Decision problem concerning security for cryptographic protocols

TL;DR: Under the sufficient condition given in this paper, the security of such cryptographic protocols as the cryptographic key distribution protocols and the digital signature protocols can be decided in a polynomial time.

Abstract: This paper discusses the decision problem concerning security for such cryptographic protocols as the cryptographic key distribution protocols and the digital signature protocols. A cryptographic protocol and its utilization environment are considered secure if an opponent cannot know the secret message or forge a signature successfully by wiretapping or communication function is secure. This paper presents a sufficient condition under which the security problem is decidable. Dolev et al. also investigated the decision problem of the security, but they discussed only the simple case where the cryptographic key is not the object of manipulation (i.e., key generation and distribution are not included in the protocol), and a decision method is presented in which the decision can be made in a polynomial time. By contrast, this paper discusses the problem including the case where the cryptographic key can be an object of manipulation. The key delivery protocol by Ehrsam et al. and the digital signature protocol by Needham et al. satisfy the sufficient condition for the decidability given in this paper. Under the sufficient condition given in this paper, the security can again be decided in a polynomial time.