Security of meta-He digital signature scheme based on factoring and discrete logarithms

To enhance the security of signature schemes, Pon et al., recently, investigated all eight variants of the He's digital signature scheme. The security of the proposed schemes is based on the difficulties of simultaneously solving the factoring and discrete logarithm problems with almost the same sizes of arithmetic modulus. This paper shows that the all eight variants of the He's digital signature scheme, as well as two more variants, are not secure if attackers can solve discrete logarithm problems. Moreover, the attackers can easily forge signatures of the most optimal signature schemes of the generalized He' signature schemes even though they can solve neither discrete logarithm problems nor factoring.