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How to obtain full privacy in auctions

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Abstract

Privacy has become a factor of increasing importance in auction design. We propose general techniques for cryptographic first-price and (M+1)st-price auction protocols that only yield the winners' identities and the selling price. Moreover, if desired, losing bidders learn no information at all, except that they lost. Our security model is merely based on computational intractability. In particular, our approach does not rely on trusted third parties, e.g., auctioneers. We present an efficient implementation of the proposed techniques based on El Gamal encryption whose security only relies on the intractability of the decisional Diffie—Hellman problem. The resulting protocols require just three rounds of bidder broadcasting in the random oracle model. Communication complexity is linear in the number of possible bids.

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References

  1. Abe, M., Suzuki, K.: M+1-st price auction using homomorphic encryption. In: Proceedings of the 5th International Conference on Public Key Cryptography (PKC). Lecture Notes in Computer Science (LNCS), vol. 2274, pp. 115–224. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  2. Baudron, O., Stern, J.: Non-interactive private auctions. In: Proceedings of the 5th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 2339, pp. 300–313. Springer, Berlin Heidelberg New York (2001)

    Google Scholar 

  3. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the 20th Annual ACM Symposium on the Theory of Computing (STOC), pp. 1–10. ACM, New York (1988)

    Google Scholar 

  4. Brandt, F.: Secure and private auctions without auctioneers. Tech. Rep. FKI-245-02, Department for Computer Science, Technical University of Munich, Munich (2002). ISSN 0941-6358

  5. Brandt, F.: A verifiable, bidder-resolved auction protocol. In: Falcone, R., Barber, S., Korba, L., Singh, M. (eds.) Proceedings of the 5th AAMAS Workshop on Deception, Fraud and Trust in Agent Societies (Special Track on Privacy and Protection with Multi-Agent Systems), pp. 18–25 (2002)

  6. Brandt, F.: Fully private auctions in a constant number of rounds. In: Wright, R.N. (ed.) Proceedings of the 7th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 2742, pp. 223–238. Springer-Verlag, Berlin Heidelberg New York (2003)

    Google Scholar 

  7. Brandt, F.: Social choice and preference protection—Towards fully private mechanism design. In: Nisan, N. (ed.) Proceedings of the 4th ACM Conference on Electronic Commerce, pp. 220–221. ACM, New York (2003)

    Chapter  Google Scholar 

  8. Brandt, F., Sandholm, T.: (Impossibility of unconditionally privacy-preserving auctions. In: Sierra, C., Sonenberg, L. (eds.) Proceedings of the 3rd International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS), pp. 810–817. ACM, New York (2004)

    Google Scholar 

  9. Brandt, F., Sandholm, T.: On correctness and privacy in distributed mechanisms. In: Faratin, P., Rodriguez-Aguilar, J.A. (eds.) Selected and revised papers from the 6th AAMAS Workshop on Agent-Mediated Electronic Commerce (AMEC). Lecture Notes in Artificial Intelligence (LNAI), vol. 3435 (2004)

  10. Brandt, F., Sandholm, T.: Efficient privacy-preserving protocols for multi-unit auctions. In: Patrick, A., Yung, M. (eds.) Proceedings of the 9th International Conference on Financial Cryptography and Data Security (FC). Lecture Notes in Computer Science (LNCS), vol. 3570, pp. 298–312. Springer, Berlin Heidelberg New York (2005)

    Google Scholar 

  11. Chaum, D., Crépeau, C., Damgård, I.: Multi-party unconditionally secure protocols. In: Proceedings of the 20th Annual ACM Symposium on the Theory of Computing (STOC), pp. 11–19. ACM, New York (1988)

    Google Scholar 

  12. Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Advances in Cryptology—Proceedings of the 12th Annual International Cryptology Conference (CRYPTO). Lecture Notes in Computer Science (LNCS), vol. 740, pp. 3.1–3.6. Springer, Berlin Heidelberg New York (1992)

    Google Scholar 

  13. Chen, W.: Kryptographische Auktionsprotokolle Implementie—rung und Analyse (2002). Systementwicklungsprojekt, Department for Computer Science, Technical University of Munich. http://www.chenwilly.info

  14. Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Advances in Cryptology—Proceedings of the 14th Annual International Cryptology Conference (CRYPTO). Lecture Notes in Computer Science (LNCS), vol. 893, pp. 174–187. Springer, Berlin Heidelberg New York (1994)

