Broadcast encryption technology enables a sender to send information securely to a group of receivers excluding specified receivers over a broadcast channel. In this paper, we propose a new key-tree structure based on Rabin cryptosystem, and an access control scheme using the structure. We show the security of the access control scheme and construct a new broadcast encryption scheme based on it. The proposed broadcast encryption scheme is a modification of the complete subtree method and it reduces the number of keys a receiver stores to one. There have been proposed some modifications of the complete subtree method which minimize the number of keys for a receiver to one, and the most efficient one among them with respect to the computational overhead at receivers is based on RSA cryptosystem. The computational overhead at receivers in our scheme is around log2e times smaller than the most efficient previously proposed one, where e is a public exponent of RSA, and the proposed scheme is the most efficient among tree based one-key schemes. This property is examined by experimental results. Our scheme achieves this reduction in the computational overhead in exchange for an increase in the size of nonsecret memory by [log n * few (e.g. eight)] bits, where n is the total number of receivers.

We extend the Rabin cryptosystem to the Eisenstein and Gauss fields. Methods for constructing the complete representation class and modulo operation of the ideal are presented. Based on these, we describe the methods of encryption and decryption. This proposed cryptosystem is shown to be as intractable as factorization, and recently presented low exponent attacks do not work against it.