Decoding random binary linear codes in 2n/20: how 1 + 1 = 0 improves information set decoding

  • Authors:
  • Anja Becker;Antoine Joux;Alexander May;Alexander Meurer

  • Affiliations:
  • Laboratoire PRISM, Université de Versailles Saint-Quentin, France;Laboratoire PRISM, Université de Versailles Saint-Quentin, France and DGA, France;Horst Görtz Institute for IT-Security, Ruhr-University Bochum, Germany;Horst Görtz Institute for IT-Security, Ruhr-University Bochum, Germany

  • Venue:
  • EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
  • Year:
  • 2012

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Abstract

Decoding random linear codes is a well studied problem with many applications in complexity theory and cryptography. The security of almost all coding and LPN/LWE-based schemes relies on the assumption that it is hard to decode random linear codes. Recently, there has been progress in improving the running time of the best decoding algorithms for binary random codes. The ball collision technique of Bernstein, Lange and Peters lowered the complexity of Stern's information set decoding algorithm to 20.0556n. Using representations this bound was improved to 20.0537n by May, Meurer and Thomae. We show how to further increase the number of representations and propose a new information set decoding algorithm with running time 20.0494n.