$\mathsf {moKHS}$moKHS: A More Lightweight Model for Multi-Client Delegatable Computation

Multi-client delegatable computation over outsourced data is an important research area in the context of cloud computing. The main target of it is to produce a function value taken data owned by different users as input while assuring the correctness of the derived result efficiently verifiable. Multi-key homomorphic signature (MK-HS), which allows for computations over signed data originating from multiple users while providing authenticity for the output value, is considered as an elegant primitive to fulfill the above functionality. However, we figure out several deficiencies in the context of MK-HS: (1) the model of MK-HS inevitably induces the participation of a large set of distinct public keys during the procedures of evaluation and verification, which leads to high communication and computation complexity; (2) current MK-HS schemes based on standard assumptions cannot prevent insider corruption attack; (3) the signature succintness of existing MK-HS constructions is far from optimal. In this work, we aim to seek a more appropriate approach for realizing multi-client delegatable computation. Our main result is the introduction of a new model we call
message-oriented key-homomorphic signatures
(
$\mathsf {moKHS}$
). This model provides more lightweight definitions and inherently resists to insider corruption attacks. Besides, we provide a
$\mathsf {moKHS}$
construction based on standard lattices which supports circuits of bounded polynomial depth, and it achieves weak security and input-independent efficiency (in an amortized sense). Furthermore, we present a transformation to obtain an adaptively-secure one from any weakly-secure
$\mathsf {moKHS}$
scheme. Notably, the signature obtained by our
$\mathsf {moKHS}$
scheme achieves
optimal
succinctness in the sense that its size is independent of both the number of users involved in the computation and the input size of the program. All these improvements show that
$\mathsf {moKHS}$
is a more preferable candidate for applications of delegating computation involving multiple users.