Abstract
The evolving k-threshold secret sharing scheme allows the dealer to distribute the secret to many participants such that only no less than k shares together can restore the secret. In contrast to the conventional secret sharing scheme, the evolving scheme allows the number of participants to be uncertain and even ever-growing. In this paper, we consider the evolving secret sharing scheme with k=3. First, we point out that the prior approach has risks in the security. To solve this issue, we then propose a new evolving 3-threshold scheme with perfect security. Given a ℓ-bit secret, the t-th share of the proposed scheme has log₂ t +O( log₄ log₂ t²)+log₂ p(2 log₄ log₂ t-1) bits, where p is a prime. Compared with the prior result 2 log₂ t+O(log₂ t)+ℓ, the proposed scheme reduces the leading constant from 2 to 1. Finally, we propose a conventional 3-threshold secret sharing scheme over a finite field. Based on this model of the revised scheme and the proposed conventional 3-threshold scheme, we present a brand-new and more concise evolving 3-threshold secret sharing scheme.