Cryptanalysis of two signature schemes based on two hard problems

Qiuxin Wu, et al proposed two digital signature schemes (WYH1 and WYH2) whose security is claimed to be based on discrete logarithms problem and factorization problem simultaneously. However, if one of the two problems can be solved, the two schemes WYHl and WYH2 are not secure any more. The attackers can universally forge a valid signature on arbitrary message if the factorization problem is easy to solve. Even more, it can break the schemes (reviving the private key) by using the method of Morrison-Brillhart's factoring if the discrete logarithms problem can be solved.