### Abstract

Evaluation of cube roots in characteristic three finite fields is required for Tate (or modified Tate) pairing computation. The Hamming weight of x1 ^{/3} means that the number of nonzero coefficients in the polynomial representation of x1^{/3} in F3_{m}= ^{F3}[x]/(f), where fâ̂̂^{F3}[x] is an irreducible polynomial. The Hamming weight of x1^{/3} determines the efficiency of cube roots computation for characteristic three finite fields. Ahmadi et al. found the Hamming weight of x1^{/3} using polynomial basis [4]. In this paper, we observe that shifted polynomial basis (SPB), a variation of polynomial basis, can reduce Hamming weights of x1^{/3} and x2 ^{/3}. Moreover, we provide the suitable SPB that eliminates modular reduction process in cube roots computation.

Original language | English |
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Pages (from-to) | 331-337 |

Number of pages | 7 |

Journal | Information Processing Letters |

Volume | 114 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2014 Jun |

### Keywords

- Cryptography
- Cube roots
- Finite field arithmetic
- Shifted polynomial basis

### ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

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## Cite this

^{m}using shifted polynomial basis.

*Information Processing Letters*,

*114*(6), 331-337. https://doi.org/10.1016/j.ipl.2014.01.001