文档介绍：2013年5月11日计算机安全技术与实践 * ^YmodZ古老的学问,崭新的应用数论是一门古老的学科。在RSA算法出现之前,数论这门精巧却枯燥的学问,只是被普通人认为好玩。RSA算法的出现改变了一般民众对数论的看法。现在,安全的网络活动几乎都在数论相关算法的保护之下,比如SSL安全传输和网上交易的数字签名。数整数负数,0,正整数(自然数)…,-3,-2,-1,0,1,2,3,…关系整除:因子、倍数 如3|15,7|14,…分类合数,如4、6、8、9、10、12、14、15、…素数,如2、3、5、7、11、13、17、19、…,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997算术基本定理任一个数总可以写成一系列素数的乘积, 而且写法唯一 a=p1a1×p2a2×p3a3×……×ptat 如 36=22×32 3600=24×32×52素数的判别2^32,582,657-1,2006合数的分解44thKnownMersennePrimeFound!!,2006,inthesameroomjustafewfeetawayfromtheirlastfind,'sCMSUteambroketheirownworldrecord,discoveringthe44thknownMersenneprime,2^32,582,657-,808,358digitsis650,,IMPStoclaimtheElectronicFrontierFoundation$100,(a,b)Euclid算法互素gcd(.,.)=1两个数的最大公因子是1可推广到n个数素数和谁都互素除了他的倍数Euclid算法辗转相除法-求最大公因子的算法18,12;12,6;6,0; 即635,6;6,5;5,1;1,0;即1(互素)即 r0=q1r1+r2 55=2×22+11 35=5×6+5 r1=q2r2+r3 22=2×11+0 6=1×5+1 r2=q3r3+r4 5=5×1+0 … rm-2=qm-1rm-1+rm(rm就是最大公因子) rm-1=qmrm+0 (即rm+1)Euclid算法函数//mondivisorintgcd(inta,intb) { if((a==0)||(b==0)) returna+b; else returngcd(a%b,b%a) }