1、B密码编码学与网络安全电子工业出版社2006 - 2007B第 8章 数论结论介绍 8.1 素数 8.2 费马定理和欧拉定理 8.3 素性检测 8.4 中国剩余定理 8.5 离散对数问题 * 8.a 计算 XY mod Z B古老的学科，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。B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|1
2、5， 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、 B8.1 素数2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,2
3、93,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,7
4、73,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997B- X=100000 x007 x037 x039 x049 x073 x081 x123 x127 x193 x213 x217 x223 x231 x237 x259 x267 x279 x357 x379 x393 x399 x421 x429 x463 x469 x471 x493 x541 x543 x561 x567 x577 x6
5、09 x627 x643 x651 x661 x669 x673 x687 x717 x721 x793 x799 x801 x837 x841 x853 x891 x921 x937 x939 x963 x969B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 p tat 如 36 22323600 243252 素数的判别232,582,657-1， 2006 合数的分解BThe 5,000 largest known primes B44th Known Mersenne Prime Lightning strikes twice. On
6、 September 4, 2006, in the same room just a few feet away from their last find, Dr. Curtis Cooper and Dr. Steven Boones CMSU team broke their own world record, discovering the 44th known Mersenne prime, 232,582,657-1. The new prime at 9,808,358 digits is 650,000 digits larger than their previous record prime found last December. However, the new prime falls short of the 10 million digits required for GIMPS to claim the Electronic Frontier Foundation $100,000 award.BGreat Internet Mersenne Prime Search
