Analyzing the HB and HB+ Protocols in the "Large Error" Case

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