扩展欧几里德除法新解及其在密码学中的应用  

New Solutions of Extended Euclidean Division andIts Application in Cryptography

作　　者：周洁 牛宪华 何明星 ZHOU Jie;NIU Xianhua;HE Mingxing(School of Computer and Software Engineering,Xihua University,Chengdu 610039,China)

机构地区：[1]西华大学计算机与软件工程学院,成都610039

出　　处：《大学数学》2025年第2期81-88,共8页College Mathematics

基　　金：国家自然科学基金青年基金(12401663)。

摘　　要：扩展欧几里德除法是计算两个整数及其最大公因数之间线性组合表达式的常用算法,是RSA密码算法中密钥生成步骤的重要基础.针对经典的扩展欧几里德除法教学方法存在的步骤繁琐、计算复杂等问题,提出了一种新的扩展欧几里德除法教学方法及其在RSA及AES密码算法中的应用,使学生能灵活运用扩展欧几里德除法.The extended Euclidean division is a commonly used algorithm to calculate the linear combination expression between two integers and their greatest common factor.It is the fundamation of the key generation step in RSA cryptographic algorithm.Aiming at the problems of the classical teaching method of extended Euclidean division,such as tedious steps and complex calculation,this paper proposes two new teaching methods of extended Euclidean division and their applications in RSA and AES cryptographic algorithms,so that students can flexibly use the extended Euclidean division.

关 键 词：欧几里德除法 扩展欧几里德除法 更相减损术 RSA密码算法 AES密码算法 

分 类 号：O156.1[理学—数学]