关键词: 基于身份的密码系统, 椭圆曲线, Weil/Tate对, 非相邻表示型, Miller算法

Abstract: The identity-based public key cryptosystem becomes a new research focus on the current because of its unique advantages after the PKI cryptosystem.The realization about the identity-based cryptosystem is based on the rapid calculation of the bilinear pairing，and the Miller algorithm is an effective way to calculate the pairing.Combining the NAF algorithm about the window width w with Miller algorithm，the paper gives an effective method to improve the calculation speed about the linear pairing，and this method makes the times of the addition operators as 2/w of the original ones.

Key words: identity-based cryptography, elliptic curves, Weil/Tate pairing, non adjacent form, Miller algorithm