5PM: Secure pattern matching
Joshua Baron, Karim El Defrawy, Kirill Minkovich, Rafail Ostrovsky, Eric Tressler · Journal of Computer Security · 2013
In this paper we consider the problem of secure pattern matching that allows single-character wildcards and substring matching in the malicious (stand-alone) setting. Our protocol, called 5PM, is executed between two parties: Server, holding a text of length n, and Client, holding a pattern of leng th m to be matched against the text, where our notion of matching is more general than traditionally considered and includes non-binary alphabets, non-binary Hamming distance and non-binary substring matching. 5PM is the first secure expressive pattern matching protocol designed to optimize round complexity by carefully specifying the entire protocol round by round. 5PM requires only eight rounds in the malicious (static corruptions) model. In the malicious model, 5PM requires O((m+n)k2) communication complexity and O(m+n) encryptions, where m is the pattern length and n is the text length. Further, 5PM can hide pattern size with no asymptotic additional costs in either computation or bandwidth.