Automata Evaluation and Text Search Protocols with Simulation-Based Security

This paper presents efficient protocols for securely computing the following two problems: (1) The fundamental problem of pattern matching. This problem is defined in the two-party setting, where party \(P_1\) holds a pattern and party \(P_2\) holds a text. The goal of \(P_1\) is to learn where the pattern appears in the text, without revealing it to \(P_2\) or learning anything else about \(P_2\)’s text. This problem has been widely studied for decades due to its broad applicability. We present several protocols for several notions of security. We further generalize one of our solutions to solve additional pattern matching-related problems of interest. (2) Our construction from above, in the malicious case, is based on a novel protocol for secure oblivious automata evaluation which is of independent interest. In this problem, party \(P_1\) holds an automaton and party \(P_2\) holds an input string, and they need to decide whether the automaton accepts the input, without learning anything else. Our protocol obtains full security in the face of malicious adversaries.