# Regarding security of blind signature schemes

I'm new to blind signatures, trying to understand security notions of it: blindness and one-more unforgeability.

I found out that in the security game for blindness property, the adversary $$\mathcal{A}$$ interacts with two users (each with messages $$m_0$$ and $$m_1$$). Without knowing who signed first, $$\mathcal{A}$$ gets a list of signatures in order $$\{\sigma(m_b),\sigma(m_{1-b})\}$$. Then $$\mathcal{A}$$ would try to guess which of them came first. That is, to guess a bit $$b'$$. So $$\mathcal{A}$$ succeeds if $$b'=b$$.

My question is: why do we need to interact with two users (or twice)? Can't we just give $$\mathcal{A}$$ a signature of randomly selected message ($$m_0$$ or $$m_1$$)? In that case, $$\mathcal{A}$$ would try to guess which of those two messages were signed.

Can anyone give me the reason why do we need two interactions in the security game?

Thanks in advance.