Paper 2024/273

Information-Theoretic 2-Party Computation from Additive Somewhat Homomorphic Encryption

Abstract

Two-party computation has been an active area of research since Yao's breakthrough results on garbled circuits. We present secret key additive somewhat homomorphic schemes where the client has perfect privacy (server can be computationally unbounded). Our basic scheme is additive somewhat homomorphic and we give protocols to handle addition and multiplication. In one scheme, the server handles circuit multiplication gates by returning the multiplicands to the client which does the multiplication and sends back the encrypted product. We give a 2-party protocol that also incorporates server inputs where the client has perfect privacy. Server privacy is not information-theoretic, but rather depends on hardness of the subset sum problem. Correctness for the server in the malicious model can be verified by a 3rd party with high probability where the client and server privacy are information-theoretically protected from the verifier. Scaling the 2PC protocol via separate encryption parameters for smaller subcircuits allows the ciphertext size to remain constant as circuit size grows.