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Practical Algebraic Attacks on the Hitag2 Stream Cipher

  • Nicolas T. Courtois
  • Sean O’Neil
  • Jean-Jacques Quisquater
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5735)

Abstract

Hitag2 is a stream cipher that is widely used in RFID car locks in the automobile industry. It can be seen as a (much) more secure version of the [in]famous Crypto-1 cipher that is used in MiFare Classic RFID products [14,20,15]. Recently, a specification of Hitag2 was circulated on the Internet [29]. Is this cipher secure w.r.t. the recent algebraic attacks [8,17,1,25] that allowed to break with success several LFSR-based stream ciphers? After running some computer simulations we saw that the Algebraic Immunity [25] is at least 4 and we see no hope to get a very efficient attack of this type.

However, there are other algebraic attacks that rely on experimentation but nevertheless work. For example Faugère and Ars have discovered that many simple stream ciphers can be broken experimentally with Gröbner bases, given an extremely small quantity of keystream, see [17]. Similarly reduced-round versions of DES [9] and KeeLoq [11,12] were broken using SAT solvers, that actually seem to outperform Gröbner basis techniques. Thus, we have implemented a generic experimental algebraic attack with conversion and SAT solvers,[10,9]. As a result we are able to break Hitag2 quite easily, the full key can be recovered in a few hours on a PC. In addition, given the specific protocol in which Hitag2 cipher is used in cars, some of our attacks are practical.

Keywords

RFID tags Hitag 2 algorithm MiFare Crypto-1 cipher stream ciphers algebraic cryptanalysis Boolean functions Gröbner bases SAT solvers 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nicolas T. Courtois
    • 1
  • Sean O’Neil
    • 2
  • Jean-Jacques Quisquater
    • 3
  1. 1.University College LondonUK
  2. 2.VEST CorporationFrance
  3. 3.Université Catholique de LouvainBelgium

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