### Abstract

The objective of this paper is to give a fast square root computation method. First the Frobenius mapping is adopted. Then a lot of calculations over an extension field are reduced to that over a proper subfield by the norm computation. In addition a inverse square root algorithm and an addition chain are adopted to save the computation cost. All of the above-mentioned steps have been proven to make the proposed algorithm much faster than the conventional algorithm. From the table which compares the computation between the conventional and the proposed algorithm, it is clearly shown that the proposed algorithm accelerates the square root computation 10 times and 20 times faster than the conventional algorithm in F_{p11} and F_{p22} respectively. At the same time, the proposed algorithm reduces the computation cost 10 times and 20 times less than the conventional algorithm.

Original language | English |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

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

Volume | 2836 |

Publication status | Published - 2003 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science
- Engineering(all)

### Cite this

**A fast square root computation using the Frobenius mapping.** / Feng, Wang; Nogami, Yasuyuki; Morikawa, Yoshitaka.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 2836, pp. 1-10.

}

TY - JOUR

T1 - A fast square root computation using the Frobenius mapping

AU - Feng, Wang

AU - Nogami, Yasuyuki

AU - Morikawa, Yoshitaka

PY - 2003

Y1 - 2003

N2 - The objective of this paper is to give a fast square root computation method. First the Frobenius mapping is adopted. Then a lot of calculations over an extension field are reduced to that over a proper subfield by the norm computation. In addition a inverse square root algorithm and an addition chain are adopted to save the computation cost. All of the above-mentioned steps have been proven to make the proposed algorithm much faster than the conventional algorithm. From the table which compares the computation between the conventional and the proposed algorithm, it is clearly shown that the proposed algorithm accelerates the square root computation 10 times and 20 times faster than the conventional algorithm in Fp11 and Fp22 respectively. At the same time, the proposed algorithm reduces the computation cost 10 times and 20 times less than the conventional algorithm.

AB - The objective of this paper is to give a fast square root computation method. First the Frobenius mapping is adopted. Then a lot of calculations over an extension field are reduced to that over a proper subfield by the norm computation. In addition a inverse square root algorithm and an addition chain are adopted to save the computation cost. All of the above-mentioned steps have been proven to make the proposed algorithm much faster than the conventional algorithm. From the table which compares the computation between the conventional and the proposed algorithm, it is clearly shown that the proposed algorithm accelerates the square root computation 10 times and 20 times faster than the conventional algorithm in Fp11 and Fp22 respectively. At the same time, the proposed algorithm reduces the computation cost 10 times and 20 times less than the conventional algorithm.

UR - http://www.scopus.com/inward/record.url?scp=0142218980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142218980&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0142218980

VL - 2836

SP - 1

EP - 10

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -