Unconditionally Secure Authenticated Encryption with Shorter Keys

Confidentiality and integrity are two main objectives of security systems and the literature of cryptography is rich with proposed techniques to achieve them. To satisfy the requirements of a wide range of applications, a variety of techniques with different properties and performances have appeared in the literature. In this work, we address the problem of confidentiality and integrity in communications over public channels. We propose an unconditionally secure authenticated encryption that requires shorter key material than current state of the art. By combining properties of the integer field Z(P), with the fact that the message to be authenticated is unknown to adversaries (encrypted), message integrity is achieved using a single modular multiplication. Against an adversary equipped with a single antenna, the adversary's probability of modifying a valid message in a way undetected by the intended receiver can be made an absolute zero. After the description of the basic scheme and its detailed security analysis are completed, we describe an extension to the main scheme that can substantially reduce the required amount of key material.