Ensemble Performance of Biometric Authentication Systems Based on Secret Key Generation

Abstract

We study the ensemble performance of biometric authentication systems, based on secret key generation, which work as follows. In the enrollment stage, an individual provides a biometric signal that is mapped into a secret key and a helper message, the former being prepared to become available to the system at a later time (for authentication), and the latter is stored in a public database. When an authorized user requests authentication, claiming his/her identity as one of the subscribers, s/he has to provide a biometric signal again, and then the system, which retrieves also the helper message of the claimed subscriber, produces an estimate of the secret key, that is finally compared to the secret key of the claimed user. In case of a match, the authentication request is approved, otherwise, it is rejected. Referring to an ensemble of systems based on Slepian-Wolf binning, we provide a detailed analysis of the false-reject and false-accept probabilities, for a wide class of stochastic decoders. We also comment on the security for the typical code in the ensemble.

False-Accept/False-Reject Trade-Offs for Ensembles of Biometric Authentication Systems

“…The problem setting is similar to the one in [9], but with a few small differences, mainly related to the fact that here, in contrast to [9], we allow variable-rate binning codes.…”

“…For the FA probability, the exact best achievable error exponent was characterized, and finally, more refined upper bounds for privacy leakage and the secrecy leakage were derived. This paper is a further development of [9], where the focus is on the trade-off between the FA error exponent and the FR error exponent. In the design of the helper message encoder, the following conflict arises: on the one hand, it is desirable that the helper message W would be informative enough about S, such that in the presence of Y , the identity of the legitimate subscriber will be approved with high probability.…”

“…But on the other hand, it is also desired that in the absence of Y , the helper message would tell as little as possible about S, in order to make it difficult for imposters to access the system. Indeed, the converse theorem in [9,Theorem 5] is based on the assumption that every type class of source sequences {X}, is mapped, by the helper-message encoder, to as many different helper messages {W } as possible, thus making it as close as possible to be a one-to-one mapping, or in other words, making W is "as informative as possible" about the source vector X, and hence also about the secret key S, generated from X. This is good for achieving a small FR probability (or, equivalently, a large FR error exponent), at the expense of a limitation on the achievable FA exponent.…”

“…To this end, we first derive an expression of the FR random coding error exponent as a function of the desired FA error exponent for fixed-rate binning. This is a relatively straightforward manipu-lation of the results of [9], but it will serve as a reference result. The more interesting part, however, is about extending the scope to the ensemble of variable-rate random binning codes, whose rate function depends on the source vector only via its type (similarly as in [12] and [3]).…”

“…On a technical note, it should be pointed out that while in [9], the error exponent expressions are provided in the Csiszár-style formulation (i.e., minimizations of certain functionals of information measures over probability distributions), here we pass to Gallager-style formulations (i.e., maximizations of functions of relatively few parameters). The reasons for our interest in Gallagerstyle expressions are that they lend themselves more conveniently to numerical calculations (see the discussion after Theorem 1 below, for more details), and that they may be of independent interest on their own right.…”