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I'm reading Cryptanalysis of the SIMON Family of Block Ciphers. In Section 3.1, it says:

For SIMON, consider an n-bit input difference $\alpha= x\oplus x'$ to $F$ of Hamming weight one. As the operation $\oplus$ is invariant with respect to rotation, say w.l.o.g. that $\alpha= (0...01)$

I understand that the operation $\oplus$ is invariant with respect to rotation, but I don't understand how apply that claim to the $F$ … According the theory of differential cryptoanalysis I understand that $\alpha$ is not evaluated by $F$ but $x$ and $x'$ are evaluated individually, then I don't understand Why say "the operation $\oplus$ is invariant with respect to rotation, say w.l.o.g. that $\alpha= (0...01)$".

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