How to Delegate Computations: The Power of No-Signaling Proofs

We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t = t ( n ), where the running time of the prover is poly ( t ) and the running time of the verifier is n · polylog ( t ). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. Our construction relies on the existence of a computational sub-exponentially secure private information retrieval ( PIR ) scheme. The proof exploits a curious connection between the problem of computation delegation and the model of multi-prover interactive proofs that are sound against no-signaling (cheating) strategies , a model that was studied in the context of multi-prover interactive proofs with provers that share quantum entanglement, and is motivated by the physical principle that information cannot travel faster than light. For any language computable in time t = t ( n ), we construct a multi-prover interactive proof ( MIP ), that is, sound against no-signaling strategies, where the running time of the provers is poly ( t ), the number of provers is polylog ( t ), and the running time of the verifier is n · polylog ( t ). In particular, this shows that the class of languages that have polynomial-time MIP s that are sound against no-signaling strategies, is exactly EXP . Previously, this class was only known to contain PSPACE . To convert our MIP into a 1-round delegation scheme, we use the method suggested by Aiello et al. (ICALP, 2000), which makes use of a PIR scheme. This method lacked a proof of security. We prove that this method is secure assuming the underlying MIP is secure against no-signaling provers.

On the Existence of XOR-Based Codes for Private Information Retrieval with Private Side Information

We consider the problem of Private Information Retrieval with Private Side Information (PIR-PSI), wherein the privacy of the demand and the side information are jointly preserved. Although the capacity of the PIR-PSI setting is known, we observe that the underlying capacity-achieving code construction uses Maximum Distance Separable (MDS) codes therefore contributing to high computational complexity when retrieving the demand. Pointing at this drawback of MDS-based PIR-PSI codes, we propose XOR-based PIR-PSI codes for a simple yet non-trivial setting of two non-colluding databases and two side information files at the user. Although our codes offer substantial reduction in complexity when compared to MDS-based codes, the code-rate marginally falls short of the capacity of the PIR-PSI setting. Nevertheless, we show that our code-rate is strictly higher than that of XOR-based codes for PIR with no side information. As a result, our codes can be useful when privately downloading a file especially after having downloaded a few other messages privately from the same database at an earlier time-instant.

You May Also Like... Privacy: Recommendation Systems Meet PIR

We describe the design, analysis, implementation, and evaluation of Pirsona, a digital content delivery system that realizes collaborative-filtering recommendations atop private information retrieval (PIR). This combination of seemingly antithetical primitives makes possible—for the first time—the construction of practically efficient e-commerce and digital media delivery systems that can provide personalized content recommendations based on their users’ historical consumption patterns while simultaneously keeping said consumption patterns private. In designing Pirsona, we have opted for the most performant primitives available (at the expense of rather strong non-collusion assumptions); namely, we use the recent computationally 1-private PIR protocol of Hafiz and Henry (PETS 2019.4) together with a carefully optimized 4PC Boolean matrix factorization.