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I don't think there is much to be gained by Rijndael-256 (it requires 2 AES-NI operations with a shuffle in between anyway).

There are more promising Feistel-like constructions on top of AES operations such as Areion: https://eprint.iacr.org/2023/794



Any extension of AES to a 256-bit block size would need to use at least a double number of AES-NI operations, but it will also process a double amount of data, so that is not the problem.

The shuffle of Rijndael-256 is suboptimal, being a derivative of the shuffle designed for an 128-bit block, so it is certainly possible to devise something better than that when designing specifically for a 256-bit size. Rijndael-256 has only the advantage that it is a quasi-standard mode, which has passed some cryptanalysis during the AES competition.

I have not studied Areion, but at a first glance I agree with you that it seems promising.




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