A Framework for Universally Composable Oblivious Transfer from One-Round Key-Exchange

Pedro Branco SQIG-Instituto de Telecomunicações, Lisbon, Portugal; Department of Mathematics, IST-University of Lisbon, Lisbon, Portugal Jintai Ding University of Cincinnati, Cincinnati, USA Manuel Goulão SQIG-Instituto de Telecomunicações, Lisbon, Portugal; Department of Mathematics, IST-University of Lisbon, Lisbon, Portugal Paulo Mateus SQIG-Instituto de Telecomunicações, Lisbon, Portugal; Department of Mathematics, IST-University of Lisbon, Lisbon, Portugal

TBD mathscidoc:2207.43085

IMACC 2019, 78–101, 2019.12
Oblivious transfer is one of the main pillars of modern cryptography and plays a major role as a building block for other more complex cryptographic primitives. In this work, we present an efficient and versatile framework for oblivious transfer (OT) using one-round key-exchange (ORKE), a special class of key exchange (KE) where only one message is sent from each party to the other. Our contributions can be summarized as follows: - We analyze carefully ORKE schemes and introduce new security definitions. Namely, we introduce a new class of ORKE schemes, called Alice-Bob one-round key-exchange (A-B ORKE), and the definitions of message and key indistinguishability. - We show that OT can be obtained from A-B ORKE schemes fulfilling message and key indistinguishability. We accomplish this by designing a new efficient, versatile and universally composable framework for OT in the Random Oracle Model (ROM). The efficiency of the framework presented depends almost exclusively on the efficiency of the A-B ORKE scheme used since all other operations are linear in the security parameter. Universally composable OT schemes in the ROM based on new hardness assumptions can be obtained from instantiating our framework. Examples are presented using the classical Diffie-Hellman KE, RLWE-based KE and Supersingular Isogeny Diffie-Hellman KE.
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@inproceedings{pedro2019a,
  title={A Framework for Universally Composable Oblivious Transfer from One-Round Key-Exchange},
  author={Pedro Branco, Jintai Ding, Manuel Goulão, and Paulo Mateus},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220715104939076878664},
  booktitle={IMACC 2019},
  pages={78–101},
  year={2019},
}
Pedro Branco, Jintai Ding, Manuel Goulão, and Paulo Mateus. A Framework for Universally Composable Oblivious Transfer from One-Round Key-Exchange. 2019. In IMACC 2019. pp.78–101. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220715104939076878664.
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