Security of two signature schemes based on two hard problems

To provide more confidence to users of digital signatures, recently, Wei and Yuan et al. proposed two digital signature schemes respectively. They claimed that the security of their schemes is based on factoring and discrete logarithms simultaneously. Moreover, they thought that their schemes accomplish three merits proposed by Shao. In this paper, we show that the two schemes are not secure at all. We can forge signatures for arbitrary messages without any knowledge about the private keys.