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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

10.1016/0370-2693(81)90818-2

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1573-7586

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Some results concerning cryptographically signific

Authors: E Pasalic P Charpin
Publish Date: 2010/02/06
Volume: 57, Issue: 3, Pages: 257-269
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Abstract

In this paper we investigate the existence of permutation polynomials of the form Fx = x d  + Lx over GF2 n L being a linear polynomial The results we derive have a certain impact on the longterm open problem on the nonexistence of APN permutations over GF2 n when n is even It is shown that certain choices of exponent d cannot yield APN permutations for even n When n is odd an infinite class of APN permutations may be derived from Gold mapping x 3 in a recursive manner that is starting with a specific APN permutation on GF2 k k odd APN permutations are derived over GF2k+2i for any i ≥ 1 But it is demonstrated that these classes of functions are simply affine permutations of the inverse coset of the Gold mapping x 3 This essentially excludes the possibility of deriving new EAinequivalent classes of APN functions by applying the method of Berveglieri et al approach proposed at Asiacrypt 2004 see 3 to arbitrary APN functions

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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. On the largest affine sub-families of a family of NFSR sequences
  4. The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
  5. On explicit factors of cyclotomic polynomials over finite fields
  6. Two classes of optimal two-dimensional OOCs
  7. Sequences with small correlation
  8. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  9. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  10. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  11. A new table of permutation codes
  12. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  13. Nonexistence of CW (110, 100)
  14. Point compression for the trace zero subgroup over a small degree extension field
  15. The Diffie–Hellman problem and generalization of Verheul’s theorem
  16. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  17. Improved lower bounds on sizes of single-error correcting codes
  18. A combinatorial problem related to sparse systems of equations
  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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