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