### Abstract

Pairing based cryptography is considered as the next generation of security for which it attracts many researcher to work on faster and efficient pairing to make it practical. Among the several challenges of efficient pairing; efficient scalar multiplication of rational point defined over extension field of degree k ≥ 12 is important. However, there exists isomorphic rational point group defined over relatively lower degree extension field. Exploiting such property, this paper has showed a mapping technique between isomorphic rational point groups in the context of Ate-based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curve of embedding degree k = 18. In the case of KSS curve, there exists sub-field sextic twisted curve that includes sextic twisted isomorphic rational point group defined over F_{p3}. This paper has showed the mapping procedure from certain F_{p}18 rational point group to its sub-field isomorphic rational point group in F_{p3} and vice versa. This paper has also showed that scalar multiplication is about 20 times faster after applying the proposed mapping which in-turns resembles that the impact of this mapping will greatly enhance the pairing operation in KSS curve.

Original language | English |
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Title of host publication | Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 629-634 |

Number of pages | 6 |

ISBN (Electronic) | 9781509026555 |

DOIs | |

Publication status | Published - Jan 13 2017 |

Event | 4th International Symposium on Computing and Networking, CANDAR 2016 - Hiroshima, Japan Duration: Nov 22 2016 → Nov 25 2016 |

### Other

Other | 4th International Symposium on Computing and Networking, CANDAR 2016 |
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Country | Japan |

City | Hiroshima |

Period | 11/22/16 → 11/25/16 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Hardware and Architecture
- Signal Processing
- Computer Networks and Communications

### Cite this

*Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016*(pp. 629-634). [7818683] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDAR.2016.38

**Isomorphic mapping for Ate-based pairing over KSS curve of embedding degree 18.** / Khandaker, Md Al Amin; Nogami, Yasuyuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016.*, 7818683, Institute of Electrical and Electronics Engineers Inc., pp. 629-634, 4th International Symposium on Computing and Networking, CANDAR 2016, Hiroshima, Japan, 11/22/16. https://doi.org/10.1109/CANDAR.2016.38

}

TY - GEN

T1 - Isomorphic mapping for Ate-based pairing over KSS curve of embedding degree 18

AU - Khandaker, Md Al Amin

AU - Nogami, Yasuyuki

PY - 2017/1/13

Y1 - 2017/1/13

N2 - Pairing based cryptography is considered as the next generation of security for which it attracts many researcher to work on faster and efficient pairing to make it practical. Among the several challenges of efficient pairing; efficient scalar multiplication of rational point defined over extension field of degree k ≥ 12 is important. However, there exists isomorphic rational point group defined over relatively lower degree extension field. Exploiting such property, this paper has showed a mapping technique between isomorphic rational point groups in the context of Ate-based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curve of embedding degree k = 18. In the case of KSS curve, there exists sub-field sextic twisted curve that includes sextic twisted isomorphic rational point group defined over Fp3. This paper has showed the mapping procedure from certain Fp18 rational point group to its sub-field isomorphic rational point group in Fp3 and vice versa. This paper has also showed that scalar multiplication is about 20 times faster after applying the proposed mapping which in-turns resembles that the impact of this mapping will greatly enhance the pairing operation in KSS curve.

AB - Pairing based cryptography is considered as the next generation of security for which it attracts many researcher to work on faster and efficient pairing to make it practical. Among the several challenges of efficient pairing; efficient scalar multiplication of rational point defined over extension field of degree k ≥ 12 is important. However, there exists isomorphic rational point group defined over relatively lower degree extension field. Exploiting such property, this paper has showed a mapping technique between isomorphic rational point groups in the context of Ate-based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curve of embedding degree k = 18. In the case of KSS curve, there exists sub-field sextic twisted curve that includes sextic twisted isomorphic rational point group defined over Fp3. This paper has showed the mapping procedure from certain Fp18 rational point group to its sub-field isomorphic rational point group in Fp3 and vice versa. This paper has also showed that scalar multiplication is about 20 times faster after applying the proposed mapping which in-turns resembles that the impact of this mapping will greatly enhance the pairing operation in KSS curve.

UR - http://www.scopus.com/inward/record.url?scp=85015213179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015213179&partnerID=8YFLogxK

U2 - 10.1109/CANDAR.2016.38

DO - 10.1109/CANDAR.2016.38

M3 - Conference contribution

AN - SCOPUS:85015213179

SP - 629

EP - 634

BT - Proceedings - 2016 4th International Symposium on Computing and Networking, CANDAR 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -