Efficient and secure generalized pattern matching via fast Fourier transform

Abstract

We present simple protocols for secure two-party computation of generalized pattern matching in the presence of malicious parties. The problem is to determine all positions in a text T where a pattern P occurs (or matches with few mismatches) allowing possibly both T and P to contain single character wildcards. We propose constant-round protocols that exhibit linear communication and quasilinear computational costs with simulation-based security. Our constructions rely on a well-known technique for pattern matching proposed by Fischer and Paterson in 1974 and based on the Fast Fourier Transform. The security of the new schemes is reduced to the semantic security of the ElGamal encryption scheme. © 2011 Springer-Verlag.