    Google Scholar 

  15. Cramer, R., Gennaro, R., Schoenmakers, B.: A secure and optimally efficient multi-authority election scheme. In: Advances in Cryptology—Proceedings of the 14th Eurocrypt Conference. Lecture Notes in Computer Science (LNCS), vol. 1233, pp. 103–118. Springer, Berlin Heidelberg New York (1997)

    Google Scholar 

  16. Damgård, I.: On Σ-protocols. Lecture Notes, University of Aarhus, Department for Computer Science (2002)

  17. El Gamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31, 469–472 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  18. Fiat, A., Shamir, A.: How to prove yourself: Practical solutions to identification and signature problems. In: Advances in Cryptology—Proceedings of the 12th Annual International Cryptology Conference (CRYPTO). Lecture Notes in Computer Science (LNCS), pp. 186–194. Springer, Berlin Heidelberg New York (1987)

    Google Scholar 

  19. Franklin, M.K., Reiter, M.K.: The design and implementation of a secure auction service. IEEE Trans. Softw. Eng. 22(5), 302–312 (1996)

    Article  Google Scholar 

  20. Garay, J., MacKenzie, P., Yang, K.: Efficient and secure multi-party computation with faulty majority and complete fairness. Cryptology ePrint Archive, Report 2004/009 (2004)

  21. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Applications of Pedersen's distributed key generation protocol. In: Proceedings of the Cryptographers' Track at the 12th RSA Conference. Lecture Notes in Computer Science (LNCS), vol. 2612, pp. 373–390. Springer, Berlin Heidelberg New York (2003)

    Google Scholar 

  22. Goldreich, O.: Foundations of Cryptography, vol. 2. Basic Applications. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  23. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Proceedings of the 19th Annual ACM Symposium on the Theory of Computing (STOC), pp. 218–229. ACM, New York (1987)

    Google Scholar 

  24. Goldwasser, S., Levin, L.: Fair computation of general functions in presence of immoral majority. In: Advances in Cryptology—Proceedings of the 10th Annual International Cryptology Conference (CRYPTO). Lecture Notes in Computer Science (LNCS), vol. 537, pp. 77–93. Springer, Berlin Heidelberg New York (1990)

    Google Scholar 

  25. Goldwasser, S., Lindell, Y.: Secure computation without agreement. In: Proceedings of the 16th International Symposium on Distributed Computing (DISC). Lecture Notes in Computer Science (LNCS), vol. 2508, pp. 17–32. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  26. Groth, J.: Efficient maximal privacy in boardroom voting and anonymous broadcast. In: Proceedings of the 8th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 3110, pp. 90–104. Springer, Berlin Heidelberg New York (2004)

    Google Scholar 

  27. Harkavy, M., Tygar, J.D., Kikuchi, H.: Electronic auctions with private bids. In: Proceedings of the 3rd USENIX Workshop on Electronic Commerce, pp. 61–74 (1998)

  28. Jakobsson, M., Juels, A.: Mix and match: Secure function evaluation via ciphertexts. In: Proceedings of the 6th Asiacrypt Conference. Lecture Notes in Computer Science (LNCS), vol. 1976, pp. 162–177. Springer, Berlin Heidelberg New York (2000)

    Google Scholar 

  29. Juels, A., Szydlo, M.: A two-server, sealed-bid auction protocol. In: Blaze, M. (ed.) Proceedings of the 6th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 2357, pp. 72–86. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  30. Kiayias, A., Yung, M.: Self-tallying elections and perfect ballot secrecy. In: Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptography (PKC), no. 2274. Lecture Notes in Computer Science (LNCS), pp. 141–158. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  31. Kiayias, A., Yung, M.: Non-interactive zero-sharing with applications to private distributed decision making. In: Proceedings of the 7th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 2742, pp. 303–320. Springer, Berlin Heidelberg New York (2003)

    Google Scholar 

  32. Kikuchi, H.: (M+1)st-price auction protocol. In: Proceedings of the 5th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 2339, pp. 351–363. Springer, Berlin Heidelberg New York (2001)

