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I know different parts of this circuit, just I have a problem with that part that I circled in picture. I want to know the function of that part. If you have useful information about it, please share it with me. Thank you so much.

It's a modular multiplication gate. It permutes the states such that, for all $k$ below $N$, state $|k\rangle$ becomes state $|k \cdot c \pmod{N}\rangle$ where $N$ is the number being factored and $c = b^{2^{2n-1}} \pmod{N}$ is a classically computed constant and $b$ is the base value chosen randomly at the start of the algorithm.

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