What is a formal definition of strong one-time-secure signatures?
It's the usual security game for digital signatures, but the adversary is only allowed to make a single signature query.

In other words:


The simulator generates a key pair, and gives the adversary the verification key.
The adversary sends the simulator a message $m$. The simulator signs the message and sends the signature $\sigma$ to the adversary.
The adversary outputs his forgery $(m',\sigma')$.


The adversary wins if $\sigma'$ is a valid signature on $m'$ and $(m',\sigma') \not= (m,\sigma)$.

In the usual signature game, the second step can be repeated many times.