第三节Gcd and Bezout's Identity 最大公约数与裴蜀定理 第四节Extended Euclidean Algorithm and Fundamental Theorem of Arithmetic 扩展欧几里得算法与算术基本定理 第五节Linear Diophantine Equations 线性丢番图方程 第六节Linear Congruences 线性同余(包含中国剩余定理) 第七节The Arithmetic of Z_p Z_p上的计...
欧几里德算法又称辗转相除法,用于计算两个整数a,b的最大公约数。 基本算法:设a=qb+r,其中a,b,q,r都是整数,则gcd(a,b)=gcd(b,r),即gcd(a,b)=gcd(b,a%b)。 第一种证明: a可以表示成a = kb + r,则r = a mod b 假设d是a,b的一个公约数,则有 d|a, d|b,而r = a - kb,因此d|...
算法进阶:从入门到找不到门www.zhihu.com/column/c_1529027607316656128 算法进阶【第九期】数学算法:Extended Euclidean Algorithm扩展欧几里得算法 喵喵提醒版 爆零是一种宿命,枚举是一种思想,打表是一种勇气,骗分是一种日常,刷题是一种出路,AC是一种原谅,AK是一种梦想,搜索是一种信仰,剪枝是一种精神,弃赛...
We know that by means of extended euclidean algorithmxandycan be calculated fromax + by = gcd(a, b).The formula is: x=prev_y;y=prev_x-(a/b)*x; and the code is: intgcd(inta,intb,int&x,int&y){if(b==0){x=1;y=0;returna;}intx1,y1;intd=gcd(b,a%b,x1,y1);x=y1;y=...
Extended euclidean algorithmLarge-scale polynomialsCloud computing gives resource-constrained clients great conveniences to outsource exorbitant computations to a public cloud. The extended Euclidean algorithm with large-scale polynomials over finite fields is fundamental and widespread in computer science and ...
Example of Extended Euclidean AlgorithmRecall that gcd(84, 33) = gcd(33, 18) = gcd(18, 15) = gcd(15, 3) = gcd(3, 0) = 3 We work backwards to write 3 as a linear combination of 84 and 33: 3 = 18 − 15 [Now 3 is a linear combination of 18 and 15] = 18 − (33...
Pure-Python extended Euclidean algorithm implementation that accepts any number of integer arguments. - lapets/egcd
DES、AES、Present、Extended Euclidean Algorithm、Miller-Rabin( 常用密码学算法)推荐书籍《现代密码学趣味之旅》---彭长根 - usecodelee/encryption-algorithm
摘要: This paper presents a method to determine a set of basis polynomials from the extended Euclidean algorithm that allows Generalized Minimum Distance decoding of Reed-Solomon codes with a complexity of O(nd).关键词: Reed-Solomon codes communication complexity decoding polynomials Reed-Solomon ...
在中文区讲解这两个算法的博客虽然不少,但是让人看得像是在云里雾里的。 本文通过一个详细的计算过程来讲解辗转相除法(即欧几里得算法),以及拓展的欧几里得算法/Extended Euclidean algorithm。这两个算法有很强的关联,因此请读者先看完辗转相除法再看拓展的欧几里得算法。