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Oblivious transfer from any non-trivial elastic noisy channel via secret key agreement. (English) Zbl 1369.94522
Hirt, Martin (ed.) et al., Theory of cryptography. 14th international conference, TCC 2016-B, Beijing, China, October 31 – November 3, 2016. Proceedings. Part I. Berlin: Springer (ISBN 978-3-662-53640-7/pbk; 978-3-662-53641-4/ebook). Lecture Notes in Computer Science 9985, 204-234 (2016).
Summary: A \((\gamma,\delta)\)-elastic channel is a binary symmetric channel between a sender and a receiver where the error rate of an honest receiver is \(\delta\) while the error rate of a dishonest receiver lies within the interval \([\gamma, \delta]\). In this paper, we show that from any non-trivial elastic channel (i.e., \(0<\gamma<\delta <\frac{1}{2}\)) we can implement oblivious transfer with information-theoretic security. This was previously [D. Khurana et al., Eurocrypt 2016, Lect. Notes Comput. Sci. 9666, 184–212 (2016; Zbl 1369.94544)] only known for a subset of these parameters. Our technique relies on a new way to exploit protocols for information-theoretic key agreement from noisy channels. We also show that information-theoretically secure commitments where the receiver commits follow from any non-trivial elastic channel.
For the entire collection see [Zbl 1347.94003].
94A60 Cryptography
Full Text: DOI
[1] Brassard, G., Chaum, D., Crépeau, C.: Minimum disclosure proofs of knowledge. J. Comput. Syst. Sci. 37(2), 156–189 (1988) · Zbl 0656.68109 · doi:10.1016/0022-0000(88)90005-0
[2] Brassard, G., Crépeau, C., Santha, M.: Oblivious transfers and intersecting codes. IEEE Trans. Inf. Theory 42(6), 1769–1780 (1996) · Zbl 0873.94015 · doi:10.1109/18.556673
[3] Brassard, G., Salvail, L.: Secret-key reconciliation by public discussion. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 410–423. Springer, Heidelberg (1994). doi: 10.1007/3-540-48285-7_35 · Zbl 0951.94536 · doi:10.1007/3-540-48285-7_35
[4] Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: Proceedings of 42nd IEEE Symposium on Foundations of Computer Science, pp. 136–145. IEEE (2001) · doi:10.1109/SFCS.2001.959888
[5] 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)
[6] Crépeau, C., Morozov, K., Wolf, S.: Efficient unconditional oblivious transfer from almost any noisy channel. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 47–59. Springer, Heidelberg (2005). doi: 10.1007/978-3-540-30598-9_4 · Zbl 1116.94319 · doi:10.1007/978-3-540-30598-9_4
[7] Crépeau, C.: Efficient cryptographic protocols based on noisy channels. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 306–317. Springer, Heidelberg (1997). doi: 10.1007/3-540-69053-0_21 · doi:10.1007/3-540-69053-0_21
[8] Crépeau, C., Savvides, G.: Optimal reductions between oblivious transfers using interactive hashing. In: Proceedings of Advances in Cryptology - EUROCRYpPT, 25th Annual International Conference on the Theory and Applications of Cryptographic Techniques, St. Petersburg, Russia, May 28–June 1, pp. 201–221 (2006) · Zbl 1140.94332 · doi:10.1007/11761679_13
[9] Crépeau, C., Graaf, J., Tapp, A.: Committed oblivious transfer and private multi-party computation. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 110–123. Springer, Heidelberg (1995). doi: 10.1007/3-540-44750-4_9 · Zbl 0876.94026 · doi:10.1007/3-540-44750-4_9
[10] Damgård, I., Fehr, S., Morozov, K., Salvail, L.: Unfair noisy channels and oblivious transfer. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 355–373. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-24638-1_20 · Zbl 1197.94183 · doi:10.1007/978-3-540-24638-1_20
[11] Damgård, I., Kilian, J., Salvail, L.: On the (im)possibility of basing oblivious transfer and bit commitment on weakened security assumptions. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 56–73. Springer, Heidelberg (1999). doi: 10.1007/3-540-48910-X_5 · Zbl 0932.68045 · doi:10.1007/3-540-48910-X_5
[12] Dodis, Y., Ostrovsky, R., Reyzin, L., Smith, A.D.: Fuzzy extractors: how to generate strong keys from biometrics and other noisy data. SIAM J. Comput. 38(1), 97–139 (2008) · Zbl 1165.94326 · doi:10.1137/060651380
[13] Estren, G.: Universally composable committed oblivious transfer and multi-party computation assuming only basic black-box primitives. Ph.D. thesis, McGill University (2004)
[14] Goldreich, O., Micali, S., Wigderson, A.: How to prove all NP statements in zero-knowledge and a methodology of cryptographic protocol design (Extended Abstract). In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 171–185. Springer, Heidelberg (1987). doi: 10.1007/3-540-47721-7_11 · Zbl 0636.94010 · doi:10.1007/3-540-47721-7_11
[15] Harnik, D., Kilian, J., Naor, M., Reingold, O., Rosen, A.: On robust combiners for oblivious transfer and other primitives. In: Proceedings of Advances in Cryptology - EUROCRYpPT, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Aarhus, Denmark, pp. 96–113, 22–26 May 2005 · Zbl 1137.94346 · doi:10.1007/11426639_6
[16] 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). doi: 10.1007/978-3-642-22792-9_38 · Zbl 1290.94092 · doi:10.1007/978-3-642-22792-9_38
[17] Kilian, J.: Founding cryptography on oblivious transfer. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp. 20–31. ACM (1988)
[18] Kilian, J.: A note on efficient zero-knowledge proofs and arguments. In: Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pp. 723–732. ACM (1992)
[19] Khurana, D., Maji, H.K., Sahai, A.: Secure computation from elastic noisy channels. In: Proceedings of Advances in Cryptology - EUROCRYpPT - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria, Part II, pp. 184–212, 8–12 May 2016 · Zbl 1369.94544 · doi:10.1007/978-3-662-49896-5_7
[20] Maurer, U.M.: Secret key agreement by public discussion from common information. IEEE Trans. Inf. Theory 39(3), 733–742 (1993) · Zbl 0784.94018 · doi:10.1109/18.256484
[21] Pinto, A.C.B., Dowsley, R., Morozov, K., Nascimento, A.C.A.: Achieving oblivious transfer capacity of generalized erasure channels in the malicious model. IEEE Trans. Inf. Theory 57(8), 5566–5571 (2011) · Zbl 1365.94129 · doi:10.1109/TIT.2011.2158898
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