1、密码学课程设计AES RSA SHA1加解密密码学基础课程设计主题: AES RSA SHA1加解密 学院: 班级: 学号: 姓名: 日期: 2012/12/30 成绩: 概述 大作业目的 1) 掌握密码学基础课程的主要知识点 2) 掌握常用的密码学算法机理与实现大作业内容 对称加密算法(AES)、非对称密码算法(RSA)、散列算法(SHA1)1.对称加密算法AES算法基本原理AES算法的主要数学基础是抽象代数,其中算法中的许多运算是按单字节(8bits)和4字节(32bits)定义的,单字节可看成有限域GF(28)中的一个元素,而4字节则可以看成系数在GF(28)中并且次数小于4的多项式(亦
2、可以理解为:GF(2564)),单字节上的运算有两种:有限域GF(28)上一个8次不可约多项式的模加、点乘(为方便代码实现,推出了X乘的概念),其中,这个不可约多项式为:m(x)= x8+x4+x3+x+1,类似地,4字节运算也分为两种:模加、乘法(为方便代码实现,推出了模乘的概念),而此时使用的模取M(x)=x4+1,由于x4+1=( x2+1)( x2+1)= ( x+1) ( x+1) ( x+1) ( x+1),即非不可约,导致非0多项式乘法逆元(逆元求取主要用到了欧几里德(Euclid)算法)不一定存在,所以在AES算法中,只限于乘一个固定的有逆元的多项式:a(x)=03x3+01x
3、2+01x+02。图中左边是加密流程,右边是解密流程,其中,Plaintext为明文,Ciphertext为密文,密钥长度可变,可指定为128、192、256比特,不同密钥长度决定了加解密算法的轮数(128位:10轮,192位:12轮,256位:14轮),算法征集之初,6轮迭代便可抵抗当时世界上已知的所有攻击,AES标准中至少留了4轮余量,按照这种说法,可以推知轮数越多,AES破解难度越大,也就是密钥越长越安全,所以今年8月份有人说256bits密钥长度的AES算法被破解,而128bits未被破解是没有根据的。理解AES需要知道以下两个概念:状态:算法中间的结果也需要分组,称之为状态,状态可以
4、用以字节为元素的矩阵阵列表示,该阵列有4行,列数Nb为分组长度除32;种子密钥:以字节为元素的矩阵阵列描述,阵列为4行,列数Nk为密钥长度除32,其中根据种子密钥,可以推导出各轮子密钥w , ,此过程亦称作密钥扩展,针对不同密钥长度的密钥扩展算法可以参照阅读AES算法标准发布文档。Sbox如下:Inverse s_box:算法流程图图中左边是加密流程,右边是解密流程,其中,Plaintext为明文,Ciphertext为密文,密钥长度可变,可指定为128、192、256比特,不同密钥长度决定了加解密算法的轮数(128位:10轮,192位:12轮,256位:14轮),算法征集之初,6轮迭代便可抵
5、抗当时世界上已知的所有攻击,AES标准中至少留了4轮余量,按照这种说法,可以推知轮数越多,AES破解难度越大,也就是密钥越长越安全,所以今年8月份有人说256bits密钥长度的AES算法被破解,而128bits未被破解是没有根据的。理解AES需要知道以下两个概念:状态:算法中间的结果也需要分组,称之为状态,状态可以用以字节为元素的矩阵阵列表示,该阵列有4行,列数Nb为分组长度除32;种子密钥:以字节为元素的矩阵阵列描述,阵列为4行,列数Nk为密钥长度除32,其中根据种子密钥,可以推导出各轮子密钥w , ,此过程亦称作密钥扩展,针对不同密钥长度的密钥扩展算法可以参照阅读AES算法标准发布文档。A
6、ES 的加密算法AES的解密算法算法测试结果测试数据为书本p119中数据程序清单#include #include / AES only supports Nb=4#define Nb 4 / number of columns in the State & expanded key#define Nk 4 / number of columns in a key#define Nr 10 / number of rounds in encryptionunsigned char Sbox256 = / forward s-box0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x
7、6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a,
8、 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x
9、02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde,
10、 0x5e, 0x0b, 0xdb,0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x
11、8a,0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16;unsigned cha
12、r InvSbox256 = / inverse s-box0x52, 0x09, 0x6a, 0xd5, 0x30, 0x36, 0xa5, 0x38, 0xbf, 0x40, 0xa3, 0x9e, 0x81, 0xf3, 0xd7, 0xfb,0x7c, 0xe3, 0x39, 0x82, 0x9b, 0x2f, 0xff, 0x87, 0x34, 0x8e, 0x43, 0x44, 0xc4, 0xde, 0xe9, 0xcb,0x54, 0x7b, 0x94, 0x32, 0xa6, 0xc2, 0x23, 0x3d, 0xee, 0x4c, 0x95, 0x0b, 0x42, 0x
