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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/bf01676190

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1573-7586

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Distinguisherbased attacks on publickey cryptosy

Authors: Alain Couvreur Philippe Gaborit Valérie GauthierUmaña Ayoub Otmani JeanPierre Tillich
Publish Date: 2014/04/20
Volume: 73, Issue: 2, Pages: 641-666
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Abstract

Because of their interesting algebraic properties several authors promote the use of generalized Reed–Solomon codes in cryptography Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure Wieschebrink proposed a variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed–Solomon code More recently new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee and a variation of the McEliece cryptosystem proposed by Baldi et al which hides the generalized Reed–Solomon code by means of matrices of very low rank In this work we show how to mount keyrecovery attacks against these publickey encryption schemes We use the concept of distinguisher which aims at detecting a behavior different from the one that one would expect from a random code All the distinguishers we have built are based on the notion of componentwise product of codes It results in a powerful tool that is able to recover the secret structure of codes when they are derived from generalized Reed–Solomon codes Lastly we give an alternative to Sidelnikov and Shestakov attack by building a filtration which enables to completely recover the support and the nonzero scalars defining the secret generalized Reed–Solomon code


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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. 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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