Abstract
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.
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Notes
- 1.
This also contradicts a prior result in [11] that claims that the one-time pad constructs a certain (fully) confidential channel, a so-called XOR-malleable channel, from an insecure channel and a shared key. The proof in that paper is flawed in that the simulation fails if more ciphertexts are injected than messages sent.
- 2.
This relates to the security of RAE schemes which ensures that the message cannot be decrypted using a wrong nonce. In our construction, the nonce is implemented as the sequence number.
- 3.
This ensures that the injected message is different from the one that the sender provided.
- 4.
Implementing the nonce as a counter allows to maintain the order of messages.
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Acknowledgments
Ueli Maurer was supported by the Swiss National Science Foundation (SNF), project no. 200020-132794. Björn Tackmann was supported by the Swiss National Science Foundation (SNF) via Fellowship no. P2EZP2_155566 and the NSF grants CNS-1228890 and CNS-1116800. Much of the work on this paper was done while Phil Rogaway was visiting Ueli Maurer’s group at ETH Zurich. Many thanks to Ueli for hosting that sabbatical. Rogaway was also supported by NSF grants CNS-1228828 and CNS-1314885
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Badertscher, C., Matt, C., Maurer, U., Rogaway, P., Tackmann, B. (2015). Robust Authenticated Encryption and the Limits of Symmetric Cryptography. In: Groth, J. (eds) Cryptography and Coding. IMACC 2015. Lecture Notes in Computer Science(), vol 9496. Springer, Cham. https://doi.org/10.1007/978-3-319-27239-9_7
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