Security Difference between DSA and Schnorr´s Signature

We investigate the security difference between DSA and Schnorr´s signature. The security of DSA can be reduced to the problem: to find m isin Omega, rho, thetas isin Zq* such that H(m) = P ((g^py)^thetas mod p) mod q, where Omega denotes the text space and the message to is not restrained. Unlike DSA evaluates the hash function only at the message to, Schnorr´s signature adopts a self-feedback mode by evaluating the hash function at (m, r, s). Thus its security becomes more robust.