Rijndael on 64-bit platform

Doesn AES (Rijndael) gain any advantages of being implemented on a 64-bit computer compared to the more traditional 32-bit computers?..

From my view it doesn't seem to gain the big advantages. AES works with bytes, so it shouldn't be an advantage to be able to calculate with bigger numbers. Or?.. The only advantage I see is that there are more registers to do parallel operations on the Assembly level, such that it may be easier to do more byte-operations at the same time.

Any facts or meanings on this?

Best Regards,
Stian Karlsen

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