Circular Encryption in Formal and Computational Cryptography

The goal of computationally sound symbolic security is to create formal systems of cryptography which have a sound interpretation with respect to complexity-based notions of security. While there has been much progress in the development of such systems, one big impediment is the treatment of circular encryptions. In many typical symbolic systems, it is secure to encrypt a key by itself, but in the computational setting, standard notions of security break down in this case. There are now approaches to this problem from both sides. On the symbolic side, Miccianico (2010) presented a system in which adversarial knowledge is modeled co-inductively, and circular encryption is no longer symbolically secure. On the computational side, systems in which circular encryptions are secure have been developed based on standard hardness assumptions. I will survey the work described above, as well as presenting some recent results on extending Micciancio's system beyond the setting of passive eavesdropping adversaries (joint work with Mohammad Hajiabadi.)