Evolving Perfect Hash Families: A Combinatorial Viewpoint of Evolving Secret Sharing

Shamir’s threshold secret sharing scheme gives an efficient way to share a secret among n participants such that any k or more of them can reconstruct the secret. For implementation, Shamir’s scheme requires a finite field. Desmedt et al. (AsiaCrypt ’94) proposed a multiplicative secret sharing scheme over non-abelian groups. In this paper, we extend (non-abelian) multiplicative secret sharing to accommodate unbounded number of participants. We introduce a new combinatorial concept of “evolving” Perfect Hash Families and present a secret sharing scheme as a consequence.

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