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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

10.1001/archfaci.10.2.116

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1573-7586

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On the largest affine subfamilies of a family of

Authors: Tian Tian WenFeng Qi
Publish Date: 2012/07/15
Volume: 71, Issue: 1, Pages: 163-181
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Abstract

Recently nonlinear feedback shift registers NFSRs have frequently been used as building blocks for designing stream ciphers Let NFSR g be an mstage NFSR with characteristic function g=x 0oplus g 1x 1cdots x m1oplus x m Up to now there has been no known method to determine whether the family of output sequences of the NFSR g denoted by Sg contains a subfamily of sequences that are exactly the output sequences of an NFSRf of stage n  m This paper studies affine cases that is finding an affine function f such that Sf is a subset of Sg If Sg contains an affine subfamily Sf whose order n is close to m then a large number of sequences generated by the NFSR g have low linear complexities First we give two methods to bound the maximal order of affine subfamilies included in Sg Experimental data indicate that if Sg contains an affine subfamily of order not smaller than m/2 then the upper bound given in the paper is tight Second we propose two algorithms to solve affine subfamilies of a given order n included in Sg both of which aim at affine subfamilies with the maximal order Algorithm 1 is applicable when n is close to m while the feasibility of Algorithm 2 relies on the distribution of nonlinear terms of g In particular if Algorithm 2 works then its computation complexity is less than that of Algorithm 1 and it is quite efficient for a number of cases

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Other Papers In This Journal:
  1. Composition of recursions and nonlinear complexity of periodic binary sequences
  2. Practical-time attacks against reduced variants of MISTY1
  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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