# (Efficient) Universally Composable Oblivious Transfer Using a Minimal Number of Stateless Tokens

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## Abstract

We continue the line of work initiated by Katz (Eurocrypt 2007) on using *tamper-proof hardware tokens* for universally composable secure computation. As our main result, we show an oblivious-transfer (OT) protocol in which two parties each create and transfer a single, stateless token and can then run an unbounded number of OTs. We also show a more efficient protocol, based only on standard symmetric-key primitives (block ciphers and collision-resistant hash functions), that can be used if a *bounded* number of OTs suffice. Motivated by this result, we investigate the number of stateless tokens needed for universally composable OT. We prove that our protocol is *optimal* in this regard for constructions making *black-box* use of the tokens (in a sense we define). We also show that nonblack-box techniques can be used to obtain a construction using only a single stateless token.

## Keywords

Secure computation Oblivious transfer Hardware tokens Universal composability## Notes

### Acknowledgements

We thank the anonymous reviewers for their careful and thorough reading of our paper and for their helpful comments.

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