On the Feasibility of Extending Oblivious Transfer

On the Feasibility of Extending Oblivious Transfer Oblivious transfer is one of the most basic and important building blocks in cryptography. As such, understanding its cost is of prime importance. Beaver (in: The 28th STOC, pp 479–488, 1996) showed that it is possible to obtain $$\mathsf{poly}(n)$$ poly ( n ) oblivious transfers given only n actual oblivious transfer calls and using one-way functions, where n is the security parameter. In addition, he showed that it is impossible to extend oblivious transfer information theoretically. The notion of extending oblivious transfer is important theoretically (to understand the complexity of computing this primitive) and practically (since oblivious transfers can be expensive and thus extending them using only one-way functions is very attractive). Despite its importance, very little is known about the feasibility of extending oblivious transfer, beyond the fact that it is impossible information theoretically. Specifically, it is not known whether or not one-way functions are actually necessary for extending oblivious transfer, whether or not it is possible to extend oblivious transfers with adaptive security, and whether or not it is possible to extend oblivious transfers when starting with $$O(\log n)$$ O ( log n ) oblivious transfers. In this paper, we address these questions and provide almost complete answers to all of them. We show that the existence of any oblivious transfer extension protocol with security for static semi-honest adversaries implies one-way functions, that an oblivious transfer extension protocol with adaptive security implies oblivious transfer with static security, and that the existence of an oblivious transfer extension protocol from only $$O(\log n)$$ O ( log n ) oblivious transfers implies oblivious transfer itself. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Cryptology Springer Journals

On the Feasibility of Extending Oblivious Transfer

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Publisher
Springer Journals
Copyright
Copyright © 2017 by International Association for Cryptologic Research
Subject
Computer Science; Coding and Information Theory; Computational Mathematics and Numerical Analysis; Combinatorics; Probability Theory and Stochastic Processes; Communications Engineering, Networks
ISSN
0933-2790
eISSN
1432-1378
D.O.I.
10.1007/s00145-017-9269-5
Publisher site
See Article on Publisher Site

Abstract

Oblivious transfer is one of the most basic and important building blocks in cryptography. As such, understanding its cost is of prime importance. Beaver (in: The 28th STOC, pp 479–488, 1996) showed that it is possible to obtain $$\mathsf{poly}(n)$$ poly ( n ) oblivious transfers given only n actual oblivious transfer calls and using one-way functions, where n is the security parameter. In addition, he showed that it is impossible to extend oblivious transfer information theoretically. The notion of extending oblivious transfer is important theoretically (to understand the complexity of computing this primitive) and practically (since oblivious transfers can be expensive and thus extending them using only one-way functions is very attractive). Despite its importance, very little is known about the feasibility of extending oblivious transfer, beyond the fact that it is impossible information theoretically. Specifically, it is not known whether or not one-way functions are actually necessary for extending oblivious transfer, whether or not it is possible to extend oblivious transfers with adaptive security, and whether or not it is possible to extend oblivious transfers when starting with $$O(\log n)$$ O ( log n ) oblivious transfers. In this paper, we address these questions and provide almost complete answers to all of them. We show that the existence of any oblivious transfer extension protocol with security for static semi-honest adversaries implies one-way functions, that an oblivious transfer extension protocol with adaptive security implies oblivious transfer with static security, and that the existence of an oblivious transfer extension protocol from only $$O(\log n)$$ O ( log n ) oblivious transfers implies oblivious transfer itself.

Journal

Journal of CryptologySpringer Journals

Published: Dec 4, 2017

References

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