    Google Scholar 

  33. Klemperer, P.: Auction theory: A guide to the literature. J. Econ. Surv. 13(3), 227–286 (1999)

    Article  Google Scholar 

  34. Krishna, V.: Auction Theory. Academic, New York (2002)

    Google Scholar 

  35. Lipmaa, H., Asokan, N., Niemi, V.: Secure Vickrey auctions without threshold trust. In: Blaze, M. (ed.) Proceedings of the 6th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 2357, pp. 87–101. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  36. Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: Proceedings of the 1st ACM Conference on Electronic Commerce (ACM-EC), pp. 129–139. ACM, New York (1999)

    Chapter  Google Scholar 

  37. Nurmi, H., Salomaa, A.: Cryptographic protocols for Vickrey auctions. Group Decis. Negot. 2, 363–373 (1993)

    Article  Google Scholar 

  38. Pass, R.: Bounded-concurrent secure multiparty computation with a dishonest majority. In: Proceedings of the 36th Annual ACM Symposium on the Theory of Computing (STOC), pp. 232–241. ACM, New York (2004)

    Google Scholar 

  39. Pedersen, T.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) Advances in Cryptology—Proceedings of the 11th Annual International Cryptology Conference (CRYPTO). Lecture Notes in Computer Science (LNCS), vol. 576, pp. 129–140. Springer, Berlin Heidelberg New York (1991)

    Google Scholar 

  40. Pinkas, B.: Fair secure two-party computation. In: Proceedings of the 20th Eurocrypt Conference. Lecture Notes in Computer Science (LNCS), vol. 2656, pp. 87–105. Springer, Berlin Heidelberg New York (2003)

    Google Scholar 

  41. Porter, R., Shoham, Y.: On cheating in sealed-bid auctions. In: Proceedings of the 4th ACM Conference on Electronic Commerce (ACM-EC), pp. 76–84. ACM, New York (2003)

    Chapter  Google Scholar 

  42. Rothkopf, M.H., Harstad, R.M.: Two models of bid-taker cheating in Vickrey auctions. J. Business 68(2), 257–267 (1995)

    Article  Google Scholar 

  43. Rothkopf, M.H., Teisberg, T.J., Kahn, E.P.: Why are Vickrey auctions rare? J. Pol. Econ. 98(1), 94–109 (1990)

    Article  Google Scholar 

  44. Sako, K.: An auction protocol which hides bids of losers. In: Proceedings of the 3rd International Conference on Public Key Cryptography (PKC). Lecture Notes in Computer Science (LNCS), vol. 1751, pp. 422–432. Springer, Berlin Heidelberg New York (2000)

    Google Scholar 

  45. Sandholm, T.: Issues in computational Vickrey auctions. International Journal of Electronic Commerce, Special Issue Intell. Agents Electron. Commer. 4(3), 107–129 (2000)

    Google Scholar 

  46. Schnorr, C.P.: Efficient signature generation by smart cards. J. Cryptol. 4(3), 161–174 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  47. Suzuki, K., Yokoo, M.: Secure combinatorial auctions by dynamic programming with polynomial secret sharing. In: Proceedings of the 6th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 2357. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  48. Suzuki, K., Yokoo, M.: Secure generalized Vickrey auction using homomorphic encryption. In: Proceedings of the 7th Annual Conference on Financial Cryptography (FC). Lecture Notes in Computer Science (LNCS), vol. 2742, pp. 239–249. Springer, Berlin Heidelberg New York (2003)

    Google Scholar 

  49. Tsiounis, Y., Yung, M.: On the security of El Gamal-based encryption. In: Proceedings of the 1st International Workshop on Practice and Theory in Public Key Cryptography (PKC). Lecture Notes in Computer Science (LNCS), vol. 1431, pp. 117–134. Springer, Berlin Heidelberg New York (1998)

    Google Scholar 

  50. Vickrey, W.: Counter speculation, auctions, and competitive sealed tenders. J. Finance 16(1), 8–37 (1961)

    Article  Google Scholar 

  51. Yao, A.C.: How to generate and exchange secrets. In: Proceedings of the 27th Symposium on Foundations of Computer Science (FOCS), pp. 162–167. IEEE Comput. Soc. Press (1986)

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  1. Computer Science Department, University of Munich, Oettingenstr 67, 80538, Munich, Germany

    Felix Brandt

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Brandt, F. How to obtain full privacy in auctions. Int. J. Inf. Secur. 5, 201–216 (2006). https://doi.org/10.1007/s10207-006-0001-y

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