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Murru Saettone RSA

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Before you ask, this is neither for a CTF or homework, this is on problems in implementing non-standard RSA. If it feels like it is a CTF problem I will remove this post if necessary.

Murru Saettone RSA is a variant and quite vulnerable (to a continued fraction attack) RSA scheme based on the cubic pell equation. When implementing this in python, my encryption function appears to (may not) encrypt the data properly, but using a valid decryption key returns the encrypted text. Why would this occur, and how does one properly implement a decryption?

Clarification: the decryption function takes $ct$ and returns the same $ct$ if the key is valid

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poncho
In "returns the encrypted text", does that refer to the original plaintext (as fgrieu stated, that's what's expected), or does it refer to the ciphertext (that is, the decryption operation returns the text it was given)?
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Yes, sorry, given encrypting the text returns $x$, running the decryption function on $x$ returns $x$, like poncho said. It’s interesting because an invalid decryption key run on ciphertext $c$ returns a value that is not $c$.
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