# Oblivious Transfer from Any Non-trivial Elastic Noisy Channel via Secret Key Agreement

## Abstract

A \((\gamma ,\delta )\)-elastic channel is a binary symmetric channel between a sender and a receiver where the error rate of an honest receiver is \(\delta \) while the error rate of a dishonest receiver lies within the interval \([\gamma , \delta ]\). In this paper, we show that from *any* non-trivial elastic channel (i.e., \(0<\gamma<\delta <\frac{1}{2}\)) we can implement oblivious transfer with information-theoretic security. This was previously (Khurana et al., Eurocrypt 2016) only known for a subset of these parameters. Our technique relies on a new way to exploit protocols for information-theoretic key agreement from noisy channels. We also show that information-theoretically secure commitments where the receiver commits follow from any non-trivial elastic channel.

### Keywords

Oblivious transfer Elastic channels Key agreement Commitments## Notes

### Acknowledgments

Part of this work was carried out while Ignacio Cascudo was with Aarhus University. The authors acknowledge support from the Danish National Research Foundation and The National Science Foundation of China (under the grant 61361136003) for the Sino-Danish Center for the Theory of Interactive Computation and from the Center for Research in Foundations of Electronic Markets (CFEM), supported by the Danish Strategic Research Council. In addition, Ignacio Cascudo acknowledges support from the Danish Council for Independent Research, grant no. DFF-4002-00367, Ivan Damgrd was also supported by the advanced ERC grant MPCPRO and Samuel Ranellucci was supported by European Research Council Starting Grant 279447. We thank Jesper Buus Nielsen, Maciej Obremski and the anonymous reviewers for their helpful comments.

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