A Weighted Threshold Changeable Multi-Secret Sharing Scheme

Abstract

Secret sharing, an essential cryptographic technique for protecting sensitive data, faces the challenge of simultaneously addressing hierarchical access control, dynamic adjustments to access policies, and the parallel safeguarding of multiple secrets in complex practical scenarios. To address this challenge, this paper presents a novel weighted threshold changeable multi-secret sharing scheme that incorporates the Chinese Remainder Theorem (CRT) and polynomial theory. This scheme introduces a weighting mechanism that associates participants with secrets, allowing distinct participants to possess independent access permission thresholds for specific secrets, thereby facilitating hierarchical access control for multiple secrets. Additionally, to enhance system flexibility and scalability, the proposed solution implements a dynamic adjustment strategy for access permissions, which involves updating the polynomial order and modulus set without reconstructing the original secret. Furthermore, by establishing a system of congruent equations with coprime moduli using CRT, the scheme enables the simultaneous distribution of multiple secrets among participants within the same group. Each secret is assigned an independently adjustable threshold value, thus achieving parallel protection of multiple secrets. Security analysis indicates that the proposed scheme meets information-theoretic security under weight constraints and threshold conditions, and effectively mitigates internal collusion attacks and external eavesdropping attacks. Performance analysis demonstrates that the scheme achieves non-interactive computation during the reconstruction phase, optimizes communication rounds to approach the theoretical lower limit, and the information rate reaches the ideal value of 1.