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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Oblivious Transfer Based on the McEliece Assumptions

Rafael Dowsley, Jeroen van de Graaf, Jörn Müller‐Quade, Anderson C. A. Nascimento

Published Jan 1, 2012• 7 citations
Publisher

Abstract

We implement one-out-of-two bit oblivious transfer (OT) based on the assumptions used in the McEliece cryptosystem: the hardness of decoding random binary linear codes, and the difficulty of distinguishing a permuted generating matrix of Goppa codes from a random matrix. To our knowledge this is the first OT reduction to these problems only. We present two different constructions for oblivious transfer, one based on cut-and-chose arguments and another one which is based on a novel generalization of Bennett-Rudich commitments which may be of independent interest. Finally, we also present a variant of our protocol which is based on the Niederreiter cryptosystem.

DOI
10.1587/transfun.e95.a.567

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We implement one-out-of-two bit oblivious transfer (OT) based on the assumptions used in the McEliece cryptosystem: the hardness of decoding random binary linear codes, and the difficulty of distinguishing a permuted generating matrix of Goppa codes from a random matrix. To our knowledge this is the first OT reduction to these problems only. We present two different constructions for oblivious transfer, one based on cut-and-choose arguments and another one which is based on a novel generalization of Bennett-Rudich commitments which may be of independent interest. Finally, we also present a variant of our protocol which is based on the Niederreiter cryptosystem.

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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2012•4 citations
We implement one-out-of-two bit oblivious transfer (OT) based on the assumptions used in the McEliece cryptosystem: the hardness of decoding random binary linear codes, and the difficulty of distinguishing a permuted generating matrix of Goppa codes from a random matrix. To our knowledge this is the first OT reduction to these problems only. We present two different constructions for oblivious transfer, one based on cut-and-chose arguments and another one which is based on a novel generalization of Bennett-Rudich commitments which may be of independent interest. Finally, we also present a variant of our protocol which is based on the Niederreiter cryptosystem.
We implement one-out-of-two bit oblivious transfer (OT) based on the assumptions used in the McEliece cryptosystem: the hardness of decoding random binary linear codes, and the difficulty of distinguishing a permuted generating matrix of Goppa codes from a random matrix. To our knowledge this is the first OT reduction to these problems only. We present two different constructions for oblivious transfer, one based on cut-and-choose arguments and another one which is based on a novel generalization of Bennett-Rudich commitments which may be of independent interest. Finally, we also present a variant of our protocol which is based on the Niederreiter cryptosystem.
We present two protocols for reducing oblivious transfer (OT) to the security of trapdoor permutations and to the hardness of some coding problems, respectively. The first protocol is the most efficient known to date, while the second one is a theoretical proof-of-concept. Our constructions leverage the power of Interactive Hashing (IH). The first protocol can be viewed as a simple modification of the well-known OT construction by Even, Goldreich and Lem-pel (1985), in which a receiver must send a random domain element to a sender through IH. Alternatively, our protocol can be viewed as a simple modification of the construction by Ostrovsky, Venkatesan and Yung (1993), in which the players substitute the one-way permutation with a trapdoor permutation. We use a similar approach to derive a second OT protocol based on coding assumptions related to security of the McEliece cryptosystem. In our second construction, the receiver inputs a public key into IH while privately keeping the corresponding secret key. Two different versions of IH are used: the computationally secure one in the first protocol, and the information-theoretically secure one in the second.
We use interactive hashing to achieve the most efficient OT protocol to date based solely on the assumption that trapdoor permutations (TDP) exist. Our protocol can be seen as the following (simple) modification of either of the two famous OT constructions: 1) In the one by Even et al (1985), a receiver must send a random domain element to a sender through IH; 2) In the one by Ostrovsky et al (1993), the players should use TDP instead of one-way permutation. A similar approach is employed to achieve oblivious transfer based on the security of the McEliece cryptosystem. In this second protocol, the receiver inputs a public key into IH, while privately keeping the corresponding secret key. Two different versions of IH are used: the computationally secure one in the first protocol, and the information-theoretically secure one in the second.
In an adaptive oblivious transfer (OT) protocol, a sender commits to a database of messages and then repeatedly interacts with a receiver in such a way that the receiver obtains one message per interaction of his choice (and nothing more) while the sender learns nothing about any of the choices. Recently, there has been significant effort to design practical adaptive OT schemes and to use these protocols as a building block for larger database applications. To be well suited for these applications, the underlying OT protocol should: (1) support an efficient initialization phase where one commitment can support an arbitrary number of receivers who are guaranteed of having the same view of the database, (2) execute transfers in time independent of the size of the database, and (3) satisfy a strong notion of security under a simple assumption in the standard model. We present the first adaptive OT protocol simultaneously satisfying these requirements. The sole complexity assumption required is that given (g, g a, g b, g c, Q), where g generates a bilinear group of prime order p and a, b, c are selected randomly from Zp, it is hard to decide if Q = g abc. All prior protocols in the standard model either do not meet our efficiency requirements or