On the Oblivious Transfer Capacity of Generalized Erasure Channels Against Malicious Adversaries: The Case of Low Erasure Probability

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

DOI

  • Rafael Dowsley
  • ,
  • Anderson C.A. Nascimento, University of Washington Tacoma

Noisy channels are a powerful resource for cryptography as they can be used to obtain information-theoretic secure key agreement, commitment, and oblivious transfer protocols, among others. Oblivious transfer (OT) is a fundamental primitive, since it is complete for secure multi-party computation, and the OT capacity characterizes how efficiently a channel can be used for obtaining string oblivious transfer. Ahlswede and Csiszár (ISIT'07) presented upper and lower bounds on the OT capacity of generalized erasure channels (GECs) against passive adversaries. In the case of GEC with erasure probability at least 1/2, the upper and lower bounds match and, therefore, the OT capacity was determined. It was later proved by Pinto et al. [IEEE Trans. Inf. Theory 57(8)] that the OT capacity is identical for passive and malicious adversaries. In the case of GEC with erasure probability smaller than 1/2, the known lower bound against passive adversaries that was established by Ahlswede and Csiszár does not match their upper bound and it was unknown whether this OT rate could be achieved against malicious adversaries as well. In this paper, we show that there is a protocol against malicious adversaries achieving the same OT rate that was obtained against passive adversaries. We obtain our results by a new combination of interactive hashing and typicality tests that are suitable for dealing with the case of low erasure probability (p <1/2).

Original languageEnglish
Article number8000673
JournalIEEE Transactions on Information Theory
Volume63
Issue10
Pages (from-to)6819-6826
Number of pages8
ISSN0018-9448
DOIs
Publication statusPublished - Oct 2017

    Research areas

  • generalized erasure channel, information-theoretic security, malicious adversaries, Oblivious transfer, oblivious transfer capacity

See relations at Aarhus University Citationformats

ID: 118166480