Abstract
We consider the anonymous mutual authentication problem, which consists of a certificate authority, single or multiple verifiers, many legitimate users (provers) and any arbitrary number of illegitimate users. The legal verifier and a legitimate user must be mutually authenticated to each other using the user's key, while the identity of the user must stay unrevealed. An attacker (illegitimate prover) as well as an illegal verifier must fail in authentication. A general interactive information theoretic framework in a finite field is proposed, where the normalized total key rate as a metric for reliability is defined. Maximizing this rate has a trade-off with establishing anonymity. The problem is studied in two different scenarios: centralized scenario (one single verifier performs the authentication process) and distributed scenario (authentication is done by N verifiers, distributively). For both scenarios, achievable schemes, which satisfy the completeness, soundness (at both verifier and prover) and anonymity properties, are proposed. Increasing the size of the field, results in the key rate approaching its upper bound.