### 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 |
---|---|

Pages (from-to) | 331-337 |

Number of pages | 7 |

Journal | Information Processing Letters |

Volume | 114 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2014 Jun 1 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

^{m}using shifted polynomial basis.

*Information Processing Letters*,

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

**Formulas for cube roots in F 3 ^{m} using shifted polynomial basis.** / Cho, Young In; Chang, Nam Su; Hong, Seokhie.

Research output: Contribution to journal › Article

^{m}using shifted polynomial basis',

*Information Processing Letters*, vol. 114, no. 6, pp. 331-337. https://doi.org/10.1016/j.ipl.2014.01.001

^{m}using shifted polynomial basis. Information Processing Letters. 2014 Jun 1;114(6):331-337. https://doi.org/10.1016/j.ipl.2014.01.001

}

TY - JOUR

T1 - Formulas for cube roots in F 3 m using shifted polynomial basis

AU - Cho, Young In

AU - Chang, Nam Su

AU - Hong, Seokhie

PY - 2014/6/1

Y1 - 2014/6/1

N2 - 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 F3m= F3[x]/(f), where fâ̂̂F3[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.

AB - 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 F3m= F3[x]/(f), where fâ̂̂F3[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.

KW - Cryptography

KW - Cube roots

KW - Finite field arithmetic

KW - Shifted polynomial basis

UR - http://www.scopus.com/inward/record.url?scp=84894262735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894262735&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2014.01.001

DO - 10.1016/j.ipl.2014.01.001

M3 - Article

VL - 114

SP - 331

EP - 337

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 6

ER -