Paper 2017/687
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.
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.
Metadata
- Available format(s)
- -- withdrawn --
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- mpc
- Contact author(s)
- rosulekm @ eecs oregonstate edu
- History
- 2017-07-23: withdrawn
- 2017-07-18: received
- See all versions
- Short URL
- https://ia.cr/2017/687
- License
-
CC BY