Optimal Improvement Ratios of Multi-Secret Sharing Schemes Can Be Achieved

Department of Computer Science & Information Engineering, National Chi Nan University, Nantou, Taiwan

^a Corresponding author: jsjuan@ncnu.edu.tw

Abstract

Secret sharing schemes (SSS) deal with activities relative to the secure distribution of a secret among a group of participants who then securely reconstruct the secret by collecting the shares which are held by individuals in qualified sets. A multi-secret sharing scheme (MSSS) is an extension of this where multiple secrets are shared simultaneously and where the performance is estimated using both the maximum improvement and average improvement ratios. In 2003, Crescenzo calculated a lower bound of maximum and average improvement ratios for a MSSS and proposed some special MSSS which achieve the lower bound of the maximum improvement ratio. Wang and Juan deployed a more flexible MSSS to achieve the optimal maxi-mum improvement ratio 2006. This paper provides evidence such that the optimal maximum improvement ratio and the optimal average improvement ratio may both be achieved through even simpler and more flexible MSSS through even simpler and more flexible multi-secret sharing schemes for any arbitrary n and m.