In this paper we show how to construct a provably secure AHS based on a coding theory problem. It allows for arbitrary many additions and for a fixed, but arbitrary number of multiplications and works over arbitrary finite fields. Besides, it possesses some useful properties: i) the plaintext space can be extended adaptively without the need for re-encryption, ii) it operates over arbitrary infinite fields as well, e.g., rational numbers, but the hardness of the underlying decoding problem in such cases is less studied, and iii) depending on the parameter choice, the scheme has inherent error-correcting up to a certain number of transmission errors in the ciphertext.
However, since our scheme is symmetric and its ciphertext size grows exponentially with the expected total number of encryptions, its deployment is limited to specific client-server-applications with few number of multiplications. Nevertheless, we believe room for improvement due to the huge number of alternative coding schemes that can serve as the underlying hardness problem. For these reasons and because of the interesting properties of our scheme, we believe that using coding theory to design AHS is a promising approach and hope to encourage further investigations.
Category / Keywords: foundations / Algebraically Homomorphic Encryption, Coding Theory, Provable Security Date: received 1 Oct 2008 Contact author: Frederik Armknecht at trust rub de Available formats: PDF | BibTeX Citation Version: 20081002:031257 (All versions of this report) Discussion forum: Show discussion | Start new discussion