Breaking and Fixing Secure Similarity Approximations: Dealing with Adversarially Perturbed Inputs

Computing similarity between data is a fundamental problem in information retrieval and data mining. To address the relevant performance and scalability challenges, approximation methods are employed for large-scale similarity computation. A common characteristic among all privacy- preserving approximation protocols based on sketching is that the sketching is performed locally and is based on common randomness. In the semi-honest model the input to the sketching algorithm is independent of the common randomness. We, however, consider a new threat model where a party is allowed to use the common randomness to perturb her input 1) offline, and 2) before the execution of any secure protocol so as to steer the approximation result to a maliciously chosen output. We formally define perturbation attacks under this adversarial model and propose two attacks on the well-studied techniques of minhash and cosine sketching. We demonstrate the power of perturbation attacks by measuring their success on synthetic and real data. To mitigate such perturbation attacks we propose a server- aided architecture, where an additional party, the server, assists in the secure similarity approximation by handling the common randomness as private data. We revise and introduce the necessary secure protocols so as to apply minhash and cosine sketching techniques in the server-aided architecture. Our implementation demonstrates that this new design can mitigate offline perturbation attacks without sacrificing the efficiency and scalability of the reconstruction protocol