Taming the round efficiency of cryptographic protocols for private web search schemes

Abstract

Private web search (PWS) schemes allow users to find information on the internet while preserving their privacy. Among them, cryptographic PWS schemes guarantee strong privacy at the cost of performance. Their design principle is that each user takes a list of ciphertexts as inputs from its predecessor and forwards a shuffled list of the input to its successor. This idea is quite reasonable but requires O(n) round complexity with respect to the number of users n. Because these cryptographic PWS schemes are interaction-intensive, this long delay causes network latency and dictates the local computational cost. This linear round complexity is the main obstacle for deploying these schemes in real-world applications.In this work, our primary goal is to improve existing cryptographic PWS solutions to reduce their complexity to O(1) rounds, thus ensuring their practicality. To this end, we first introduce the notion of vertical mixing, which hides the linkability between messages and their sources without horizontally cascaded shuffling. Second, we design a method to achieve vertical mixing by adopting additive secret sharing and modifying the widely used cryptographic PWS framework, CVH, originally developed by Castellà-Roca et al. (Computer Communications 2009). This yields enhanced round efficiency while ensuring security in the semi-honest model. Furthermore, we provide a formal proof of our PWS solution using the standard simulation-based proof. In contrast, the existing works only provide heuristic proofs. Finally, we perform a set of microbenchmarks by varying the number of users and evaluate the effectiveness of our construction. Our PWS scheme runs 1.48∼3.63× faster than the original CVH framework.