**Impossibility of Secure Multi-Party Products in Non-Abelian Groups**

*Jessica Covington and Megan Golbek and Mike Rosulek*

**Abstract: **Suppose $n$ parties have respective inputs $x_1, \ldots, x_n \in \mathbb{G}$, where $\mathbb{G}$ is a finite group. The parties would like to privately compute $x_1 x_2 \cdots x_n$ (where multiplication refers to the group operation in $\mathbb{G}$). There is a well-known secure protocol that works for any number of parties $n$ when $\mathbb{G}$ is abelian.
In this note we consider private group-product protocols for non-abelian groups. We show that such protocols are possible for if and only if $n$ (the number of parties) is less than 4.

**Category / Keywords: **foundations / mpc

**Date: **received 8 Jul 2017, last revised 18 Jul 2017, withdrawn 22 Jul 2017

**Contact author: **rosulekm at eecs oregonstate edu

**Available format(s): **(-- withdrawn --)

**Note: **We are withdrawing this report after discovering that its results have previously appeared in the following paper:
Desmedt, Pieprzyk, Steinfeld & Wang: "On Secure Multi-Party Computation in Black-Box Groups", CRYPTO 2007.

**Version: **20170723:020505 (All versions of this report)

**Short URL: **ia.cr/2017/687

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