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The Hardness of Code Equivalence over \(\mathbb{F}_q\) and Its Application to Code-Based Cryptography

  • Nicolas Sendrier
  • Dimitris E. Simos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7932)

Abstract

The code equivalence problem is to decide whether two linear codes over \(\mathbb{F}_{q}\) are identical up to a linear isometry of the Hamming space. In this paper, we review the hardness of code equivalence over \(\mathbb{F}_q\) due to some recent negative results and argue on the possible implications in code-based cryptography. In particular, we present an improved version of the three-pass identification scheme of Girault and discuss on a connection between code equivalence and the hidden subgroup problem.

Keywords

Code Equivalence Isometry Hardness Zero-Knowledge Protocols Quantum Fourier Sampling Linear Codes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nicolas Sendrier
    • 1
  • Dimitris E. Simos
    • 1
    • 2
  1. 1.Project-Team SECRETINRIA Paris-RocquencourtLe Chesnay CedexFrance
  2. 2.SBA ResearchViennaAustria

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