Abstract
We present protocols for two flavors of oblivious transfer (OT): the Rabin and 1-out-of-2 OT based on the assumptions related to security of the McEliece cryptosystem and two zero-knowledge identification (ZKID) schemes, Stern’s from Crypto ’93 and Shamir’s from Crypto ’89, which are based on syndrome decoding and permuted kernels, respectively. This is a step towards diversifying computational assumptions on which OT – cryptographic primitive of central importance – can be based.
As a by-product, we expose new interesting applications for both ZKID schemes: Stern’s can be used for proving correctness of McEliece encryption, while Shamir’s – for proving that some matrix represents a permuted subcode of a given code.
Unfortunately, it turned out to be difficult to reduce the sender’s security of both schemes to a hard problem, although the intuition suggests a successful attack may allow to solve some long-standing problems in coding theory.
Keywords
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Kobara, K., Morozov, K., Overbeck, R. (2008). Coding-Based Oblivious Transfer. In: Calmet, J., Geiselmann, W., Müller-Quade, J. (eds) Mathematical Methods in Computer Science. Lecture Notes in Computer Science, vol 5393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89994-5_12
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