A Note on the Behaviour of the Number Field Sieve in the Medium Prime Case: Smoothness of Norms

作     者：BENGER Naomi CHARLEMAGNE Manuel 陈克非 

作者机构：School of Mathematical Sciences University of Adelaide University of Michigan-Shanghai Jiao Tong University Joint InstituteShanghai Jiao Tong University School of Science Hangzhou Normal University 

出 版 物：《Journal of Shanghai Jiaotong university(Science)》 (上海交通大学学报（英文版）)

年 卷 期：2018年第23卷第1期

页      面：138-145页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程] 070101[理学-基础数学] 

主　　题：number field sieve(NFS) pairing friendly elliptic curves polynomial selection 

摘      要：As we examine the behaviour of the number field sieve(NFS) in the medium prime case, we notice various patterns that can be exploited to improve the running time of the sieving stage. The contributions of these observations to the computational mathematics community are twofold. Firstly, we clarify the understanding of the true practical effectiveness of the algorithm. Secondly, we propose a test for a better choice of the polynomials used in the NFS. These results are of particular interest to cryptographers as the run-time of the NFS directly determines the security level of some discrete logarithm problem based protocols.