Security Difference between DSA and Schnorr's Signature

Abstract

We investigate the security difference between DSA and Schnorr's signature. The security of DSA can be reduced to the problem: to find $m\in \Omega, \rho, \theta\in \mathcal {Z}_q^*$ such that $\mathcal {H}(m) =\rho\left((g^{\rho}y)^{\theta}\, \mbox{mod}\, p\right) \,\mbox{mod}\, q$,where $\Omega $ denotes the text space and the message$m$ is not restrained. Unlike DSA evaluates the hash function only at the message $m$, Schnorr's signature adopts a self-feedback mode by evaluating the hash function at $(m, r, s)$. Thus its security becomes more robust.