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ModOnions addressed the replay attacks, but it turned out that they are susceptible to the detour attack [8], where a ModOnion is redirected to go back to the attacker after each routing step, and a mix is used as a decryption oracle.
Our first attack uses the fact that a form of oracle decryption is still possible even in the modified scheme.
Moreover, given two ciphertexts, it seems to be infeasible in practice to say whether they have been encrypted under the same key (unless, of course, the decryption key is given).
x](m) denotes an URE ciphertext of a message m for a secret decryption key x.
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (m) is a ciphertext of m with the decryption key equal to [[lambda].
It is obvious that it still is a correct URE ciphertext for the "reduced" decryption key [[lambda].
MARS provides average performance for encryption, decryption and key setup.
RC6 provides average to high-end performance for encryption and decryption, and average performance for key setup.
Rijndael provides consistently high-end performance for encryption, decryption and key setup, although performance decreases for the 192 bit and 256 bit key sizes.
Serpent provides consistently low-end performance for encryption and decryption, and platform-dependent performance for key setup.
Twofish provides platform-dependent performance for encryption and decryption, and consistently low-end performance for key setup.
Twofish experienced the greatest percentage improvement for encryption and decryption, while MARS and RC6 also executed significantly more quickly.