A New Identification Scheme Based on the Perceptrons Problem

Abstract

Identification is a useful cryptographic tool. Since zero-know- ledge theory appeared [3], several interactive identification schemes have been proposed (in particular Fiat-Shamir [2] and its variants [8, 5, 4], Schnorr [9]). These identifications are based on number theoretical prob- lems. More recently, new schemes appeared with the peculiarity that they are more efficient from the computational point of view and that their security is based on NP-complete problems: PKP (Permuted Ker- nels Problem) [10], SD (Syndrome Decoding) [12] and CLE (Constrained Linear Equations) [13].We present a new NP-complete linear problem which comes from learn- ing machines: the Perceptrons Problem. We have some constraints, m vectors X i of {−1, +1}n, and we want to find a vector V of {−1, +1}n such that X i · V ≥ 0 for all i.Next, we provide some zero-knowledge interactive identification protocols based on this problem, with an evaluation of their security. Eventually, those protocols are well suited for smart card applications.