Which of the following are possible security violations?

A birthday attack on a cryptographic hash function exploits the birthday paradox to find a collision (two distinct messages $m_1$ and $m_2$ such that $H(m_1) = H(m_2)$) in $\mathcal{O}(2^{n/2})$ operations.

• Sender S: Before signing, sender S can generate many valid variations of an innocent message $m$ and many variations of a fraudulent message $m^{\prime}$ until finding a collision pair with $H(m) = H(m^{\prime})$. S can then digitally sign $m$ using their private key and later substitute $m^{\prime}$ with the same signature. Thus, statement (I) is possible.

• Third-party attacker and Receiver R: Neither a third-party attacker nor the receiver R has sender S's private key. Furthermore, for an existing message $m$ that has already been signed by S, finding another message $m^{\prime}$ such that $H(m^{\prime}) = H(m)$ requires a preimage/second-preimage attack (complexity $\mathcal{O}(2^n)$), not a birthday attack. Thus, statements (II) and (III) are not possible via a birthday attack.

Therefore, only (I) is a possible security violation, which corresponds to option B.