Distinguishing Attack on CBC-MACs I want to ask again about distinguishing attack on CBC MAC, based on the paper published by Ketting Jia, Xiaoyun Wang, Zheng Yuan, and Guangwu Xu: Distinguishing Attack and Second-Preimage Attack on the CBC-like MACs.

That paper says: "The adversary makes $2^{(n+1)/2}$ queries with $m$-block messages that have the same last $m−1$ blocks."

What I want to ask is why the authors choose $2^{(n+1)/2}$?

As we know, block cipher's input width is usually even, so if we operated it with $2^{(n+1)/2}$ the result will not be an integer, but fractional.
Why approximately $2^{(n+1)/2}$ queries?  Because it makes the attack work.

As far as your final comment, it sounds like you are confusing $(n+1)/2$ with $2^{(n+1)/2}$.  If we use AES, then $n=128$, so $(n+1)/2=64.5$.  However, $2^{64.5}$ is a very large number.  The exact number of queries is not important as long as it is approximately $2^{64.5}$, and it is easy to choose an integer near that number.