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One of the functions used in ITUbee's round function is $L$ which is defined as $L(A, B, C, D, E) = [E \oplus A \oplus B, A \oplus B \oplus C, B \oplus C \oplus D, C \oplus D \oplus E, D \oplus E \oplus A]$. Is this operation invertible?

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Yes, it's invertible. Consider:

$(E \oplus A \oplus B) \oplus (B \oplus C \oplus D) \oplus (C \oplus D \oplus E)$

to get the value of $A$. The values of $B, C, D$ and $E$ can be calculated in a similar manner.

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