IACR News item: 08 March 2016
Sanjam Garg, Pratyay Mukherjee, Omkant Pandey, Antigoni Polychroniadou
ePrint Report
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.
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.
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