Difference between Multi-linear and Multi-Secret Sharing Schemes

Question

I've been reading papers on secret sharing schemes and came to two different terms, namely, multi-linear secret sharing schemes and multi-secret sharing schemes. As an example, the term multi-linear is used by Beimel et al. in Multi-linear secret-sharing schemes publication. On the other hand, the term multi-secret is used by Yang et al. and Chien et al. in A $(t, n)$ multi-secret sharing scheme and A Practical $(t,n)$ Multi-Secret Sharing Scheme respectively. Are these two terms the same?

I would appreciate someone helping me with this.

Answer 1

As quoted by Yang's A (t,n) multi-secret sharing scheme line 76.

In fact, various secret sharing schemes have different approaches.

So by using the term Multi-secret sharing means to share multiple secret by any means. That makes Multi-Linear secret sharing is a subset of Multi-secret sharing.

I'm not 100% sure on this but it appears to me that for Linear secret sharing scheme, it involves solving matrix to find a linear recombination of each part of the secret and used it to reconstruct the hidden secret.

In this sense, Chien's A Practical (t,n) Multi-Secret Sharing Scheme is close to Multi-Linear secret sharing scheme in the sense that it has a matrix and you need to solve an equation to find the secret. The different between the two scheme is on how you construct the matrix.

On the other hand, Yang's work relies on Shamir's Secret Sharing as quoted in line 80.

In this article, we will propose a multi-secret sharing scheme based on Shamir's secret sharing