A Comparative Study of Twist Property in KSS Curves of Embedding Degree 16 and 18 from the Implementation Perspective

• Published in: Journal of Information and Communication Convergence Engineering, 15(2) Vol. 15; no. 2; pp. 97 - 103
• Main Authors: Howon Kim, Yasuyuki Nogami, Taehwan Park, Md. Al-Amin Khandaker
• Format: Journal Article
• Language: English
• Published: 한국정보통신학회JICCE 01.06.2017; 한국정보통신학회
• Subjects: 전자/정보통신공학; KSS curve; Sextic twist; Isomorphic mapping; Pairing-based cryptography; Quartic twist
• ISSN: 2234-8255; 2234-8883
• DOI: 10.6109/jicce.2017.15.2.97

Implementation of faster pairing calculation is the basis of efficient pairing-based cryptographic protocol implementation. Generally, pairing is a costly operation carried out over the extension field of degree k≥12. But the twist property of the pairing friendly curve allows us to calculate pairing over the sub-field twisted curve, where the extension degree becomes k/d and twist degree d= 2,3,4,6. The calculation cost is reduced substantially by twisting but it makes the discrete logarithm problem easier if the curve parameters are not carefully chosen. Therefore, this paper considers the most recent parameters setting presented by Barbulescu and Duquesne [1] for pairing-based cryptography; that are secure enough for 128-bit security level; to explicitly show the quartic twist (d= 4) and sextic twist (d= 6) mapping between the isomorphic rational point groups for KSS (Kachisa-Schaefer-Scott) curve of embedding degree k=16 and k=18, receptively. This paper also evaluates the performance enhancement of the obtained twisted mapping by comparing the elliptic curve scalar multiplications. KCI Citation Count: 0