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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.

Naor and Shamir proposed the visual cryptography in 1995, they encrypted secret image into two meaningless random images, called shares, and it can be decrypted by human vision without any calculations. However, there would be problems in alignment when these two shares are staked by hand in practical. Therefore, this paper presents the fault-tolerant schemes of stacking two shares which are acquired from secret image encryption without pixel expansion. The main idea of these schemes is combining several pixels to be a unit, then encrypting every unit into a specific combination of pixels. It makes visual secret sharing scheme more practical.