Provable Security in Cryptographic Protocols

The goal of a security protocol (cryptographic protocol) is to satisfy a set of security requirements. The security analysis of these protocols has a great degree of importance, as in practice, proposing a cryptographic protocol without the security analysis is not valuable. There are three approaches in security analysis of cryptographic protocols: heuristic, formal and provable approaches. Recently, provable approaches have been of a great attention. The security proof of a protocol is based on usual mathematical methods in cryptography. In these proofs, first the adversarial power and the concept of breaking the protocol are defined in a formal model. Afterwards, it is shown that if the adversary can break the protocol in defined model, a hard problem in computational complexity theory can be solved. This approach is called reduction to a hard problem. The concepts such as random oracle model, standard model and universally composable model are discussed in the field of provable security. If ideal assumptions (such as the assumption of randomness of the output of hash functions) are considered in the process of the proof, the proof will be in ideal models (such as random oracle model), otherwise, the proof will be in the standard model. Recently, the concept of the universally composable (UC) model is defined in the proof of security. If the security of a protocol is proved in the UC model, its security will be guaranteed, even if the protocol is used in a larger and more complex system. The purpose of this paper is an introduction to approaches in provable security.