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The Retracing Boomerang Attack

Authors:
Orr Dunkelman , University of Haifa
Nathan Keller , Bar-Ilan University
Eyal Ronen , Tel Aviv University and KU Leuven
Adi Shamir , Weizmann Institute of Science
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DOI: 10.1007/978-3-030-45721-1_11 (login may be required)
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Conference: EUROCRYPT 2020
Abstract: Boomerang attacks are extensions of differential attacks, that make it possible to combine two unrelated differential properties of the first and second part of a cryptosystem with probabilities p and q into a new differential-like property of the whole cryptosystem with probability p2q2 (since each one of the properties has to be satisfied twice). In this paper we describe a new version of boomerang attacks which uses the counterintuitive idea of throwing out most of the data in order to force equalities between certain values on the ciphertext side. In certain cases, this creates a correlation between the four probabilistic events, which increases the probability of the combined property to p2q and increases the signal to noise ratio of the resultant distinguisher. We call this variant a {\it retracing boomerang attack} since we make sure that the boomerang we throw follows the same path on its forward and backward directions. To demonstrate the power of the new technique, we apply it to the case of 5-round AES. This version of AES was repeatedly attacked by a large variety of techniques, but for twenty years its complexity had remained stuck at 232. At Crypto'18 it was finally reduced to 224 (for full key recovery), and with our new technique we can further reduce the complexity of full key recovery to the surprisingly low value of 216.5 (i.e., only 90,000 encryption/decryption operations are required for a full key recovery on half the rounds of AES). In addition to improving previous attacks, our new technique unveils a hidden relationship between boomerang attacks and two other cryptanalytic techniques, the yoyo game and the recently introduced mixture differentials.
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BibTeX
@inproceedings{eurocrypt-2020-30187,
  title={The Retracing Boomerang Attack},
  booktitle={39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  keywords={boomerang attack;yoyo;mixture differentials;rectangle attack;AES},
  volume={12105},
  doi={10.1007/978-3-030-45721-1_11},
  author={Orr Dunkelman and Nathan Keller and Eyal Ronen and Adi Shamir},
  year=2020
}