### Abstract

Efficiency of the next generation pairing based security protocols rely not only on the faster pairing calculation but also on efficient scalar multiplication on higher degree rational points. In this paper we proposed a scalar multiplication technique in the context of Ate based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curves with embedding degree k = 18 at the 192-bit security level. From the systematically obtained characteristics p, order r and Frobenious trace t of KSS curve, which is given by certain integer z also known as mother parameter, we exploit the relation #E(F p) = p+1−t mod r by applying Frobenius mapping with rational point to enhance the scalar multiplication. In addition we proposed z-adic representation of scalar s. In combination of Frobenious mapping with multi-scalar multiplication technique we efficiently calculate scalar multiplication by s. Our proposed method can achieve 3 times or more than 3 times faster scalar multiplication compared to binary scalar multiplication, sliding-window and non-adjacent form method.

Original language | English |
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Title of host publication | Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers |

Publisher | Springer Verlag |

Pages | 221-232 |

Number of pages | 12 |

Volume | 10144 LNCS |

ISBN (Print) | 9783319565484 |

DOIs | |

Publication status | Published - 2017 |

Event | 17th International Workshop on Information Security Applications, WISA 2016 - Jeju Island, Korea, Republic of Duration: Aug 25 2016 → Aug 25 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10144 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th International Workshop on Information Security Applications, WISA 2016 |
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Country | Korea, Republic of |

City | Jeju Island |

Period | 8/25/16 → 8/25/16 |

### Fingerprint

### Keywords

- Frobenius mapping
- KSS curve
- Scalar multiplication

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers*(Vol. 10144 LNCS, pp. 221-232). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10144 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-56549-1_19

**Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18.** / Khandaker, Md Al Amin; Nogami, Yasuyuki; Seo, Hwajeong; Duquesne, Sylvain.

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

*Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers.*vol. 10144 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10144 LNCS, Springer Verlag, pp. 221-232, 17th International Workshop on Information Security Applications, WISA 2016, Jeju Island, Korea, Republic of, 8/25/16. https://doi.org/10.1007/978-3-319-56549-1_19

}

TY - GEN

T1 - Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18

AU - Khandaker, Md Al Amin

AU - Nogami, Yasuyuki

AU - Seo, Hwajeong

AU - Duquesne, Sylvain

PY - 2017

Y1 - 2017

N2 - Efficiency of the next generation pairing based security protocols rely not only on the faster pairing calculation but also on efficient scalar multiplication on higher degree rational points. In this paper we proposed a scalar multiplication technique in the context of Ate based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curves with embedding degree k = 18 at the 192-bit security level. From the systematically obtained characteristics p, order r and Frobenious trace t of KSS curve, which is given by certain integer z also known as mother parameter, we exploit the relation #E(F p) = p+1−t mod r by applying Frobenius mapping with rational point to enhance the scalar multiplication. In addition we proposed z-adic representation of scalar s. In combination of Frobenious mapping with multi-scalar multiplication technique we efficiently calculate scalar multiplication by s. Our proposed method can achieve 3 times or more than 3 times faster scalar multiplication compared to binary scalar multiplication, sliding-window and non-adjacent form method.

AB - Efficiency of the next generation pairing based security protocols rely not only on the faster pairing calculation but also on efficient scalar multiplication on higher degree rational points. In this paper we proposed a scalar multiplication technique in the context of Ate based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curves with embedding degree k = 18 at the 192-bit security level. From the systematically obtained characteristics p, order r and Frobenious trace t of KSS curve, which is given by certain integer z also known as mother parameter, we exploit the relation #E(F p) = p+1−t mod r by applying Frobenius mapping with rational point to enhance the scalar multiplication. In addition we proposed z-adic representation of scalar s. In combination of Frobenious mapping with multi-scalar multiplication technique we efficiently calculate scalar multiplication by s. Our proposed method can achieve 3 times or more than 3 times faster scalar multiplication compared to binary scalar multiplication, sliding-window and non-adjacent form method.

KW - Frobenius mapping

KW - KSS curve

KW - Scalar multiplication

UR - http://www.scopus.com/inward/record.url?scp=85017607789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017607789&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-56549-1_19

DO - 10.1007/978-3-319-56549-1_19

M3 - Conference contribution

AN - SCOPUS:85017607789

SN - 9783319565484

VL - 10144 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 221

EP - 232

BT - Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers

PB - Springer Verlag

ER -