Paper 2017/309

Perfectly Secure Message Transmission Scheme against Rational Adversaries

Maiki Fujita and Takeshi Koshiba

Abstract

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 $t\ge n/2$ 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. \end{abstract}