Cryptology ePrint Archive: Report 2006/326

Analyzing the HB and HB+ Protocols in the ``Large Error'' Case

Jonathan Katz and Adam Smith

Abstract: HB and HB+ are two shared-key, unidirectional authentication protocols whose extremely low computational cost makes them potentially well-suited for severely resource-constrained devices. Security of these protocols is based on the conjectured hardness of learning parity with noise; that is, learning a secret $s$ given ``noisy'' dot products of $s$ that are incorrect with probability $\epsilon$.

Although the problem of learning parity with noise is meaningful for any constant $\epsilon < 1/2$, existing proofs of security for HB and HB+ only imply security when $\epsilon < 1/4$. In this note, we show how to extend these proofs to the case of arbitrary $\epsilon < 1/2$.

Category / Keywords: cryptographic protocols / RFID

Date: received 26 Sep 2006

Contact author: jkatz at cs umd edu

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Version: 20060928:144456 (All versions of this report)

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