Cryptology ePrint Archive: Report 2008/241

Practical Attacks on HB and HB+ Protocols

Zbigniew Golebiewski and Krzysztof Majcher and Filip Zagorski and Marcin Zawada

Abstract: HB and HB+ are a shared-key authentication protocol designed for low-cost devices such as RFID tags. It was proposed by Juels and Weis at Crypto 2005. The security of the protocol relies on the ``learning parity with noise'' (LPN) problem, which was proved to be NP-hard.

The best known attack on LPN (by Levieil and Fouque, SCN 2006) requires exponential number of samples and exponential number of operations to be performed. This makes this attack impractical because it is infeasible to collect exponentially-many observations of the protocol execution.

We present a passive attack on HB protocol which requires only linear (to the length of the secret key) number of samples. Number of performed operations is still exponential, but attack is efficient for some real-life values of the parameters, i.~e.~noise $\frac{1}{8}$ and key length $144$-bits.

Category / Keywords: cryptographic protocols / lightweight cryptography, RFID, HB, HB+, passive attack

Date: received 29 May 2008

Contact author: filipz at im pwr wroc pl

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Version: 20080602:220707 (All versions of this report)

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