Linear Complexity of Pseudorandom Sequences Derived from Polynomial Quotients: General Cases

• DU Xiaoni

  College of Mathematics and Statistics, Northwest Normal Univ. State Key Lab. of Integrated Service Networks, Xidian Univ.

• ZHANG Ji

  College of Mathematics and Statistics, Northwest Normal Univ. State Key Lab. of Integrated Service Networks, Xidian Univ.

• WU Chenhuang

  Key Lab of Applied Mathematics, Putian University

抄録

We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by $F(u)\equiv \frac{f(u)-f_p(u)}{p} ~(\bmod~ p), \qquad 0 \le F(u) \le p-1,~u\ge 0,$ where f_p(u)≡f(u) (mod p), for general polynomials $f(x)\in \mathbb{Z}[x]$. The linear complexity equals to one of the following values {p²-p,p²-p+1,p²-1,p²} if 2 is a primitive root modulo p², depending on p≡1 or 3 modulo 4 and the number of solutions of f'(u)≡0 (mod) p, where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d|(p-1) and d being a primitive root modulo p².

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E97.A (4), 970-974, 2014

  一般社団法人 電子情報通信学会

キーワード

• cryptography
• pseudorandom binary sequences
• polynomial quotients
• finite fields
• linear complexity

詳細情報

• CRID: 1390282681286774400
• NII論文ID: 130003394815
• DOI: 10.1587/transfun.e97.a.970
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E97.A/4/E97.A_970/_pdf
• 本文言語コード: en
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