Efficient Implementation of the Weil Pairing

• Main Authors: Yi-shan Lu, 呂易珊
• Other Authors: D. J. Guan
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/q6664b

碩士 === 國立中山大學 === 資訊工程學系研究所 === 97 === The most efficient algorithm for solving the elliptic curve discrete logarithm problem can only be done in exponential time. Hence, we can use it in many cryptographic applications. Weil pairing is a mapping which maps a pair of points on elliptic curves to a multiplicative group of a finite field with nondegeneracy and bilinearity. Pairing was found to reduce the elliptic curve discrete logarithm problem into the discrete logarithm problem of a finite field, and became an important issue since then. In 1986, Miller proposed an efficient algorithm for computing Weil pairings. Many researchers focus on the improvement of this algorithm. In 2006, Blake et al. proposed the reduction of total number of lines based on the conjugate of a line. Liu et al. expanded their concept and proposed two improved methods. In this paper, we use both NAF and segmentation algorithm to implement the Weil pairing and analyse its complexity.