On the linear complexity profile of some sequences derived from elliptic curves

详细信息    查看全文

• 作者：László Mérai ; Arne Winterhof
• 刊名：Designs, Codes and Cryptography
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：81
• 期：2
• 页码：259-267
• 全文大小：395 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Coding and Information Theory
  Data Structures, Cryptology and Information Theory
  Data Encryption
  Discrete Mathematics in Computer Science
  Information, Communication and Circuits
  
• 出版者：Springer Netherlands
• ISSN：1573-7586
• 卷排序：81

文摘

For a given elliptic curve \(\mathbf {E}\) over a finite field of odd characteristic and a rational function f on \(\mathbf {E}\) we first study the linear complexity profiles of the sequences f(nG), \(n=1,2,\dots \) which complements earlier results of Hess and Shparlinski. We use Edwards coordinates to be able to deal with many f where Hess and Shparlinski’s result does not apply. Moreover, we study the linear complexities of the (generalized) elliptic curve power generators \(f(e^nG)\), \(n=1,2,\dots \) We present large families of functions f such that the linear complexity profiles of these sequences are large.KeywordsLinear complexityElliptic curvesEdwards coordinatesElliptic curve generatorPower generatorElliptic curve power generator