Abstract
We propose a protocol for secure comparison of integers based on homomorphic encryption. We also propose a homomorphic encryption scheme that can be used in our protocol and makes it more efficient than previous solutions. Our protocol is well-suited for application in on-line auctions, both with respect to functionality and performance. It minimizes the amount of information bidders need to send, and for comparison of 16 bit numbers with security based on 1024 bit RSA (executed by two parties), our implementation takes 0.28 seconds including all computation and communication. Using precomputation, one can save a factor of roughly 10.
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Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Groth, J.: Cryptography in subgroups of ℤn. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 50–65. Springer, Heidelberg (2005)
Blake, I.F., Kolesnikov, V.: Strong conditional oblivious transfer and computing on intervals. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 515–529. Springer, Heidelberg (2004)
Fischlin, M.: A cost-effective pay-per-multiplication comparison method for millionaires. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 457–472. Springer, Heidelberg (2001)
Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: EC’99, pp. 129–139. ACM Press, New York (1999)
Blake, I.F., Kolesnikov, V.: Conditional encrypted mapping and comparing encrypted numbers. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, Springer, Heidelberg (2006)
Garay, J., Schoenmakers, B., Villegas, J.: Practical and secure solutions for integer comparison. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 330–342. Springer, Heidelberg (2007)
Canetti, R.: Security and composition of multiparty cryptographic protocols. Journal of Cryptology 13(1), 143–202 (2000)
Toft, T.: Primitives and Applications for Multi-party Computation. PhD thesis, University of Aarhus, Aarhus, Denmark (2007)
Schnorr, C.P.: Efficient signature generation by smart cards. Journal of Cryptology 4(3), 161–174 (1991)
Fujisaki, E., Okamoto, T.: Statistical zero knowledge protocols to prove modular polynomial relations. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16–30. Springer, Heidelberg (1997)
Brands, S.: Rapid demonstration of linear relations connected by boolean operators. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 318–333. Springer, Heidelberg (1997)
Groth, J.: A verifiable secret shuffle of homomorphic encryptions. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 145–160. Springer, Heidelberg (2002)
Cramer, R., Damgård, I., Nielsen, J.B.: Multiparty computation from threshold homomorphic encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280–299. Springer, Heidelberg (2001)
Pohlig, S.C., Hellman, M.E.: An improved algorithm for computing logarithms over GF(p) and its cryptographic significance. IEEE Transactions on Information Theory 24, 106–110 (1978)
eBay Inc.: Bid increments (2006), Available online http://pages.ebay.com/help/buy/bid-increments.html
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Damgård, I., Geisler, M., Krøigaard, M. (2007). Efficient and Secure Comparison for On-Line Auctions. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds) Information Security and Privacy. ACISP 2007. Lecture Notes in Computer Science, vol 4586. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73458-1_30
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DOI: https://doi.org/10.1007/978-3-540-73458-1_30
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