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If we are talking about symmetric encryption, the PAGES block cipher based on Speck support key size 1024 bits and PAGES+/PAGES— variants support key sizes up to 2048 bits. However, I have not seen any independent cryptanalysis of these, so I can't recommend them. If we talk about the ciphers which have some cryptanalysis available, the Kalyna block cipher ...


Nope. Besides old RC4, you can use RSA directly as your cipher at arbitrarily large bitness. We normally don't because its too slow.

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