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Perfectly Secure Message Transmission Scheme against Rational Adversaries

Secure Message Transmission (SMT) is a two-party cryptographic scheme by which a sender securely and reliably sends messages to a receiver using n channels. Suppose that an adversary corrupts at most t out of n channels and makes eavesdropping or tampering over the corrupted channels. It is known that if t < n/2 then the perfect SMT (PSMT) in the information-theoretic sense is achievable and if t ≥ n/2 then no PSMT scheme is possible to construct. If we are allowed to use a public channel in addition to the normal channels, we can achieve the almost reliable SMT (ARSMT), which admits transmission failures of small probability, against t < n corruptions. In the standard setting in cryptography, the participants are classified into honest ones and corrupted ones: every honest participant follows the protocol but corrupted ones are controlled by the adversary and behave maliciously. As a real setting, the notion of rationality in the game theory is often incorporated into cryptography. In this paper, we first consider “rational adversary” who behaves according to his own preference in SMT. We show that it is possible to achieve PSMT even against any t < n corruptions under some reasonable settings for rational adversaries.