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 \(\mathcal{T}\) where a pattern \(\mathcal{P}\) occurs (or matches with few mismatches) allowing possibly both \(\mathcal{T}\) and \(\mathcal{P}\) 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.
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References
Abe, M., Cramer, R., Fehr, S.: Non-interactive distributed-verifier proofs and proving relations among commitments. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 206–223. Springer, Heidelberg (2002)
Abrahamson, K.R.: Generalized String Matching. SIAM J. Comput. 16(6), 1039–1051 (1987)
Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptology 13(1), 143–202 (2000)
Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)
Cheon, J.H., Jarecki, S., Seo, J.H.: Multi-Party Privacy-Preserving Set Intersection with Quasi-Linear Complexity. IACR ePrint Archive, Report 2010/512 (2010)
Clifford, P., Clifford, R.: Simple Deterministic Wildcard Matching. Inf. Process. Lett. 101(2), 53–54 (2007)
Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex fourier series. Math. Comp. 19, 297–301 (1965)
Cramer, R., Gennaro, R., Schoenmakers, B.: A secure and optimally efficient multi-authority election scheme. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 103–118. Springer, Heidelberg (1997)
Crochemore, M., Rytter, W.: Jewels of Stringology, p. 310. World Scientific Publishing, Hong-Kong (2002)
ElGamal, T.: A Public Key Cryptosystem and a Signature Scheme based on Discrete Logarithms. IEEE Trans. Inf. Theory 31, 469–472 (1985)
Fischer, M., Paterson, M.: Paterson, M.: String Matching and Other Products. Complexity of Computation. In: Karp, R. (ed.) Complexity of Computation, SIAM-AMS, vol. 7, pp. 113–125. American Mathematical Society, Providence (1974)
Gennaro, R., Hazay, C., Sorensen, J.S.: Text search protocols with simulation based security. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 332–350. Springer, Heidelberg (2010)
Groth, J.: A verifiable secret shuffle of homomorphic encryptions. In: Desmedt, Y. (ed.) PKC 2003. LNCS, vol. 2567, pp. 145–160. Springer, Heidelberg (2002)
Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008)
Hazay, C., Lindell, Y.: Efficient Protocols for Set Intersection and Pattern Matching with Security Against Malicious and Covert Adversaries. J. Cryptology 23(3), 422–456 (2010)
Hazay, C., Lindell, Y.: Efficient Secure Two-Party Protocols. In: Information Security and Cryptography. Springer, Heidelberg (2010)
Hazay, C., Toft, T.: Computationally secure pattern matching in the presence of malicious adversaries. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 195–212. Springer, Heidelberg (2010)
Jarrous, A., Pinkas, B.: Secure hamming distance based computation and its applications. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 107–124. Springer, Heidelberg (2009)
Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast Pattern Matching in Strings. SIAM J. Comput. 6(2), 323–350 (1977)
Rahman, M.S., Iliopoulos, C.S.: Pattern Matching Algorithms with Don’t Cares. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plasil, F., Bieliková, M. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 116–126. Springer, Heidelberg (2007)
Schnorr, C.-P.: Efficient Signature Generation by Smart Cards. J. Cryptology 4(3), 161–174 (1991)
Schoenmeyr, T., Zhang, D.Y.: FFT-based algorithms for the string matching with mismatches problem. J. Algorithms 57(2), 130–139 (2005)
Troncoso-Pastoriza, J.R., Katzenbeisser, S., Celik, M.: Privacy preserving error resilient dna searching through oblivious automata. In: Ning, P., di Vimercati, S.D.C., Syverson, P.F. (eds.) ACM CCS 2007: 14th Conference on Computer and Communications Security, pp. 519–528. ACM Press, New York (2007)
Tsiounis, Y., Yung, M.: On the security of elGamal based encryption. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, pp. 117–134. Springer, Heidelberg (1998)
Yao, A.C.: Protocols for Secure Computations. In: 23rd Annual Symposium on Foundations of Computer Science, pp. 160–164. IEEE Computer Society Press, Los Alamitos (1982)
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Vergnaud, D. (2011). Efficient and Secure Generalized Pattern Matching via Fast Fourier Transform. In: Nitaj, A., Pointcheval, D. (eds) Progress in Cryptology – AFRICACRYPT 2011. AFRICACRYPT 2011. Lecture Notes in Computer Science, vol 6737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21969-6_3
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DOI: https://doi.org/10.1007/978-3-642-21969-6_3
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