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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Efficient Fully Simulatable Oblivious Transfer from the McEliece Assumptions

Bernardo David, Anderson C. A. Nascimento, Rafael T. de Sousa

Published Jan 1, 2012• 4 citations
Publisher

Abstract

We introduce an efficient fully simulatable construction of oblivious transfer based on the McEliece assumptions in the common reference string model. This is the first efficient fully simulatable oblivious protocol based on coding assumptions. Moreover, being based on the McEliece assumptions, the proposed protocol is a good candidate for the post-quantum scenario.

DOI
10.1587/transfun.e95.a.2059

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We introduce an efficient fully simulatable construction of oblivious transfer based on the McEliece assumptions in the common reference string model. This is the first efficient fully simulatable oblivious protocol based on coding assumptions. Moreover, being based on the McEliece assumptions, the proposed protocol is a good candidate for the post-quantum scenario.
We introduce a general construction of fully simulatable oblivious transfer based on lossy encryption. Furthermore, we extend the common definition of lossy encryption by introducing the notion of computationally lossy encryption. If the cryptosystem used is computationally lossy, our general construction yields oblivious transfer protocols with computational security for both parties. Otherwise, when regular statistically lossy cryptosystems are employed in this construction, it yields oblivious transfer protocols with statistical security for the sender. The construction introduced in this paper is realizable from rerandomizable, homomorphic and lossy cryptosystems in general. Thus, it yields specific constructions based on different assumptions, such as DDH, LWE and McEliece. Moreover, it proves the equivalence of fully simulatable oblivious transfer and lossy encryption.
Oblivious transfer, first introduced by Rabin, is one of the basic building blocks of cryp-tographic protocols. In an oblivious transfer (or more exactly, in its 1-out-of-2 variant), one party known as the sender has a pair of messages and the other party known as the receiver obtains one of them. Somewhat paradoxically, the receiver obtains exactly one of the messages (and learns nothing of the other), and the sender does not know which of the messages the receiver obtained. Due to its importance as a building block for secure protocols, the efficiency of oblivious transfer protocols has been extensively studied. However, to date, there are almost no known oblivious transfer protocols that are secure in the presence of malicious adversaries under the real/ideal model simulation paradigm (without using general zero-knowledge proofs). Thus, efficient protocols that reach this level of security are of great interest. In this paper we present efficient oblivious transfer protocols that are secure according to the ideal/real model simulation paradigm. We achieve constructions under the DDH, Nth residuosity and quadratic residuosity assumptions, as well as under the assumption that homomorphic encryption exists. 1
Secure computation is a powerful cryptographic tool that encompasses the evaluation of any multivariate function with arbitrary inputs from mutually distrusting parties. The oblivious transfer primitive serves is a basic building block for the general task of secure multi-party computation. Therefore, analyzing the security in the universal composability framework becomes mandatory when dealing with multi-party computation protocols composed of oblivious transfer subroutines. Furthermore, since the required number of oblivious transfer instances scales with the size of the circuits, oblivious transfer remains as a bottleneck for large-scale multi-party computation implementations. Techniques that allow one to extend a small number of oblivious transfers into a larger one in an efficient way make use of the oblivious transfer variant called randomized oblivious transfer. In this work, we present randomized versions of two known oblivious transfer protocols, one quantum and another post-quantum with ring learning with an error assumption. We then prove their security in the quantum universal composability framework, in a common reference string model.