Resource-Efficient OT Combiners with Active Security
An OT-combiner takes n candidate implementations of the oblivious transfer (OT) functionality, some of which may be faulty, and produces a secure instance of oblivious transfer as long as a large enough number of the candidates are secure. We see an OT-combiner as a 2-party protocol that can make several black-box calls to each of the n OT candidates, and we want to protect against an adversary that can corrupt one of the parties and a certain number of the OT candidates, obtaining their inputs and (in the active case) full control of their outputs.
In this work we consider perfectly (unconditionally, zero-error) secure OT-combiners and we focus on minimizing the number of calls to the candidate OTs.
First, we construct a single-use (one call per OT candidate) OT-combiner which is perfectly secure against active adversaries corrupting one party and a constant fraction of the OT candidates. This extends a previous result by Ishai et al. (ISIT 2014) that proves the same fact for passive adversaries.
Second, we consider a more general asymmetric corruption model where an adversary can corrupt different sets of OT candidates depending on whether it is Alice or Bob who is corrupted. We give sufficient and necessary conditions for the existence of an OT combiner with a given number of calls to the candidate OTs in terms of the existence of secret sharing schemes with certain access structures and share-lengths. This allows in some cases to determine the optimal number of calls to the OT candidates which are needed to construct an OT combiner secure against a given adversary.
We thank the anonymous reviewers for their suggestions, which have helped us to improve this work.
- [BI01]Beimel, A., Ishai, Y.: On the power of nonlinear secret-sharing. In: Proceedings of the 16th Annual IEEE Conference on Computational Complexity, Chicago, Illinois, USA, 18–21 June 2001, pp. 188–202 (2001)Google Scholar
- [Bla79]Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the 1979 AFIPS National Computer Conference, vol. 48, pp. 313–317, June 1979Google Scholar
- [Can01]Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd IEEE Symposium on Foundations of Computer Science, Proceedings. pp. 136–145. IEEE (2001)Google Scholar
- [CCM98]Cachin, C., Crépeau, C., Marcil, J.: Oblivious transfer with a memory-bounded receiver. In: 39th Annual Symposium on Foundations of Computer Science, FOCS 1998, 8–11 November 1998, Palo Alto, California, USA, pp. 493–502 (1998)Google Scholar
- [CK88]Crépeau, C., Kilian, J.: Achieving oblivious transfer using weakened security assumptions (extended abstract). In: 29th Annual Symposium on Foundations of Computer Science, White Plains, New York, USA, 24–26 October 1988, pp. 42–52 (1988)Google Scholar
- [Gab]Gaborit, P.: Tables of self-dual codes. http://www.unilim.fr/pages_perso/philippe.gaborit/SD/
- [IKO+11]Ishai, Y., Kushilevitz, E., Ostrovsky, R., Prabhakaran, M., Sahai, A., Wullschleger, J.: Constant-rate oblivious transfer from noisy channels. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 667–684. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_38 CrossRefGoogle Scholar
- [IMSW13]Ishai, Y., Maji, H.K., Sahai, A., Wullschleger, J.: Single-use oblivious transfer combiners (2013). Full version of [IMSW14] https://www.cs.purdue.edu/homes/hmaji/papers/IshaiMaSaWu13.pdf
- [IMSW14]Ishai, Y., Maji, H.K., Sahai, A., Wullschleger, J.: Single-use OT combiners with near-optimal resilience. In: 2014 IEEE International Symposium on Information Theory, Honolulu, HI, USA, 29 June – 4 July 2014, pp. 1544–1548 (2014)Google Scholar
- [ISN87]Ito, M., Saito, A., Nishizeki, T.: Secret sharing schemes realizing general access structures. In: Proceedings of IEEE GlobeCom 1987 Tokyo, pp. 99–102 (1987)Google Scholar
- [Kil88]Kilian, J.: Founding cryptography on oblivious transfer. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, 2–4 May 1988, Chicago, Illinois, USA, pp. 20–31 (1988)Google Scholar
- [Mas93]Massey, J.L.: Minimal codewords and secret sharing. In: Proceedings of the 6th Joint Swedish-Russian International Workshop on Information Theory, pp. 276–279 (1993)Google Scholar
- [Rab81]Rabin, M.: How to exchange secrets with oblivious transfer. Technical report, Aiken Computation Lab, Harvard University (1981)Google Scholar