NLHB : A Non-Linear Hopper Blum Protocol

TL;DR

This paper introduces the NLHB protocol, a lightweight, provably secure authentication scheme based on non-linear codes, which resists passive attacks more effectively than the original HB protocol and is suitable for low-cost devices.

Contribution

The paper presents the NLHB protocol, a novel non-linear variant of the HB protocol, with proven security against passive and active attacks, and demonstrates its efficiency for low-cost hardware.

Findings

Passive attacks are ineffective against NLHB.

NLHB achieves similar security with smaller keys.

Lower complexity implementation for RFID devices.

Abstract

In this paper, we propose a light-weight provably-secure authentication protocol called the NLHB protocol, which is a variant of the HB protocol. The HB protocol uses the complexity of decoding linear codes for security against passive attacks. In contrast, security for the NLHB protocol is proved by reducing passive attacks to the problem of decoding a class of non-linear codes that are provably hard. We demonstrate that the existing passive attacks on the HB protocol family, which have contributed to considerable reduction in its effective key-size, are ineffective against the NLHB protocol. From the evidence, we conclude that smaller-key sizes are sufficient for the NLHB protocol to achieve the same level of passive attack security as the HB Protocol. Further, for this choice of parameters, we provide an implementation instance for the NLHB protocol for which the Prover/Verifier complexity is lower than the HB protocol, enabling authentication on very low-cost devices like RFID tags. Finally, in the spirit of the HB$^{+}$ protocol, we extend the NLHB protocol to the NLHB$^{+}$ protocol and prove security against the class of active attacks defined in the DET Model.