Abstract
Existing stable matching algorithms reveal the preferences of all participants, as well as the history of matches made and broken in the course of computing a stable match. This information leakage not only violates the privacy of participants, but also leaves matching algorithms vulnerable to manipulation[8,10,25].
To address these limitations, this paper proposes a private stable matching algorithm, based on the famous algorithm of Gale and Shapley[6]. Our private algorithm is run by a number of independent parties whom we call the Matching Authorities. As long as a majority of Matching Authorities are honest, our protocol correctly outputs a stable match, and reveals no other information than what can be learned from that match and from the preferences of participants controlled by the adversary. The security and privacy of our protocol are based on re-encryption mix networks and on an additively homomorphic semantically secure public-key encryption scheme such as Paillier.
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References
Association of Psychology Postdoctoral and Internship Centers, http://www.appic.org/match/
Bandela, C., Chen, Y., Kahng, A., Mandoiu, I., Zelikovsky, A.: Multiple-object XOR auctions with buyer preferences and seller priorities. In: Lai, K.K., Wang, S. (eds.) Competitive Bidding and Auctions, Kluwer Academic Publishers, Dordrecht
Canadian Resident Matching Service (CaRMS), http://www.carms.ca/jsp/main.jsp
Cramer, R., Damgård, I., Dziembowski, S., Hirt, M., Rabin, T.: Efficient multiparty computations secure against an adaptive adversary. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 311–326. Springer, Heidelberg (1999)
Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Proc. of Public Key Cryptography 2001, pp. 119–136 (2001)
Gale, D., Shapley, H.S.: College Admissions and the Stability of Marriage. American Mathematical Monthly (1962)
Fouque, P.-A., Poupard, G., Stern, J.: Sharing decryption in the context of voting or lotteries. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 90–104. Springer, Heidelberg (2001)
Gale, D., Sotomayor, M.: Ms Machiavelli and the Stable Matching Problem. American Mathematical Monthly 92, 261–268 (1985)
Goldreich, O., Micali, S., Widgerson, A.: How to play any mental game. In: STOC 1987, pp. 218–229. ACM, New York (1987)
Gusfield, D., Irving, R.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge
Jakobsson, M., Juels, A., Rivest, R.: Making mix nets robust for electronic voting by randomized partial checking. In: Proc. of USENIX 2002, pp. 339–353
Jakobsson, M., Schnorr, C.: Efficient Oblivious Proofs of Correct Exponentiation. In: Proc. of CMS 1999 (1999)
Lipmaa, H.: Verifiable homomorphic oblivious transfer and private equality test. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 416–433. Springer, Heidelberg (2003)
National Matching Services Inc., http://www.natmatch.com/
National Resident Matching Program (NRMP), http://www.nrmp.org/
Neff, A.: A verifiable secret shuffle and its application to e-voting. In: Proc. of ACM CCS 2001, pp. 116–125 (2001)
Ostrovsky, M.: Stability in supply chain networks, available on the web at economics.uchicago.edu/download/Supply%20Chains%20-%20December%2012.pdf
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)
Roth, A.: The Economics of Matching: Stability and Incentives. Mathematics of Operations Research 7, 617–628 (1982)
Roth, A., Sotomayor, M.: Two-sided matching: a study in game-theoretic modeling and analysis. Econometric Society Monograph Series. Cambridge University Press, New York (1990)
Al Roth’s game theory, experimental economics, and market design page. Bibliography of two-sided matching, on the web at http://kuznets.fas.harvard.edu/~aroth/bib.html#matchbib
Santis, A.D., Crescenzo, G.D., Persiano, G., Yung, M.: On monotone formula closure of szk. In: Proc. of the IEEE FOCS 1994, pp. 454–465 (1994)
Scottish PRHO Allocation (SPA) scheme, http://www.nes.scot.nhs.uk/spa/
Soerensen, M.: How smart is smart money? An empirical two-sided matching model of venture capital, available on the web at http://finance.wharton.upenn.edu/department/Seminar/2004SpringRecruiting/Micro/SorensenPaper-micro-012204.pdf
Teo, C.-P., Sethuraman, J., Tan, W.-P.: Gale-Shapley stable marriage problem revisited: strategic issues and applications. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds.) IPCO 1999. LNCS, vol. 1610, pp. 429–438. Springer, Heidelberg (1999)
Yao, A.C.: Protocols for secure computations. In: FOCS 1982, pp. 160–164. IEEE Computer Society Press, Los Alamitos (1982)
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Golle, P. (2006). A Private Stable Matching Algorithm. In: Di Crescenzo, G., Rubin, A. (eds) Financial Cryptography and Data Security. FC 2006. Lecture Notes in Computer Science, vol 4107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889663_5
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DOI: https://doi.org/10.1007/11889663_5
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