Cryptology ePrint Archive: Report 2016/252

The Exact Round Complexity of Secure Computation

Sanjam Garg and Pratyay Mukherjee and Omkant Pandey and Antigoni Polychroniadou

Abstract: We revisit the exact round complexity of secure computation in the multi-party and two-party settings. For the special case of two-parties without a simultaneous message exchange channel, this question has been extensively studied and resolved. In particular, Katz and Ostrovsky (CRYPTO '04) proved that 5 rounds are necessary and sufficient for securely realizing every two-party functionality where both parties receive the output. However, the exact round complexity of general multi-party computation, as well as two-party computation with a simultaneous message exchange channel, is not very well understood.

These questions are intimately connected to the round complexity of non-malleable commitments. Indeed, the exact relationship between the round complexities of non-malleable commitments and secure multi-party computation has also not been explored.

In this work, we revisit these questions and obtain several new results. First, we establish the following main results. Suppose that there exists a k-round non-malleable commitment scheme, and let k' = max(4, k + 1); then,

– (Two-party setting with simultaneous message transmission): there exists a k'-round protocol for securely realizing every two-party functionality;

– (Multi-party setting):there exists a k'-round protocol for securely realizing the multi-party coin-flipping functionality.

As a corollary of the above results, by instantiating them with existing non-malleable commitment protocols (from the literature), we establish that four rounds are both necessary and sufficient for both the results above. Furthermore, we establish that, for every multi-party functionality five rounds are sufficient. We actually obtain a variety of results offering trade-offs between rounds and the cryptographic assumptions used, depending upon the particular instantiations of underlying protocols.

Category / Keywords: cryptographic protocols / Exact Round Complexity,Multi-Party Computation, Two-Party Computation, Simultaneous Model Exchange Channel, Lower Bound

Original Publication (in the same form): IACR-EUROCRYPT-2016

Date: received 7 Mar 2016, last revised 24 Jul 2017

Contact author: antigoni at cs au dk

Available format(s): PDF | BibTeX Citation

Note: Revised version according to the Ph.D. thesis of Antigoni Polychroniadou. More specifically, the requirement of 3-robust non-malleable commitments is incorporated in this version.

Version: 20170725:050951 (All versions of this report)

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