On Mignotte Secret Sharing Schemes over Gaussian Integers
This work provides a theoretical extension for secret sharing in cryptography, but it appears incremental as it builds directly on existing Mignotte schemes.
The authors extended Mignotte's secret sharing scheme from integers to Gaussian integers, addressing a gap in prior work and demonstrating that any access structure can be implemented using this scheme over Gaussian integers.
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]$.