### Abstract

AES is probably the most widely studied and used block cipher. Also versions with a reduced number of rounds are used as a building block in many cryptographic schemes, e.g. several candidates of the SHA-3 and CAESAR competition are based on it. So far, non-random properties which are independent of the secret key are known for up to 4 rounds of AES. These include differential, impossible differential, and integral properties. In this paper we describe a new structural property for up to 5 rounds of AES, differential in nature and which is independent of the secret key, of the details of the MixColumns matrix (with the exception that the branch number must be maximal) and of the SubBytes operation. It is very simple: By appropriate choices of difference for a number of input pairs it is possible to make sure that the number of times that the difference of the resulting output pairs lie in a particular subspace is always a multiple of 8. We not only observe this property experimentally (using a small-scale version of AES), we also give a detailed proof as to why it has to exist. As a first application of this property, we describe a way to distinguish the 5-round AES permutation (or its inverse) from a random permutation with only 2^{32} chosen texts that has a computational cost of 2^{35.6} lookups into memory of size 2^{36} bytes which has a success probability greater than 99%.

Original language | English |
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Title of host publication | Advances in Cryptology – EUROCRYPT 2017 - 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |

Publisher | Springer Verlag Wien |

Pages | 289-317 |

Number of pages | 29 |

Volume | 10211 LNCS |

ISBN (Print) | 9783319566139 |

DOIs | |

Publication status | Published - 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 10211 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Fingerprint

### Keywords

- AES
- Block cipher
- Permutation
- Secret-key distinguisher

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Advances in Cryptology – EUROCRYPT 2017 - 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings*(Vol. 10211 LNCS, pp. 289-317). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10211 LNCS). Springer Verlag Wien. https://doi.org/10.1007/978-3-319-56614-6_10

**A new structural-differential property of 5-round AES.** / Grassi, Lorenzo; Rechberger, Christian; Rønjom, Sondre.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*Advances in Cryptology – EUROCRYPT 2017 - 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings.*vol. 10211 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10211 LNCS, Springer Verlag Wien, pp. 289-317. https://doi.org/10.1007/978-3-319-56614-6_10

}

TY - GEN

T1 - A new structural-differential property of 5-round AES

AU - Grassi, Lorenzo

AU - Rechberger, Christian

AU - Rønjom, Sondre

PY - 2017

Y1 - 2017

N2 - AES is probably the most widely studied and used block cipher. Also versions with a reduced number of rounds are used as a building block in many cryptographic schemes, e.g. several candidates of the SHA-3 and CAESAR competition are based on it. So far, non-random properties which are independent of the secret key are known for up to 4 rounds of AES. These include differential, impossible differential, and integral properties. In this paper we describe a new structural property for up to 5 rounds of AES, differential in nature and which is independent of the secret key, of the details of the MixColumns matrix (with the exception that the branch number must be maximal) and of the SubBytes operation. It is very simple: By appropriate choices of difference for a number of input pairs it is possible to make sure that the number of times that the difference of the resulting output pairs lie in a particular subspace is always a multiple of 8. We not only observe this property experimentally (using a small-scale version of AES), we also give a detailed proof as to why it has to exist. As a first application of this property, we describe a way to distinguish the 5-round AES permutation (or its inverse) from a random permutation with only 232 chosen texts that has a computational cost of 235.6 lookups into memory of size 236 bytes which has a success probability greater than 99%.

AB - AES is probably the most widely studied and used block cipher. Also versions with a reduced number of rounds are used as a building block in many cryptographic schemes, e.g. several candidates of the SHA-3 and CAESAR competition are based on it. So far, non-random properties which are independent of the secret key are known for up to 4 rounds of AES. These include differential, impossible differential, and integral properties. In this paper we describe a new structural property for up to 5 rounds of AES, differential in nature and which is independent of the secret key, of the details of the MixColumns matrix (with the exception that the branch number must be maximal) and of the SubBytes operation. It is very simple: By appropriate choices of difference for a number of input pairs it is possible to make sure that the number of times that the difference of the resulting output pairs lie in a particular subspace is always a multiple of 8. We not only observe this property experimentally (using a small-scale version of AES), we also give a detailed proof as to why it has to exist. As a first application of this property, we describe a way to distinguish the 5-round AES permutation (or its inverse) from a random permutation with only 232 chosen texts that has a computational cost of 235.6 lookups into memory of size 236 bytes which has a success probability greater than 99%.

KW - AES

KW - Block cipher

KW - Permutation

KW - Secret-key distinguisher

UR - http://www.scopus.com/inward/record.url?scp=85018687641&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-56614-6_10

DO - 10.1007/978-3-319-56614-6_10

M3 - Conference contribution

SN - 9783319566139

VL - 10211 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 289

EP - 317

BT - Advances in Cryptology – EUROCRYPT 2017 - 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings

PB - Springer Verlag Wien

ER -