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In this paper, we describe a new protocol for secure evaluation of Deterministic Finite Automata (DFA) between two parities (client and server). The protocol has no restrictions on the DFA's input alphabet and runs in a single client-server communication round. It uses O(mn) operations for client-side computations, O(mn|Q|) operations for server-side computations, and the network communication bandwidth is O(mnk|Q|) bytes where k is the security parameter of the protocol, m is the size of the DFA's input alphabet, n is the length of the input text and |Q| is the number of the DFA states. As a building block our algorithm uses the white-box based 1-out-of-n oblivious transfer protocol, which results that the protocol does no public-key operations. Apart from the description of the protocol, the paper also contains results of efficiency benchmarks done on our implementation of the protocol.
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