On Prime-Order Elliptic Curves with Embedding Degrees 3, 4 and 6

pairing based cryptography;elliptic curves;embedding degree;Combinatorics and Optimization

Karabina, Koray

University of Waterloo

关键词: pairing based cryptography;    elliptic curves;    embedding degree;    Combinatorics and Optimization;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/2671/1/thesis_uw.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Bilinear pairings on elliptic curves have many cryptographicapplications such as identity based encryption, one-round three-party key agreement protocols, and short signature schemes.The elliptic curves which are suitable for pairing-based cryptography are called pairing friendly curves. The prime-orderpairing friendly curves with embedding degrees k=3,4and 6 were characterized by Miyaji, Nakabayashi and Takano. We study this characterization of MNT curves in details. We present explicit algorithms to obtain suitable curve parameters and to construct the corresponding elliptic curves.We also give a heuristic lower bound for the expected number of isogeny classes of MNT curves. Moreover,the related theoretical findings are compared with our experimental results.