Abstract
In a distributed oblivious transfer (DOT) the sender is replaced with m servers, and the receiver must contact k (k ≤ m) of these servers to learn the secret of her choice. Naor and Pinkas introduced the first unconditionally secure DOT for a sender holding two secrets. Blundo, D’Arco, Santis, and Stinson generalized Naor and Pinkas’s protocol, in the case that the sender holds n secrets, in the first so-called (k, m)-DOT-\(\binom{n}{1}\) protocol. Such a protocol should be secure against a coalition of less than k parties. However, Blundo et al. have shown that this level of security is impossible to achieve in one-round polynomial-based constructions.
In this paper, we show that if communication is allowed amongst the servers, we are able to construct an unconditionally secure, polynomial-based (k, m)-DOT-\(\binom{n}{1}\) protocol with the highest level of security. More precisely, in our construction, a receiver who contacts k servers and corrupt up to k − 1 servers (not necessarily from the set of the contacted servers) cannot learn more than one secret.
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
Beaver, D.: Multiparty protocols tolerating half faulty processors. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 560–572. Springer, Heidelberg (1990)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing - STOC 1988, pp. 1–10. ACM, New York (1988)
Blundo, C., D’Arco, P., Santis, A.D., Stinson, D.R.: New results on unconditionally secure distributed oblivious transfer. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 291–309. Springer, Heidelberg (2003)
Blundo, C., D’Arco, P., Santis, A.D., Stinson, D.R.: On unconditionally secure distributed oblivious transfer. J. Cryptology 20(3), 323–373 (2007)
Brassard, G., Crépeau, C., Robert, J.M.: All-or-nothing disclosure of secrets. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 234–238. Springer, Heidelberg (1987)
Desmedt, Y.G., Jajodia, S.: Redistributing secret shares to new access structures and its applications. Technical report, George Mason University (1997)
Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Communications of the ACM 28, 637–647 (1985)
Naor, M., Pinkas, B.: Distributed oblivious transfer. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 205–219. Springer, Heidelberg (2000)
Nikov, V., Nikova, S., Preneel, B., Vandewalle, J.: On unconditionally secure distributed oblivious transfer. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 395–408. Springer, Heidelberg (2002)
Rabin, M.O.: How to exchange secrets with oblivious transfer. Technical report, Aiken Computation Lab, Harvard University (1981)
Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Corniaux, C.L.F., Ghodosi, H. (2011). Scalar Product-Based Distributed Oblivious Transfer. In: Rhee, KH., Nyang, D. (eds) Information Security and Cryptology - ICISC 2010. ICISC 2010. Lecture Notes in Computer Science, vol 6829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24209-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-24209-0_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24208-3
Online ISBN: 978-3-642-24209-0
eBook Packages: Computer ScienceComputer Science (R0)