Prism: Privacy-Preserving and Verifiable Set Computation over Multi-Owner Secret Shared Outsourced Databases

Abstract

Private set computation over multi-owner databases is an important problem with many applications — the most well studied of which is private set intersection (PSI). This paper proposes <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Prism</small> , a secret-sharing based approach to compute private set operations ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , intersection and union, as well as aggregates such as count, sum, average, maximum, minimum, and median) over outsourced databases belonging to multiple owners. <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Prism</small> enables data owners to pre-load the data onto non-colluding servers and exploits the additive and multiplicative properties of secret-shares to compute the above-listed operations. <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Prism</small> takes (at most) two rounds of communication between non-colluding servers (storing the secret-shares) and the querier for executing the above-mentioned operations, resulting in a very efficient implementation. <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Prism</small> also supports result verification techniques for each operation to detect malicious adversaries. Experimental results show that <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Prism</small> scales both in terms of the number of data owners and database sizes, to which prior approaches do not scale.