#### Information Theoretic Framework for Single and Multi-Server Private Authentication

##### Narges Kazempour, Mahtab Mirmohseni, Mohammad Reza Aref

In this paper, the private authentication problem is considered that consists of a certificate authority, a verifier (or verifiers), many legitimate users (prover) and arbitrary number of attackers. Each legitimate user wants to be authenticated (using his personal key) by the verifier(s), while simultaneously staying anonymous. However, an attacker must fail to be authenticated. We analyze this problem from an information theoretical perspective. First, we propose a general interactive information-theoretic model. As a metric to measure reliability, we consider the key rate whose rate maximization has a trade-off with establishing privacy. We consider the problem in two different setups: single server and multi-server scenarios. In single server scenario one verifier is considered, which all the provers connected to. In multi-server scenario, $n$ verifiers are assumed, where each verifier is connected to a subset of users. For both scenarios, two regimes are considered: finite size and asymptotic regimes. In single server scenario, for both regimes, we propose schemes that satisfy completeness, soundness and privacy properties. Moreover, we show that our scheme achieves capacity in the asymptotic regime. For finite size regime our scheme achieves capacity for large field size. In multi-server scenario two methods are considered: individual and distributed authentication. In individual authentication, the process of authentication is done by one single verifier. In this case, for both regimes, we propose schemes that satisfy completeness, soundness and privacy properties. In distributed authentication, the process of authentication is done collaboratively by all the verifiers. For this case, when all the provers are connected to all the verifiers, we propose an optimal scheme in finite size regime.

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