Paper 2026/2422

Verifiable Computation on Encrypted Data from Homomorphic Encryption over Random Encodings

Abstract

Verifiable Computation on Encrypted Data (vCOED) enables clients to outsource computation while providing both privacy and integrity. A promising vCOED paradigm is blind proofs, which use homomorphic encryption (HE) to evaluate verifiable computation (VC) proofs on encrypted data. Despite their efficiency, blind proofs do not provide strong client privacy: a malicious server can exploit reaction attacks to learn information about the client's inputs, intermediate values or final outputs. Our work addresses this limitation by introducing Homomorphic Encryption over Random Encodings (HERE). We formalize a new security notion, indistinguishability under chosen-plaintext attacks in the presence of an equality oracle over encodings (IND-CPA-E). We prove that combining IND-CPA-E-secure HERE schemes with blind proofs that verify computation over the encodings yields vCOED protocols with strong client privacy. We then instantiate a HERE scheme for functions of bounded degree $d$, using Shamir secret sharing at $(d+1)$ evaluation points under $(d+1)$ distinct HE keys. Finally, we demonstrate the concrete efficiency of our approach through an application to matrix-vector multiplication (MVM), a linear computation corresponding to $d=1$. The proof overhead (i.e. the ratio of the vCOED prover runtime to the homomorphic MVM runtime) in our combined vCOED protocol is as low as $2\times$, as demonstrated in our prototype implementation.