Robust Authenticated Encryption and the Limits of Symmetric Cryptography

Robust authenticated encryption (RAE) is a primitive for symmetric encryption that allows to flexibly specify the ciphertext expansion, i.e., how much longer the ciphertext is compared to the plaintext. For every ciphertext expansion, RAE aims at providing the best-possible authenticity and confidentiality. To investigate whether this is actually achieved, we characterize exactly the guarantees symmetric cryptography can provide for any given ciphertext expansion. Our characterization reveals not only that RAE reaches the claimed goal, but also, contrary to prior belief, that one cannot achieve full confidentiality without ciphertext expansion. This provides new insights into the limits of symmetric cryptography. Moreover, we provide a rigorous treatment of two previously only informally stated additional features of RAE; namely, we show how redundancy in the message space can be exploited to improve the security and we analyze the exact security loss if multiple messages are encrypted with the same nonce.