Universal Optimality of Apollonian Cell Encoders

Biondi, Fabrizio Given-Wilson, Thomas Legay, Axel [UCL]

Preserving privacy of private communication against an attacker is a fundamental concern of computer science security. Unconditional encryption considers the case where an attacker has unlimited computational power, hence no complexity result can be relied upon for encryption. Optimality criteria are defined for the best possible encryption over a general collection of entropy measures. This paper introduces Apollonian cell encoders, a class of shared-key cryptosystems that are proven to be universally optimal. In addition to the highest possible security for the message, Apollonian cell encoders prove to have perfect secrecy on their key allowing unlimited key reuse. Conditions for the existence of Apollonian cell encoders are presented, as well as a constructive proof. Further, a compact representation of Apollonian cell encoders is presented, allowing for practical implementation.