SECURING INFORMATION CONFIDENTIALITY: A MATHEMATICAL APPROACH TO DETECTING CHEATING IN ASMUTH-BLOOM SECRET SHARING

The Secret Sharing Scheme (SSS) based on the Chinese Remainder Theorem (CRT) is a crucial method for safeguarding confidential information. However, this scheme is vulnerable to collaborative cheating involving multiple participants. This study aims to modify the Asmuth-Bloom scheme by introducing two detection mechanisms: Threshold Range Detection and Detection Parameter Verification, to identify and prevent collaborative fraudulent activities. The research design is based on mathematical algorithms and tests the effectiveness of detection against predetermined cheating scenarios using structured parameters. The results indicate that the proposed modifications can accurately detect the manipulation of secret fragments, even in cases involving participant collusion. This robustness is achieved through the mathematical structure of the CRT, which enables the detection of inconsistencies during the secret reconstruction process. In addition to maintaining the efficiency of the original Asmuth-Bloom scheme, these modifications enhance the reliability of the scheme in protecting sensitive data. The study concludes that the implementation of dual detection mechanisms significantly strengthens the security of the SSS, particularly in applications prone to dishonest participant collaboration. Future research is recommended to explore computational efficiency and the implementation of this scheme in real-world environments, such as financial systems and blockchain technology.