Trustable donation monitor schemes based on randomized Hash signature scheme

An enhanced RMX randomized Hash signature scheme is developed through changing the elective mode of the random value, which does not need the presupposition that the signer should be honest. Based on the enhanced scheme, two trustable donation monitor schemes are put forward. When the donators agree to reveal the donations, an accurate donation monitor scheme can be proposed. Through comparing the received donations, any two donators can judge whether the charity proclaims the right total number of the donation or not. When the donators refuse to reveal the donations, an ambiguous donation monitor scheme is advanced based on the enhanced RMX scheme and the millionaires' problem. And the donators also can supervise the charity. The analysis results demonstrate that the computation complexities with lying by the charity and forging by the evil donators are both O (2^n/2), where n is the output length of the Hash function. Thus, these schemes are secure enough under the existing computer power when n > 160 bit.