Is Threefish the only cipher with 1024 bits of security?

Question

Threefish has up to a massive 1024 bits of security. Is it the only cipher with such overkill security?

Answer 1

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 supports up to 512-bit keys.

Answer 2

ISAAC can have up to $2^{2^{13}}$ bit keys and has no known attacks better than at least $4.67⋅10^{1240} > 2^{4121}$ complexitiy (assuming that the initial state is chosen uniformly at random). It is a stream cipher, but this can still be used for AEAD.

While old and with only minimal cryptanalysis, the best known attack is still much harder than the brute-force attack against Threefish-1024 (note that this is purely theoretical – not even a quantum computer with the entire universe as fuel could conduct either attack with a reasonable success probability).

Answer 3

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