In this paper, we present a private voting system that consists of N voters who may vote to one of the K candidates or vote abstain. Each voter wants to compute the final tally, while staying private and robust against malicious voters, who try to gain information about the vote of the other voters beyond the final result, or send incorrect information to affect the final tally. We design an information-theoretic voting system that uses verifiable secret sharing and multi-party computation, which is secure and private as long as there are up to $\left\lfloor {\frac{{N - 1}}{3}} \right\rfloor $ malicious voters.

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 information-theoretic model for the problem. As a metric to measure the reliability, we consider the authentication key rate whose rate maximization has a trade-off 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.