2003年Akavia基于列表译码提出研究硬核谓词的一般框架,并将该方法成功地应用于许多硬核谓词的研究.但是,对于ax+b mod p的任意比特是任意单向函数的硬核谓词,这个关于单向函数的一般性结论能否适用,仍是一个公开问题.文章利用这种新方法研究积性码可接近的单向陷门函数的比特安全性,并且证明ax+b mod p的任意比特是p阶循环群上该类单向函数的硬核谓词.
This paper proposes a variation of Miller＇s algorithm for Tate pairing computation on Weierstrass curves. Unlike the original Miller＇s algorithm which consists of two major operations： the doubling operation and the addition operation, this new algorithm replaces the addition with a doubling-addition （DA） operation to take the advantage of the fast point doubling-addition formula. Explicit formulae are given for the new algorithm. We suggest to use the new formulae for Weierstrass curves with general parameters for Tate pairing to gain a better performance.
