Private Authentication: Optimal Information Theoretic Schemes 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 (using his personal key) 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 informationtheoretic model for the problem. As a metric to measure the reliability, we consider the authentication key rate whose rate maximization has a tradeoff with establishing privacy. Then, we analyze the problem in two different regimes: finite size regime (i.e., the variables are elements of a finite field) and asymptotic regime (i.e., the variables are considered to have large enough length). For both regimes, we propose schemes that satisfy the completeness, soundness and privacy properties. In finite size regime, the idea is to generate the authentication keys according to a secret sharing scheme. In asymptotic regime, we use a random binning based scheme which relies on the joint typicality to generate the authentication keys. Moreover, providing the converse proof, we show that our scheme achieves capacity in the asymptotic regime. For finite size regime our scheme achieves capacity for large field size.

Intersectionpolicy private mutual authentication from authorized private set intersection Private mutual authentication (PMA) enables twoway anonymous authentication between two users certified by the same trusted group authority. Most existing PMA schemes focus on acquiring a relatively onefold authentication policy that ensures affiliationhiding or designated singleattribute matching. However, in practice, users are typically provided with multiple attributes. In addition to the affiliationhiding requirement, how to effectively achieve a more flexible authentication policy for multiattribute applications remains a challenging issue. The intersection policy for authentication is also required when the attribute intersection is not an empty set or its cardinality is no less than a threshold value. To solve the above problems, we first propose an optimal authorized private set intersection protocol with forward security based on identitybased encryption and then design a new PMA protocol with intersectionpolicy called IPPMA, which provides a simple solution for secret handshakes between two members (holding multiple attributes) from the same organization. Formal security analyses proved that our two proposed protocols are secure in the random oracle model. Empirical tests demonstrated that the IPPMA protocol is optimized with linear complexity and may be more suitable for resourceconstrained applications.