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Yes, it's bijective. For every input value, it provides a unique output that will decrypt back to that input.

You might be misunderstanding the algorithm. We're only encrypting an incrementing number, not ever encrypting something that is already encrypted.

Ah, okay. Thanks! Maybe I was thinking of hash functions, for which it's not guaranteed that every output has an (n-sized) pre-image?

Edit: To clarify, I do now understand that you were proposing:

random number X -> output encrypt(X), encrypt(X+1), encrypt(X+2), etc

Which I had misinterpreted as:

random number X -> output encrypt(X), encrypt(encrypt(X)), encrypt(encrypt(encrypt(X))) etc.