Oblivious Transfer Based on the McEliece Assumptions

Rafael DOWSLEY  Jeroen van de GRAAF  Jorn MULLER-QUADE  Anderson C. A. NASCIMENTO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.2   pp.567-575
Publication Date: 2012/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.567
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Cryptography and Information Security
oblivious transfer,  McEliece cryptosystem,  post-quantum security,  

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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-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.