Abstract
Reducing the minimum assumptions needed to construct various cryptographic primitives is an important and interesting task in theoretical cryptography. Oblivious transfer, one of the most basic cryptographic building blocks, could be also studied under this scenario. Reducing the minimum assumptions for oblivious transfer seems not an easy task, as there are a few impossibility results under black-box reductions.
Until recently, it is widely believed that oblivious transfer can be constructed with trapdoor permutations. Goldreich pointed out some flaw in the folklore and introduced some enhancement to cope with the flaw. Haitner then revised the enhancement more properly. As a consequence they showed that some additional properties for trapdoor permutations are necessary to construct oblivious transfers. In this paper, we discuss possibilities of basing not on trapdoor permutations but on trapdoor functions in general. We generalize previous results and give an oblivious transfer protocol based on a collection of trapdoor functions with some extra properties with respect to the length-expansion and the pre-image size. We discuss that our reduced assumption is almost minimal and show the necessity for the extra properties.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Bellare, M., Halevi, S., Sahai, A., Vadhan, S.P.: Many-to-one trapdoor functions and their relation to public-key cryptosystems. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 283–299. Springer, Heidelberg (1998)
Brassard, G., Crépeau, C., Santha, M.: Oblivious transfers and intersecting codes. IEEE Transactions on Information Theory 42(6), 1769–1780 (1996)
Brassard, G., Crépeau, C., Wolf, S.: Oblivious transfers and privacy amplification. Journal of Cryptology 16(4), 219–237 (2003)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: Proc. 42nd IEEE Symposium on Foundations of Computer Science, pp. 136–145 (2001)
Carter, J., Wegman, M.: Universal classes of hash functions. Journal of Computer and System Sciences 18(2), 143–154 (1979)
Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Simple, black-box constructions of adaptively secure protocols. In: Theory of Cryptography Conference 2009. LNCS, vol. 5444, pp. 387–402 (2009)
Crépeau, C.: Equivalence between two flavours of oblivious transfers. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 350–354. Springer, Heidelberg (1988)
Crépeau, C., Savvides, G.: Optimal reductions between oblivious transfers using interactive hashing. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 201–221. Springer, Heidelberg (2006)
Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory 22(6), 644–654 (1976)
Even, S., Goldreich, O.: A Lempel: A randomized protocol for signing contracts. Communications of the ACM 28(6), 637–647 (1985)
Gertner, Y., Kannan, S., Malkin, T., Reingold, O., Viswanathan, M.: The relationship between public key encryption and oblivious transfer. In: Proc. 41st IEEE Symposium on Foundations of Computer Science, pp. 325–335 (2000)
Goldreich, O.: Foundations of Cryptography, vol II. Cambridge University Press, Cambridge (2004)
Goldreich, O., Levin, L.: A hard-core predicate for all one-way functions. In: Proc. 21st ACM Symposium on Theory of Computing, pp. 25–32 (1989)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or A completeness theorem for protocols with honest majority. In: Proc. 19th ACM Symposium on Theory of Computing, pp. 218–229 (1987)
Haitner, I.: Implementing oblivious transfer using collection of dense trapdoor permutations. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 394–409. Springer, Heidelberg (2004)
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)
Haitner, I., Horvitz, O., Katz, J., Koo, C.-Y., Morselli, R., Shaltiel, R.: Reducing complexity assumptions for statistically-hiding commitment. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 58–77. Springer, Heidelberg (2005)
Haitner, I., Reingold, O.: Statistically-hiding commitment from any one-way function. In: Proc. 39th ACM Symposium on Theory of Computing, pp. 1–10 (2007)
Harnik, D., Naor, M.: On the compressibility of NP instances and cryptographic applications. In: Proc. 47th IEEE Symposium on Foundations of Computer Science, pp. 719–728 (2006)
Impagliazzo, R., Luby, M.: One-way functions are essential for complexity based cryptography. In: Proc. 30th IEEE Symposium on Foundations of Computer Science, pp. 230–235 (1989)
Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proc. 21st ACM Symposium on Theory of Computing, pp. 44–61 (1989)
Kilian, J.: Founding cryptography on oblivious tranfer. In: Proc. 20th ACM Symposium on Theory of Computing, pp. 20–31 (1988)
Naor, M., Ostrovsky, R., Venkatesan, R., Yung, M.: Perfect zero-knowledge arguments for NP using any one-way permutation. Journal of Cryptology 11(2), 87–108 (1998)
Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Proc. 12th ACM-SIAM Symposium on Discrete Algorithms, pp. 448–457 (2001)
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: Proc. 40th ACM Symposium on Theory of Computing, pp. 187–196 (2008)
Rabin, M.: How to exchange secrets by oblivious transfer, Technical Report TR-81, Aiken Computation Laboratory, Harvard University (1981)
Reingold, O., Trevisan, L., Vadhan, S.P.: Notions of reducibility between cryptographic primitives. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 1–20. Springer, Heidelberg (2004)
Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)
Shannon, C.: Communication theory of secrecy systems. Bell System Technical Journal 28(4), 656–715 (1949)
Wiesner, S.: Conjugate coding. SIGACT News 15(1), 78–88 (1983)
Wolf, S., Wullschleger, J.: Oblivious transfer is symmetric. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 222–232. Springer, Heidelberg (2006)
Wullschleger, J.: Oblivious-transfer amplification. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 555–572. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cheong, K.Y., Koshiba, T. (2009). Reducing Complexity Assumptions for Oblivious Transfer. In: Takagi, T., Mambo, M. (eds) Advances in Information and Computer Security. IWSEC 2009. Lecture Notes in Computer Science, vol 5824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04846-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-04846-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04845-6
Online ISBN: 978-3-642-04846-3
eBook Packages: Computer ScienceComputer Science (R0)