Threshold Changeable Secret Sharing (TCSS) via Skew Polynomials

Abstract

Secret sharing is a tool to divide a secret into multiple shares, so that to reconstruct the secret, it is necessary to collect several shares under certain conditions. Secret sharing was first introduced by Adi Shamir, the scheme is based on polynomials. The secret is represented as a constant value polynomial, and the points on the polynomial graph serve as shares. Secret reconstruction is performed through Lagrange interpolation at a minimum of k out of n points, known as a threshold scheme (k, n). In 2010, Zhang Y. designed a secret sharing scheme through skew polynomials. Involving the role of the automorphism σ in the skew polynomial ring increases the complexity in share distribution and secret reconstruction. In 2012, Zhang Z. designed a secret sharing scheme with a threshold that can change according to the participants present during the reconstruction process, known as Threshold Changeable Secret Sharing (TCSS). This aims to prevent external parties from pretending to be valid participants in order to learn the secret. In this research, a TCSS scheme will be designed using skew polynomials. The aim is to make the TCSS scheme's calculations more complex, making it harder for adversaries to access the secret.