## 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 P^{2}q^{2} (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 P^{2}q and increases the signal to noise ratio of the resultant distinguisher. We call this variant a 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 2^{32}. At Crypto’18 it was finally reduced to 2^{24} (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 2^{16.5} (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.

Original language | English |
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Title of host publication | Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |

Editors | Anne Canteaut, Yuval Ishai |

Publisher | Springer |

Pages | 280-309 |

Number of pages | 30 |

ISBN (Print) | 9783030457204 |

DOIs | |

State | Published - 2020 |

Event | 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 - Zagreb, Croatia Duration: 10 May 2020 → 14 May 2020 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12105 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 |
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Country/Territory | Croatia |

City | Zagreb |

Period | 10/05/20 → 14/05/20 |