Private Authentication: Optimal Information Theoretic Schemes
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The main security service in the connected world of cyber physical systems necessitates to authenticate a large number of nodes privately. In this paper, the private authentication problem is considered, that consists of a certificate authority, a verifier, many legitimate users (prover) and any arbitrary number of illegitimate users. Each legitimate user wants to be authenticated by the verifier, while simultaneously wants to stay completely anonymous (even to the verifier and the CA). On the other hand, an illegitimate user must fail to authenticate himself. We analyze this problem from an information theoretical perspective. First, we propose a general interactive information-theoretic model for the problem. Then, we consider the problem in two different setups: finite size setup (i.e., the variables are elements of a finite field) and asymptotic setup (i.e., the variables are considered to have large enough length). For both setups, we propose optimal schemes that satisfy the completeness, soundness and privacy properties optimally. In finite field scheme, the idea is to generate the authentication keys according to a secret sharing scheme. In asymptotic scheme, we use a random binning based scheme which relies on the joint typicality to generate the authentication keys.
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