• Journal of KIISE:Information Networking
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• v.30 no.4
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• pp.474-483
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• 2003

The secret sharing is the basic concept of the threshold cryptosystem and has an important position in the modern cryptography. At 1995, Jarecki proposed the proactive secret sharing to be a solution of existing the mobile adversary and also proposed the share renewal scheme for (k, n) threshold scheme. For n participants in the protocol, his method needs O($n^2$) modular exponentiation per one participant. It is very high computational cost and is not fit for the scalable cryptosystem. In this paper, we propose the efficient share renewal scheme that need only O(n) modular exponentiation per participant. And we prove our scheme is secure if less that ${\frac}\frac{1}{2}n-1$ adversaries exist and they static adversary.