Cryptology ePrint Archive: Report 2020/116

Separating Two-Round Secure Computation from Oblivious Transfer

Benny Applebaum and Zvika Brakerski and Sanjam Garg and Yuval Ishai and Akshayaram Srinivasan

Abstract: We consider the question of minimizing the round complexity of protocols for secure multiparty computation (MPC) with security against an arbitrary number of semi-honest parties. Very recently, Garg and Srinivasan (Eurocrypt 2018) and Benhamouda and Lin (Eurocrypt 2018) constructed such 2-round MPC protocols from minimal assumptions. This was done by showing *a round preserving reduction* to the task of secure *2-party* computation of the oblivious transfer functionality (OT). These constructions made a novel non-black-box use of the underlying OT protocol. The question remained whether this can be done by only making black-box use of 2-round OT. This is of theoretical and potentially also practical value as black-box use of primitives tends to lead to more efficient constructions.

Our main result proves that such a black-box construction is impossible, namely that non-black-box use of OT is necessary. As a corollary, a similar separation holds when starting with any 2-party functionality other than OT.

As a secondary contribution, we prove several additional results that further clarify the landscape of black-box MPC with minimal interaction. In particular, we complement the separation from 2-party functionalities by presenting a complete 4-party functionality, give evidence for the difficulty of ruling out a complete 3-party functionality and for the difficulty of ruling out black-box constructions of 3-round MPC from 2-round OT, and separate a relaxed ``non-compact'' variant of 2-party *secret sharing* from 2-round OT.

Category / Keywords: cryptographic protocols / secure multiparty computation, black-box reductions, oblivious transfer

Original Publication (with major differences): ITCS 2020

Date: received 4 Feb 2020

Contact author: zvika brakerski at weizmann ac il

Available format(s): PDF | BibTeX Citation

Version: 20200206:144342 (All versions of this report)

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