Abstract: The security of several partial blind signature schemes based on the discrete logarithm proposed recently by Zhang et al. is analyzed, and it is found that the adversary can get rid of the partial blind property of the signature without being detected by multiplying the reverse of the partial blind factor to the blind message, and the adversary can forge the embedding parameter in the signature. Then, by using the factoring difficulty and covering the order of the generator of the finite field, the improved partial blind signature schemes not only have the partial blind property but also can withstand the forgery of the embedding parameter, and at the same time they have the same other security requirements as those of the schemes by Zhang et al.

Key words: blind signature, partial blind signature, security analysis, discrete logarithm