In 1998, Shao proposed two digital signature schemes and claimed that the security of which is based on the difficulties of computing both integer factorization and discrete logarithm. However, at the same year, Li and Xiao demonstrated that Shao’s schemes are insecure are not based on any hard problem. Recently, Wei proposed two “Digital Signature Schemes Based on Two Hard Problems” to improve Shao’s schemes, and showed that it can resist Li and Xiao’s attack. We show that neither scheme is as secure as the author claim. One can forge a valid signature of an arbitrary message by using Pollard and Schnorr’s method without solving the discrete logarithm problem or the factorization hard problem.

digital signature, factorization problem, discrete logarithm problem, two hard problems