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With my new idea I seem to solve the problem and answer my question, so I'll go ahead and post it as the answer. I choose the new $m'$ as $m'=t+m$ with $t>0$. Now the verification works like this: $v'=g^{m'w} y^{rw}=g^{m'w+xrw}=g^{tw+mw+xrw}=g^{tw} \cdot g^k=r' \mod q$ So my new $r'=g^{tw}r=g^{ts^{-1}}r$ This means I can create a legit signature to any ...

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