Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes Academic Article

journal

  • Designs, Codes, and Cryptography

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 key-recovery attacks against these public-key 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 component-wise 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 non-zero scalars defining the secret generalized Reed-Solomon code. © 2014 Springer Science+Business Media New York.

publication date

  • 2014/1/1

keywords

  • Alternatives
  • Attack
  • Business
  • Concepts
  • Cryptography
  • Cryptosystem
  • Filtration
  • Generator
  • Homomorphic Encryption
  • Industry
  • Key Recovery
  • Public Key Encryption
  • Public-key Cryptosystem
  • Recovery
  • Reed-Solomon Codes
  • Reed-Solomon codes
  • Scalar

International Standard Serial Number (ISSN)

  • 0925-1022

number of pages

  • 26

start page

  • 641

end page

  • 666