An algorithm for solving the LPN problem and its application to security evaluation of the HB protocols for RFID authentication. (English) Zbl 1175.94078

Fossorier, Marc P. C.; Mihaljević, Miodrag J.; Imai, Hideki; Cui, Yang; Matsuura, Kanta

Barua, Rana (ed.) et al., Progress in cryptology – INDOCRYPT 2006. 7th international conference on cryptology in India, Kolkata, India, December 11-13, 2006. Proceedings. Berlin: Springer (ISBN 978-3-540-49767-7/pbk). Lecture Notes in Computer Science 4329, 48-62 (2006).

Summary: 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.
For the entire collection see [Zbl 1133.94005].

MSC:

94A60	Cryptography
94A62	Authentication, digital signatures and secret sharing

Keywords:

cryptanalysis; LPN problem; fast correlation attacks; HB protocols; RFID authentication