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On the security of HB\(^{\#}\) against a man-in-the-middle attack. (English) Zbl 1206.94084
Pieprzyk, Josef (ed.), Advances in cryptology – ASIACRYPT 2008. 14th international conference on the theory and application of cryptology and information security, Melbourne, Australia, December 7–11, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-89254-0/pbk). Lecture Notes in Computer Science 5350, 108-124 (2008).
Summary: At EuroCrypt ’08, H. Gilbert, M. J. B. Robshaw and Y. Seurin [“HB\(^{\#}\): increasing the security and efficiency of HB\(^{+}\)”, Lect. Notes Comput. Sci. 4965, 361–378 (2008; Zbl 1149.94334)] proposed HB\(^{\#}\) to improve on HB\(^{ + }\) in terms of transmission cost and security against man-in-the-middle attacks. Although the security of HB\(^{\#}\) is formally proven against a certain class of man-in-the-middle adversaries, it is only conjectured for the general case. In this paper, we present a general man-in-the-middle attack against HB\(^{\#}\) and Random-HB\(^{\#}\), which can also be applied to all anterior HB-like protocols, that recovers the shared secret in \(2^{25}\) or \(2^{20}\) authentication rounds for HB\(^{\#}\) and \(2^{34}\) or \(2^{28}\) for Random-HB\(^{\#}\), depending on the parameter set. We further show that the asymptotic complexity of our attack is polynomial under some conditions on the parameter set which are met on one of those proposed in [loc. cit.].
For the entire collection see [Zbl 1155.94008].

MSC:
94A60 Cryptography
94A62 Authentication, digital signatures and secret sharing
Software:
HB-MP
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