Encryption Cycles and Two Views of Cryptography

The work by Abadi and Rogaway has started the process of bringing together the two approaches —formal and computational— to cryptography. Their work has also shown, that it is impossible to completely unify these two approaches in their typical forms — there are some principal differences in their security definitions. The difference is in the security of encryption cycles. An encryption cycle is a sequence of keys, where each key is encrypted under the next one, and the last key is encrypted under the first one. In formal treatment, they are considered to be secure, but in computational treatment, insecure. In this paper we make the encryption cycles insecure in the formal model (the Dolev-Yao model) as well, by slightly strengthening the attacker. For the modified formal model and the classical computational model, the unifying results by Abadi and Rogaway hold unconditionally.