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Title of Journal: Des Codes Cryptogr

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Abbravation: Designs, Codes and Cryptography

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Springer US

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DOI

10.1007/978-3-642-02965-3_9

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1573-7586

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Composition of recursions and nonlinear complexity

Authors: George Petrides Johannes Mykkeltveit
Publish Date: 2008/03/06
Volume: 49, Issue: 1-3, Pages: 251-264
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Abstract

We investigate further the new approach towards the classification of periodic binary sequences into nonlinear complexity classes that commenced in the paper by Petrides and Mykkeltveit Proceedings of SETA’06 international conference on sequences and their applications 2006 Nonlinear complexity was first introduced by Jansen Investigations on nonlinear streamcipher systems construction and evaluation methods PhD thesis 1989 and several attempts have since been made to make it of more practical cryptographic interest In this direction we will follow with this article In particular we perform composition of the recursions found in the 2006 article which are related to nonlinear complexity and prove some of its missing results Studying the properties of the composition operation for a certain type of recursions is an alternative to study all possible recursions as required for completing the above mentioned classification A complete classification will allow amongst other things construction of statistical tests to assess the cryptographic strength of binary sequences used in stream ciphers

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Other Papers In This Journal:
  1. Practical-time attacks against reduced variants of MISTY1
  2. On the largest affine sub-families of a family of NFSR sequences
  3. The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
  4. On explicit factors of cyclotomic polynomials over finite fields
  5. Two classes of optimal two-dimensional OOCs
  6. Sequences with small correlation
  7. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  8. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  9. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  10. A new table of permutation codes
  11. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  12. Nonexistence of CW (110, 100)
  13. Point compression for the trace zero subgroup over a small degree extension field
  14. The Diffie–Hellman problem and generalization of Verheul’s theorem
  15. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  16. Improved lower bounds on sizes of single-error correcting codes
  17. A combinatorial problem related to sparse systems of equations
  18. Some results concerning cryptographically significant mappings over GF(2 n )
  19. A note on the reducibility of binary affine polynomials
  20. Primitive normal bases for quartic and cubic extensions: a geometric approach
  21. Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$
  22. Some cyclic codes of length 2 p n
  23. On the correlation distribution of Delsarte–Goethals sequences
  24. Algebraic decoding of folded Gabidulin codes
  25. Inner balance of symmetric designs
  26. On the construction of Griesmer codes of dimension 5
  27. Applications of representation theory to wireless communications
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