On Mignotte Secret Sharing Schemes over Gaussian Integers

TL;DR

This paper extends Mignotte's secret sharing scheme to Gaussian integers, analyzing its properties and demonstrating that any access structure can be realized over this ring, thus broadening the scheme's applicability.

Contribution

It introduces an extension of Mignotte's scheme to Gaussian integers and addresses a previous gap, showing universal access structure realization over [ i ].

Findings

Extended Mignotte's scheme to Gaussian integers.

Resolved a gap in previous scheme constructions.

Any access structure can be implemented over [ i ].

Abstract

Secret Sharing Schemes (SSS) are methods for distributing a secret among a set of participants. One of the first Secret Sharing Schemes was proposed by M. Mignotte, based on the Chinese remainder theorem over the ring of integers. In this article we extend the Mignotte's scheme to the ring of Gaussian Integers and study some of its properties. While doing this we aim to solve a gap in a previous construction of such extension. In addition we show that any access structure can be made through a SSS over $ \mathbb{Z}[i]$.