## Cryptology ePrint Archive: Report 2017/464

On the Structure of Unconditional UC Hybrid Protocols

Mike Rosulek and Morgan Shirley

Abstract: We study the problem of secure two-party computation in the presence of a trusted setup. If there is an unconditionally UC-secure protocol for $f$ that makes use of calls to an ideal $g$, then we say that $f$ reduces to $g$ (and write $f \sqsubseteq g$). Some $g$ are complete in the sense that all functions reduce to $g$. However, almost nothing is known about the power of an incomplete $g$ in this setting. We shed light on this gap by showing a characterization of $f \sqsubseteq g$ for incomplete $g$.

Very roughly speaking, we show that $f$ reduces to $g$ if and only if it does so by the simplest possible protocol: one that makes a single call to ideal $g$ and uses no further communication. Furthermore, such simple protocols can be characterized by a natural combinatorial condition on $f$ and $g$.

Looking more closely, our characterization applies only to a very wide class of $f$, and only for protocols that are deterministic or logarithmic-round. However, we give concrete examples showing that both of these limitations are inherent to the characterization itself. Functions not covered by our characterization exhibit qualitatively different properties. Likewise, randomized, superlogarithmic-round protocols are qualitatively more powerful than deterministic or logarithmic-round ones.

Category / Keywords: mpc, uc

Original Publication (with minor differences): IACR-TCC-2018

Date: received 24 May 2017, last revised 22 Sep 2018

Contact author: shirley at cs toronto edu

Available format(s): PDF | BibTeX Citation

Note: Revisions based on comments by TCC 2018 reviewers.

Short URL: ia.cr/2017/464

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