Proceedings of CRYPTO 84 on Advances in cryptology
Fully dynamic secret sharing schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Communications of the ACM
Efficient and Unconditionally Secure Verifiable Threshold Changeable Scheme
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
Updating the parameters of a threshold scheme by minimal broadcast
IEEE Transactions on Information Theory
Lattice-based threshold-changeability for standard CRT secret-sharing schemes
Finite Fields and Their Applications
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In a (r ,n )-threshold secret sharing scheme, nogroup of (r - 1) colluding members can recover the secretvalue s . However, the number of colluders is likely toincrease over time. In order to deal with this issue, one may alsorequire to have the ability to increase the threshold value fromr to r '( r ), such an increment islikely to happen several times. In this paper, we study the problem of threshold changeabilityin a dealer-free environment. First, we compute a theoretical boundon the information and security rate for such a secret sharing.Second, we show how to achieve multiple threshold change for aChinese Remainder Theorem like scheme. We prove that the parametersof this new scheme asymptotically reach the previous bound.