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## Abstract

In recent years, methods to securely mask S-boxes against side-channel attacks by representing them as polynomials over finite binary fields have become quite efficient. A good cost model for this is to count how many non-linear multiplications are needed. In this work we improve on the current state-of-the-art generic method published by Coron–Roy–Vivek at CHES 2014 by working over slightly larger fields than strictly needed. This leads us, for example, to evaluate DES S-boxes with only 3 non-linear multiplications and, as a result, obtain 25% improvement in the running time for secure software implementations of DES when using three or more shares.

On the theoretical side, we prove a logarithmic upper bound on the number of non-linear multiplications required to evaluate any d-bit S-box, when ignoring the cost of working in unreasonably large fields. This upper bound is lower than the previous lower bounds proved under the assumption of working over the field F_{2^d}, and we show this bound to be sharp. We also achieve a way to evaluate the AES S-box using only 3 non-linear multiplications over F_{2^{16}}.

On the theoretical side, we prove a logarithmic upper bound on the number of non-linear multiplications required to evaluate any d-bit S-box, when ignoring the cost of working in unreasonably large fields. This upper bound is lower than the previous lower bounds proved under the assumption of working over the field F_{2^d}, and we show this bound to be sharp. We also achieve a way to evaluate the AES S-box using only 3 non-linear multiplications over F_{2^{16}}.

Original language | English |
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Title of host publication | Cryptographic Hardware and Embedded Systems – CHES 2016 |

Subtitle of host publication | 18th International Conference, Santa Barbara, CA, USA, August 17-19, 2016, Proceedings |

Editors | Benedikt Gierlichs, Axel Y Poschmann |

Publisher | Springer |

Pages | 479-497 |

Number of pages | 19 |

ISBN (Electronic) | 9783662531402 |

ISBN (Print) | 9783662531396 |

DOIs | |

Publication status | Published - 4 Aug 2016 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer Verlag |

Volume | 9813 |

ISSN (Print) | 0302-9743 |

## Keywords

- Side-channel countermeasure
- Masking
- Probing security
- Block cipher
- oftware implementation
- Polynomial evaluation

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## Projects

- 1 Finished