Small error in security proof on the paper On the Multi-User Security of Short Schnorr Signatures with Preprocessing

Question

I think I found a small error in the security proof Link end of page 37. It states that

$ \sum_{i\leq q} \frac{3i+2}{p-(3q +2)^2/4} \leq \frac{3(q +1)q/2+2}{p - (3q +2)^2 /4}$.

But shouldn't it be

$\sum_{i\leq q} \frac{3i+2}{p-(3q +2)^2/4} \leq \frac{3(q+1)q/2+2q}{p - (3q +2)^2 /4}$ ?

I think that the proof still works, since we want to show that you need $\mathcal{O}(\sqrt{q})$ queries to succeed but it still bothers me.

Thanks in advance!

Answer 1

Yes, you've raised a flaw, you can contact the authors, they will probably update their proof in the paper.

But as you've noticed, it's not a big deal because $2q$ is much smaller than $\frac{3q^2}{2}$ asymptotically. Then both expressions are indeed $\mathcal{O}(\sqrt q)$.