Highly Efficient and Re-executable Private Function Evaluation with Linear Complexity

Abstract

Private function evaluation aims to securely compute a function f (x1,. .. , xn) without leaking any information other than what is revealed by the output, where f is a private input of one of the parties (say Party 1) and xi is a private input of the i-th party Party i. In this work, we propose a novel and secure two-party private function evaluation (2PFE) scheme based on the DDH assumption. Our scheme introduces a reusability feature that significantly improves the state-of-the-art. Accordingly, our scheme has two variants, one is utilized in the initial execution of the function f , and the other is utilized in its subsequent evaluations. To the best of our knowledge, this is the first and most efficient 2PFE scheme that enjoys a reusablity feature. Our protocols achieve linear communication and computation complexities and a constant number of rounds which is at most three.

m-Stability

“…Designs and analyses of novel mechanisms from more diverse areas by using our definitions seem as interesting research. These areas include (but not limited to) secure outsourced computation [51], secure multi-party computation (as in [7] or combination of game theory with known secure protocols [52] for efficiency), more dependable and multi-party versions of private function evaluation [53,54,55], ad hoc network security [11,12], Byzantine fault tolerant systems [37,56] where rational and collaborating processors are involved, blockchain mining (as in [57]), and mining pool games (as in [58,59]). We note that further definitions incorporating ours for more specific or sophisticated use cases, such as modelling conflict of interests, are left as future work as well.…”

Oblivious Turing Machine

“…PFE schemes primarily aim to reduce communication cost, round complexity, and improve efficiency of the private computation of a function. Several protocols based on boolean circuits have been proposed, for example [16], [21], [22], [7]. For example, the scheme proposed by Biçer et al [7] is a two-party private function evaluation scheme for boolean circuits, designed to provide security in the semi-honest model.…”

“…Several protocols based on boolean circuits have been proposed, for example [16], [21], [22], [7]. For example, the scheme proposed by Biçer et al [7] is a two-party private function evaluation scheme for boolean circuits, designed to provide security in the semi-honest model. This scheme achieves cost reductions by reusing tokens in the two-party computation stage, thereby eliminating redundant computations and message exchanges during subsequent evaluations of the same function.…”

Quantum private function evaluation

“…The other class of classical PFE does not rely on universal circuits [2,6,7]. Compared to the previous type of PFE, this type of PFE can achieve higher efficiency by opening the black box of MPC.…”

“…Compared to the previous type of PFE, this type of PFE can achieve higher efficiency by opening the black box of MPC. We refer the reader to the related work section of [7] for a recent review of this line of PFE. We only add the remark here that these classical PFEs usually involve copying the output of a gate several times as the inputs of further gates.…”