Decoding Random Binary Linear Codes in 2n/20: How 1 + 1 = 0 Improves Information Set Decoding

  • Anja Becker
  • Antoine Joux
  • Alexander May
  • Alexander Meurer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7237)

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.

Keywords

Information Set Decoding Representation Technique 

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Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Anja Becker
    • 1
  • Antoine Joux
    • 1
    • 2
  • Alexander May
    • 3
  • Alexander Meurer
    • 3
  1. 1.Laboratoire PRISMUniversité de Versailles Saint-QuentinFrance
  2. 2.DGAFrance
  3. 3.Horst Görtz Institute for IT-SecurityRuhr-University BochumGermany

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