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A New Analysis of the McEliece Cryptosystem Based on QC-LDPC Codes

  • Marco Baldi
  • Marco Bodrato
  • Franco Chiaraluce
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5229)

Abstract

We improve our proposal of a new variant of the McEliece cryptosystem based on QC-LDPC codes. The original McEliece cryptosystem, based on Goppa codes, is still unbroken up to now, but has two major drawbacks: long key and low transmission rate. Our variant is based on QC-LDPC codes and is able to overcome such drawbacks, while avoiding the known attacks. Recently, however, a new attack has been discovered that can recover the private key with limited complexity. We show that such attack can be avoided by changing the form of some constituent matrices, without altering the remaining system parameters. We also propose another variant that exhibits an overall increased security level. We analyze the complexity of the encryption and decryption stages by adopting efficient algorithms for processing large circulant matrices. The Toom-Cook algorithm and the short Winograd convolution are considered, that give a significant speed-up in the cryptosystem operations.

Keywords

McEliece cryptosystem QC-LDPC codes Cryptanalysis Toom-Cook Winograd 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Marco Baldi
    • 1
  • Marco Bodrato
    • 2
  • Franco Chiaraluce
    • 1
  1. 1.DEIT, Università Politecnica delle MarcheAnconaItaly
  2. 2.Centro Vito VolterraUniversità di Roma Tor VergataRomaItaly

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