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To improve the real-time efficiency of proxy re-signature schemes, a notion called divisible on-line/off-line proxy resignatures is introduced in this paper. The idea of this notion is to split the re-signing algorithm into two phases: the off-line and on-line phases. The proxy can perform the bulk of re-signature computation in the off-line phase before seeing the message to be re-signed. The results of this pre-computation are saved and then used in the on-line phase after the message to be re-signed is given. Divisible on-line/off-line proxy re-signatures are very useful in a particular scenario where the proxy must respond quickly once the message to be re-signed is presented. In a divisible on-line/off-line proxy re-signature scheme, the partial re-signature might be exposed before the message to be re-signed arrives. We then propose a generic divisible on-line/off-line proxy re-signature scheme, which can transform any proxy re-signature scheme into a highly efficient divisible on-line/off-line proxy re-signature scheme. Compared to existing proxy re-signature schemes, our scheme demonstrates higher efficiency. The security of the scheme relies on the unforgeability of its underlying proxy re-signature scheme and the difficulty to solve the discrete logarithm problem.

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