Abstract
Auctions have a long history, having been recorded as early as 500 B.C. [17]. Nowadays, electronic auctions have been a great success and are increasingly used. Many cryptographic protocols have been proposed to address the various security requirements of these electronic transactions, in particular to ensure privacy. Brandt [4] developed a protocol that computes the winner using homomorphic operations on a distributed ElGamal encryption of the bids. He claimed that it ensures full privacy of the bidders, i.e. no information apart from the winner and the winning price is leaked. We first show that this protocol – when using malleable interactive zero-knowledge proofs – is vulnerable to attacks by dishonest bidders. Such bidders can manipulate the publicly available data in a way that allows the seller to deduce all participants’ bids. Additionally we discuss some issues with verifiability as well as attacks on non-repudiation, fairness and the privacy of individual bidders exploiting authentication problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bangerter, E., Camenisch, J.L., Maurer, U.M.: Efficient proofs of knowledge of discrete logarithms and representations in groups with hidden order. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 154–171. Springer, Heidelberg (2005)
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, pp. 18–25 (2002)
Brandt, F.: Fully private auctions in a constant number of rounds. In: Wright, R.N. (ed.) FC 2003. LNCS, vol. 2742, pp. 223–238. Springer, Heidelberg (2003)
Brandt, F.: How to obtain full privacy in auctions. International Journal of Information Security 5, 201–216 (2006)
Burmester, M., Desmedt, Y.G., Piper, F., Walker, M.: A general zero-knowledge scheme. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 122–133. Springer, Heidelberg (1990)
Chaum, D., Evertse, J.-H., van de Graaf, J., Peralta, R.: Demonstrating possession of a discrete logarithm without revealing it. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 200–212. Springer, Heidelberg (1987)
Chaum, D., Evertse, J.-H., van de Graaf, J.: An improved protocol for demonstrating possession of discrete logarithms and some generalizations. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 127–141. Springer, Heidelberg (1988)
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)
Chow, S.S.M., Ma, C., Weng, J.: Zero-Knowledge Argument for Simultaneous Discrete Logarithms. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 520–529. Springer, Heidelberg (2010)
Cramer, R., Damgård, I.B.: Zero-Knowledge Proofs for Finite Field Arithmetic or: Can Zero-Knowledge Be for Free? In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 424–441. Springer, Heidelberg (1998)
Curtis, B., Pieprzyk, J., Seruga, J.: An efficient eAuction protocol. In: ARES, pp. 417–421. IEEE Computer Society (2007)
El Gamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985)
Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Fischer, M.J., Lynch, N.A., Paterson, M.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)
Fischlin, M., Fischlin, R.: Efficient non-malleable commitment schemes. Journal of Cryptology 22, 530–571 (2009)
Katz, J.: Efficient cryptographic protocols preventing “man-in-the-middle” attacks. PhD thesis, Columbia University (2002)
Krishna, V.: Auction Theory. Academic Press, San Diego (2002)
Maurer, U.: Unifying zero-knowledge proofs of knowledge. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 272–286. Springer, Heidelberg (2009)
Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: ACM Conference on Electronic Commerce, pp. 129–139 (1999)
Omote, K., Miyaji, A.: A Practical English Auction with One-Time Registration. In: Varadharajan, V., Mu, Y. (eds.) ACISP 2001. LNCS, vol. 2119, pp. 221–234. Springer, Heidelberg (2001)
Peng, K., Boyd, C., Dawson, E., Viswanathan, K.: Robust, Privacy Protecting and Publicly Verifiable Sealed-Bid Auction. In: Deng, R.H., Qing, S., Bao, F., Zhou, J. (eds.) ICICS 2002. LNCS, vol. 2513, pp. 147–159. Springer, Heidelberg (2002)
Sadeghi, A.R., Schunter, M., Steinbrecher, S.: Private auctions with multiple rounds and multiple items. In: DEXA Workshops, pp. 423–427. IEEE (2002)
Sako, K.: An Auction Protocol Which Hides Bids of Losers. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 422–432. Springer, Heidelberg (2000)
Schnorr, C.P.: Efficient signature generation by smart cards. Journal of Cryptology 4, 161–174 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dreier, J., Dumas, JG., Lafourcade, P. (2013). Brandt’s Fully Private Auction Protocol Revisited. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds) Progress in Cryptology – AFRICACRYPT 2013. AFRICACRYPT 2013. Lecture Notes in Computer Science, vol 7918. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38553-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-38553-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38552-0
Online ISBN: 978-3-642-38553-7
eBook Packages: Computer ScienceComputer Science (R0)