Flexible Threshold Proxy Re-signature Schemes

Threshold proxy re-signatures are extensions of proxy re-signatures where re-signature keys are shared among $n$ proxies in such a way that at least $k$ out of $n$ proxies must collaborate to generate the delegator's signatures. The adversary must compromise at least $k$ proxies to learn the re-signing key. Threshold proxy re-signature can protect re-signature key from the attack of internal and external adversaries. However, threshold values in previous threshold proxy re-signatures are fixed. Two flexible threshold proxy re-signature schemes are proposed in this paper, which are existentially unforgeable and robust in the standard model. Based on the Chinese Remainder Theorem, threshold value and the number of proxies can be altered with the significance of the document to be signed. According to the variable threshold value, each proxy can locally generate his re-signature key share and the corresponding verification key. Meanwhile, the proxy re-signature share generation and verification algorithms are non-interactive.