Calculating the value of a function for given inputs, especially, in the context of secure multi-party computation and/or homomorphic encryption, without disclosing the inputs to some or all parties carrying out the calculation.

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What criteria make the theta step of Keccak's round function reversible?

From what I've been reading, Keccak's round function is reversible. That's pretty obvious for the $\rho$, $\pi$ and $\iota$ transforms. For $\chi$ to be reversible, $x$'s range has to be odd — but ...