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A homomorphic encryption (HE) scheme is an advanced encryption technology which allows any user receiving ciphertexts to perform computations over them in a public manner. An important application of an HE scheme is a private delegating computation where clients encrypt their secret data, send the ciphertexts to a (computationally powerful) server who perform computations over encrypted data. In this application, one of the crucial problems is that the delegated server might be not trusted one and in this case, we cannot believe that a server always returns correct computation results. To solve this problem, Lai <italic>et al.</italic> (ESORICS 2014) proposed a verifiable homomorphic encryption (VHE) as a core primitive realizing private and verifiable secure delegating computation. However, their VHE scheme only supports homomorphic evaluation over ciphertexts generated by a <italic>single</italic> user. In this paper, we propose a formalization and its construction of <italic>multi-key verifiable homomorphic encryption</italic> (MVHE), which is a new cryptographic primitive for realizing private and verifiable delegated computation in the <italic>multi-client</italic> setting. Our construction can be obtained by combining a multi-key homomorphic encryption scheme and a multi-key homomorphic encrypted authentication scheme, which is also a new primitive provided in this work.

Multikey Verifiable Homomorphic Encryption