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An Algorithm for Solving the LPN Problem and Its Application to Security Evaluation of the HB Protocols for RFID Authentication

  • Marc P. C. Fossorier
  • Miodrag J. Mihaljević
  • Hideki Imai
  • Yang Cui
  • Kanta Matsuura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4329)

Abstract

An algorithm for solving the “learning parity with noise” (LPN) problem is proposed and analyzed. The algorithm originates from the recently proposed advanced fast correlation attacks, and it employs the concepts of decimation, linear combining, hypothesizing and minimum distance decoding. However, as opposed to fast correlation attacks, no preprocessing phase is allowed for the LPN problem. The proposed algorithm appears as more powerful than the best one previously reported known as the BKW algorithm proposed by Blum, Kalai and Wasserman. In fact the BKW algorithm is shown to be a special instance of the proposed algorithm, but without optimized parameters. An improved security evaluation, assuming the passive attacks, of Hopper and Blum HB and HB +  protocols for radio-frequency identification (RFID) authentication is then developed. Employing the proposed algorithm, the security of the HB protocols is reevaluated, implying that the previously reported security margins appear as overestimated.

Keywords

cryptanalysis LPN problem fast correlation attacks HB protocols RFID authentication 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marc P. C. Fossorier
    • 1
  • Miodrag J. Mihaljević
    • 2
    • 4
  • Hideki Imai
    • 3
    • 4
  • Yang Cui
    • 5
  • Kanta Matsuura
    • 5
  1. 1.Department of Electrical EngineeringUniversity of HawaiiHonoluluUSA
  2. 2.Mathematical InstituteSerbian Academy of Sciences and ArtsBelgradeSerbia
  3. 3.Faculty of Science and EngineeringChuo UniversityTokyoJapan
  4. 4.Research Center for Information Security (RCIS)National Institute of Advanced Industrial Science and Technology (AIST)TokyoJapan
  5. 5.Institute of Industrial Science (IIS)University of TokyoTokyoJapan

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