## Abstract

Plateaued functions are very important cryptographic functions due to theirdesirable cryptographic characteristics. We find explicit criteria forthe construction of p-ary r-plateaued functions with an odd prime p. We point out that 0-plateaued functions are bent functions, and so plateaued functions generalize the notion of bent functions. We first derive an explicit form forthe Walsh-Hadamard transform of a p-ary r-plateaued function. We then obtain an upperbound on the degree of p-ary r-plateaued functions, and we classify p-ary (n-1) -plateaued functions in n variables. We also obtain explicit criteria forthe existence of p-ary r-plateaued functions. Accordingly, these results lead to improved bounds on the existence of p-ary bent functions.

Original language | English |
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Article number | 7506113 |

Pages (from-to) | 7555-7565 |

Number of pages | 11 |

Journal | IEEE Transactions on Information Theory |

Volume | 62 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2016 |

## Keywords

- Plateaued function
- Walsh-Hadamard transform
- bent function
- cryptographic function
- p-ary function