A consideration of towering scheme for efficient arithmetic operation over extension field of degree 18

Md Al Amin Khandaker; Yasuyuki Nogami

doi:10.1109/ICCITECHN.2016.7860209

A consideration of towering scheme for efficient arithmetic operation over extension field of degree 18

Md Al Amin Khandaker, Yasuyuki Nogami

School of Engineering

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

2 Citations (Scopus)

Abstract

Barreto-Naehrig (BN) curve is a well studied pairing friendly curve of embedding degree 12, that uses arithmetic in Fp12 . Therefore the arithmetic of Fp12 extension field is well studied. In this paper, we have proposed an efficient approach of arithmetic operation over the extension field of degree 18 by towering. Fp18 extension field arithmetic is considered to be the basis of implementing the next generation pairing based security protocols. We have proposed to use Fp element to construct irreducible binomial for building tower of extension field up to Fp6 , where conventional approach uses the root of previous irreducible polynomial to create next irreducible polynomials. Therefore using Fp elements in irreducible binomial construction, reduces the number of multiplications in Fp to calculate inversion and multiplication over Fp18 , which effects acceleration in total arithmetic operation over Fp18 .

Original language	English
Title of host publication	19th International Conference on Computer and Information Technology, ICCIT 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	276-281
Number of pages	6
ISBN (Electronic)	9781509040896
DOIs	https://doi.org/10.1109/ICCITECHN.2016.7860209
Publication status	Published - Feb 21 2017
Event	19th International Conference on Computer and Information Technology, ICCIT 2016 - Dhaka, Bangladesh Duration: Dec 18 2016 → Dec 20 2016

Other

Other	19th International Conference on Computer and Information Technology, ICCIT 2016
Country/Territory	Bangladesh
City	Dhaka
Period	12/18/16 → 12/20/16

Keywords

Extension field arithmetic
KSS curve
Pairing based cryptography
Towering scheme

ASJC Scopus subject areas

Computer Science(all)

Access to Document

10.1109/ICCITECHN.2016.7860209

Cite this

A consideration of towering scheme for efficient arithmetic operation over extension field of degree 18. / Khandaker, Md Al Amin; Nogami, Yasuyuki.
19th International Conference on Computer and Information Technology, ICCIT 2016. Institute of Electrical and Electronics Engineers Inc., 2017. p. 276-281 7860209.

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

Khandaker, MAA & Nogami, Y 2017, A consideration of towering scheme for efficient arithmetic operation over extension field of degree 18. in 19th International Conference on Computer and Information Technology, ICCIT 2016., 7860209, Institute of Electrical and Electronics Engineers Inc., pp. 276-281, 19th International Conference on Computer and Information Technology, ICCIT 2016, Dhaka, Bangladesh, 12/18/16. https://doi.org/10.1109/ICCITECHN.2016.7860209

@inproceedings{e108fe99f8f344dcbb1b7506a4ce6675,

title = "A consideration of towering scheme for efficient arithmetic operation over extension field of degree 18",

abstract = "Barreto-Naehrig (BN) curve is a well studied pairing friendly curve of embedding degree 12, that uses arithmetic in Fp12 . Therefore the arithmetic of Fp12 extension field is well studied. In this paper, we have proposed an efficient approach of arithmetic operation over the extension field of degree 18 by towering. Fp18 extension field arithmetic is considered to be the basis of implementing the next generation pairing based security protocols. We have proposed to use Fp element to construct irreducible binomial for building tower of extension field up to Fp6 , where conventional approach uses the root of previous irreducible polynomial to create next irreducible polynomials. Therefore using Fp elements in irreducible binomial construction, reduces the number of multiplications in Fp to calculate inversion and multiplication over Fp18 , which effects acceleration in total arithmetic operation over Fp18 .",

keywords = "Extension field arithmetic, KSS curve, Pairing based cryptography, Towering scheme",

author = "Khandaker, {Md Al Amin} and Yasuyuki Nogami",

year = "2017",

month = feb,

day = "21",

doi = "10.1109/ICCITECHN.2016.7860209",

language = "English",

pages = "276--281",

booktitle = "19th International Conference on Computer and Information Technology, ICCIT 2016",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "19th International Conference on Computer and Information Technology, ICCIT 2016 ; Conference date: 18-12-2016 Through 20-12-2016",

}

TY - GEN

T1 - A consideration of towering scheme for efficient arithmetic operation over extension field of degree 18

AU - Khandaker, Md Al Amin

AU - Nogami, Yasuyuki

PY - 2017/2/21

Y1 - 2017/2/21

N2 - Barreto-Naehrig (BN) curve is a well studied pairing friendly curve of embedding degree 12, that uses arithmetic in Fp12 . Therefore the arithmetic of Fp12 extension field is well studied. In this paper, we have proposed an efficient approach of arithmetic operation over the extension field of degree 18 by towering. Fp18 extension field arithmetic is considered to be the basis of implementing the next generation pairing based security protocols. We have proposed to use Fp element to construct irreducible binomial for building tower of extension field up to Fp6 , where conventional approach uses the root of previous irreducible polynomial to create next irreducible polynomials. Therefore using Fp elements in irreducible binomial construction, reduces the number of multiplications in Fp to calculate inversion and multiplication over Fp18 , which effects acceleration in total arithmetic operation over Fp18 .

AB - Barreto-Naehrig (BN) curve is a well studied pairing friendly curve of embedding degree 12, that uses arithmetic in Fp12 . Therefore the arithmetic of Fp12 extension field is well studied. In this paper, we have proposed an efficient approach of arithmetic operation over the extension field of degree 18 by towering. Fp18 extension field arithmetic is considered to be the basis of implementing the next generation pairing based security protocols. We have proposed to use Fp element to construct irreducible binomial for building tower of extension field up to Fp6 , where conventional approach uses the root of previous irreducible polynomial to create next irreducible polynomials. Therefore using Fp elements in irreducible binomial construction, reduces the number of multiplications in Fp to calculate inversion and multiplication over Fp18 , which effects acceleration in total arithmetic operation over Fp18 .

KW - Extension field arithmetic

KW - KSS curve

KW - Pairing based cryptography

KW - Towering scheme

UR - http://www.scopus.com/inward/record.url?scp=85016227383&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016227383&partnerID=8YFLogxK

U2 - 10.1109/ICCITECHN.2016.7860209

DO - 10.1109/ICCITECHN.2016.7860209

M3 - Conference contribution

AN - SCOPUS:85016227383

SP - 276

EP - 281

BT - 19th International Conference on Computer and Information Technology, ICCIT 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 19th International Conference on Computer and Information Technology, ICCIT 2016

Y2 - 18 December 2016 through 20 December 2016

ER -

A consideration of towering scheme for efficient arithmetic operation over extension field of degree 18

Abstract

Other

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this