Abstract
In this paper, we propose an efficient code-based 1-out-of-N oblivious transfer, \(OT_1^N\), based on McEliece assumptions without invoking the \(OT_1^2\) several times as in the paradigm proposed in [20,6]. We also show that the protocol is computationally secure against passive and active adversaries. To our knowledge, this is the first practical code-based \(OT_1^N\) protocol. The proposed protocol is compared with some existing number-theoretic \(OT_1^N\) protocols for efficiency.
Also, the passively secure 1-out-of-2 OT protocol proposed by Dowsley et al. [10] is reviewed. A formal argument of the computational security of the protocol against active adversaries is furnished.
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References
Bellare, M., Micali, S.: Non-interactive oblivious transfer and applications. In: Brassard [5], pp. 547–557
Berlekamp, E.R., Mceliece, R.J., Vantilborg, H.C.: On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory (1978)
Bernstein, D.J.: List decoding for binary goppa codes (2008)
Bernstein, D.J., Buchmann, J., Dahmen, E.: Post Quantum Cryptography, 1st edn. Springer, Heidelberg (2008) (incorporated)
Brassard, G. (ed.): CRYPTO 1989. LNCS, vol. 435. Springer, Heidelberg (1990)
Brassard, G., Crépeau, C., Robert, J.-M.: Information theoretic reductions among disclosure problems. In: FOCS, pp. 168–173. IEEE (1986)
Faugère, J.C., Otmani, A., Perret, L., Tillich, J.P.: A distinguisher for high rate mceliece cryptosystems
Courtois, N.T., Finiasz, M., Sendrier, N.: How to Achieve a McEliece-Based Digital Signature Scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001)
Crépeau, C.: Equivalence between Two Flavours of Oblivious Transfers. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 350–354. Springer, Heidelberg (1988)
Dowsley, R., van de Graaf, J., Müller-Quade, J., Nascimento, A.C.A.: Oblivious Transfer Based on the McEliece Assumptions. In: Safavi-Naini, R. (ed.) ICITS 2008. LNCS, vol. 5155, pp. 107–117. Springer, Heidelberg (2008)
Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)
Finiasz, M., Sendrier, N.: Security Bounds for the Design of Code-Based Cryptosystems. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 88–105. Springer, Heidelberg (2009)
Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: Johnson, D.S. (ed.) STOC, pp. 25–32. ACM (1989)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229. ACM (1987)
Haitner, I.: Semi-honest to Malicious Oblivious Transfer—The Black-Box Way. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 412–426. Springer, Heidelberg (2008)
Kalai, Y.T.: Smooth Projective Hashing and Two-Message Oblivious Transfer. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 78–95. Springer, Heidelberg (2005)
Kilian, J.: Founding cryptography on oblivious transfer. In: STOC, pp. 20–31. ACM (1988)
Kobara, K., Morozov, K., Overbeck, R.: Coding-Based Oblivious Transfer. In: Calmet, J., Geiselmann, W., Müller-Quade, J. (eds.) MMICS 2008. LNCS, vol. 5393, pp. 142–156. Springer, Heidelberg (2008)
Morozov, K., Savvides, G.: Efficient computational oblivious transfer using interactive hashing. In: Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security, ASIACCS 2011, pp. 448–452. ACM, New York (2011)
Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: STOC, pp. 245–254 (1999)
Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: SODA, pp. 448–457 (2001)
Naor, M., Pinkas, B.: Computationally secure oblivious transfer. J. Cryptology 18(1), 1–35 (2005)
Ostrovsky, R., Venkatesan, R., Yung, M.: Fair games against an all-powerful adversary. In: AMS DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 155–169 (1991)
Peikert, C., Vaikuntanathan, V., Waters, B.: A Framework for Efficient and Composable Oblivious Transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Dwork, C. (ed.) STOC, pp. 187–196. ACM (2008)
Rabin, M.O.: How to exchange secrets with oblivious transfer. Cryptology ePrint Archive, Report 2005/187 (2005), http://eprint.iacr.org/
McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. JPL DSN Progress Report, 114–116 (1978)
Salomaa, A., Santean, L.: Secret selling of secrets with several buyers. Bulletin of the EATCS 42, 178–186 (1990)
De Santis, A., Di Crescenzo, G., Persiano, G.: Zero-knowledge arguments and public-key cryptography. Inf. Comput. 121(1), 23–40 (1995)
Sendrier, N.: The tightness of security reductions in code-based cryptography. In: 2011 IEEE Information Theory Workshop (ITW), pp. 415–419 (October 2011)
Sendrier, N.: Decoding One Out of Many. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 51–67. Springer, Heidelberg (2011)
Shamir, A.: An efficient identification scheme based on permuted kernels (extended abstract). In: Brassard [5], pp. 606–609
Shor, P.W.: Polynominal Time Algorithms for Discrete Logarithms and Factoring on a Quantum Computer. In: Adleman, L.M., Huang, M.-D.A. (eds.) ANTS 1994. LNCS, vol. 877, p. 289. Springer, Heidelberg (1994)
Stern, J.: A New Identification Scheme Based on Syndrome Decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994)
Tzeng, W.-G.: Efficient 1-out-of-n oblivious transfer schemes with universally usable parameters. IEEE Trans. Computers 53(2), 232–240 (2004)
Wang, H., Pieprzyk, J.: Efficient One-Time Proxy Signatures. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 507–522. Springer, Heidelberg (2003)
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K., P.M., Vasant, S., Venkatesan, S., Pandu Rangan, C. (2012). A Code-Based 1-out-of-N Oblivious Transfer Based on McEliece Assumptions. In: Ryan, M.D., Smyth, B., Wang, G. (eds) Information Security Practice and Experience. ISPEC 2012. Lecture Notes in Computer Science, vol 7232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29101-2_10
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DOI: https://doi.org/10.1007/978-3-642-29101-2_10
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