Communication Complexity in Algebraic Two-Party Protocols

In cryptography, there has been tremendous success in building various two-party protocols with small communication complexity out of homomorphic semantically-secure encryption schemes, using their homomorphic properties in a black-box way. A few notable examples of such primitives include items like single database Private Information Retrieval (PIR) schemes (introduced in [15]) and private database update with small communication (introduced in [5]). In this paper, we illustrate a general methodology for determining what types of protocols can and cannot be implemented with small communication by using homomorphic encryption in a black-box way. We hope that this work will provide a simple "litmus test" of feasibility for black-box use of known homomorphic encryption schemes by other cryptographic researchers attempting to develop new protocols with low communication. Additionally, a precise mathematical language for reasoning about such problems is developed in this work, ...

• Type: Conference
• Year: 2008
• Where: CRYPTO
• Authors: Rafail Ostrovsky, William E. Skeith III
• Keywords: CRYPTO 2008, Cryptology, Encryption Scheme, Homomorphic Encryption, Small Communication