Sequences with almost perfect linear complexity profiles and curves over finite fields

  • Authors:
  • Chaoping Xing;Kwok Yan Lam

  • Affiliations:
  • Sch. of Comput., Nat. Univ. of Singapore;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

For stream ciphers, we need to generate pseudorandom sequences which are of properties of unpredictability and randomness. A important measure of unpredictability and randomness is the linear complexity profile (l.c.p.) la(n) of a sequence a. A sequence a is called almost perfect if the l.c.p. is la(n)=n/2+O(1). Based on curves over finite fields, we present a method to construct almost perfect sequences. We also illustrate our construction by explicit examples from the projective line and elliptic curves over the binary field