
[2] Special distribution of the shortest linear recurring sequences in Z/(p) field
Yin, Q
Luo, YL
Guo, P
COMPUTATIONAL INTELLIGENCE AND SECURITY, PT 2, PROCEEDINGS, 2005, 3802 : 43 - 48
[3] DISTRIBUTION OF LINEAR RECURRING SEQUENCES
NIEDERREITER, H
ARCHIV DER MATHEMATIK, 1980, 34 (06) : 526 - 533
[4] LINEAR RECURRING SEQUENCES
ZIERLER, N
JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1959, 7 (01): : 31 - 48
[5] Uniform distribution of linear recurring sequences modulo prime powers
Herendi, T
FINITE FIELDS AND THEIR APPLICATIONS, 2004, 10 (01) : 1 - 23
[6] Decimations of linear recurring sequences
Buck, M
Zierler, N
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 39 (11) : 95 - 102
[7] PRODUCTS OF LINEAR RECURRING SEQUENCES
ZIERLER, N
MILLS, WH
JOURNAL OF ALGEBRA, 1973, 27 (01) : 147 - 157
[8] SUBSEQUENCES IN LINEAR RECURRING SEQUENCES
IKAI, T
KOSAKO, H
KOJIMA, Y
ELECTRONICS & COMMUNICATIONS IN JAPAN, 1970, 53 (12): : 159 - &
[9] ON DECIMATION OF LINEAR RECURRING SEQUENCES
GOLIC, JD
FIBONACCI QUARTERLY, 1995, 33 (05): : 407 - 411
[10] A NOTE ON LINEAR RECURRING SEQUENCES
SINGH, S
LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 104 : 97 - 101

← 1 2 3 4 5 →