13、fa, 0xc3, 0x4e,0x08, 0x2e, 0xa1, 0x66, 0x28, 0xd9, 0x24, 0xb2, 0x76, 0x5b, 0xa2, 0x49, 0x6d, 0x8b, 0xd1, 0x25,0x72, 0xf8, 0xf6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xd4, 0xa4, 0x5c, 0xcc, 0x5d, 0x65, 0xb6, 0x92,0x6c, 0x70, 0x48, 0x50, 0xfd, 0xed, 0xb9, 0xda, 0x5e, 0x15, 0x46, 0x57, 0xa7, 0x8d, 0x9d, 0x84,
14、0x90, 0xd8, 0xab, 0x00, 0x8c, 0xbc, 0xd3, 0x0a, 0xf7, 0xe4, 0x58, 0x05, 0xb8, 0xb3, 0x45, 0x06,0xd0, 0x2c, 0x1e, 0x8f, 0xca, 0x3f, 0x0f, 0x02, 0xc1, 0xaf, 0xbd, 0x03, 0x01, 0x13, 0x8a, 0x6b,0x3a, 0x91, 0x11, 0x41, 0x4f, 0x67, 0xdc, 0xea, 0x97, 0xf2, 0xcf, 0xce, 0xf0, 0xb4, 0xe6, 0x73,0x96, 0xac, 0x7
15、4, 0x22, 0xe7, 0xad, 0x35, 0x85, 0xe2, 0xf9, 0x37, 0xe8, 0x1c, 0x75, 0xdf, 0x6e,0x47, 0xf1, 0x1a, 0x71, 0x1d, 0x29, 0xc5, 0x89, 0x6f, 0xb7, 0x62, 0x0e, 0xaa, 0x18, 0xbe, 0x1b,0xfc, 0x56, 0x3e, 0x4b, 0xc6, 0xd2, 0x79, 0x20, 0x9a, 0xdb, 0xc0, 0xfe, 0x78, 0xcd, 0x5a, 0xf4,0x1f, 0xdd, 0xa8, 0x33, 0x88,
16、0x07, 0xc7, 0x31, 0xb1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xec, 0x5f,0x60, 0x51, 0x7f, 0xa9, 0x19, 0xb5, 0x4a, 0x0d, 0x2d, 0xe5, 0x7a, 0x9f, 0x93, 0xc9, 0x9c, 0xef,0xa0, 0xe0, 0x3b, 0x4d, 0xae, 0x2a, 0xf5, 0xb0, 0xc8, 0xeb, 0xbb, 0x3c, 0x83, 0x53, 0x99, 0x61,0x17, 0x2b, 0x04, 0x7e, 0xba, 0x77, 0xd6, 0x2
17、6, 0xe1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0c, 0x7d;/ combined Xtimes2Sboxunsigned char Xtime2Sbox256 = 0xc6, 0xf8, 0xee, 0xf6, 0xff, 0xd6, 0xde, 0x91, 0x60, 0x02, 0xce, 0x56, 0xe7, 0xb5, 0x4d, 0xec, 0x8f, 0x1f, 0x89, 0xfa, 0xef, 0xb2, 0x8e, 0xfb, 0x41, 0xb3, 0x5f, 0x45, 0x23, 0x53, 0xe4, 0x9b, 0x75,
18、0xe1, 0x3d, 0x4c, 0x6c, 0x7e, 0xf5, 0x83, 0x68, 0x51, 0xd1, 0xf9, 0xe2, 0xab, 0x62, 0x2a, 0x08, 0x95, 0x46, 0x9d, 0x30, 0x37, 0x0a, 0x2f, 0x0e, 0x24, 0x1b, 0xdf, 0xcd, 0x4e, 0x7f, 0xea, 0x12, 0x1d, 0x58, 0x34, 0x36, 0xdc, 0xb4, 0x5b, 0xa4, 0x76, 0xb7, 0x7d, 0x52, 0xdd, 0x5e, 0x13, 0xa6, 0xb9, 0x00,
19、0xc1, 0x40, 0xe3, 0x79, 0xb6, 0xd4, 0x8d, 0x67, 0x72, 0x94, 0x98, 0xb0, 0x85, 0xbb, 0xc5, 0x4f, 0xed, 0x86, 0x9a, 0x66, 0x11, 0x8a, 0xe9, 0x04, 0xfe, 0xa0, 0x78, 0x25, 0x4b, 0xa2, 0x5d, 0x80, 0x05, 0x3f, 0x21, 0x70, 0xf1, 0x63, 0x77, 0xaf, 0x42, 0x20, 0xe5, 0xfd, 0xbf, 0x81, 0x18, 0x26, 0xc3, 0xbe,
20、0x35, 0x88, 0x2e, 0x93, 0x55, 0xfc, 0x7a, 0xc8, 0xba, 0x32, 0xe6, 0xc0, 0x19, 0x9e, 0xa3, 0x44, 0x54, 0x3b, 0x0b, 0x8c, 0xc7, 0x6b, 0x28, 0xa7, 0xbc, 0x16, 0xad, 0xdb, 0x64, 0x74, 0x14, 0x92, 0x0c, 0x48, 0xb8, 0x9f, 0xbd, 0x43, 0xc4, 0x39, 0x31, 0xd3, 0xf2, 0xd5, 0x8b, 0x6e, 0xda, 0x01, 0xb1, 0x9c,
21、0x49, 0xd8, 0xac, 0xf3, 0xcf, 0xca, 0xf4, 0x47, 0x10, 0x6f, 0xf0, 0x4a, 0x5c, 0x38, 0x57, 0x73, 0x97, 0xcb, 0xa1, 0xe8, 0x3e, 0x96, 0x61, 0x0d, 0x0f, 0xe0, 0x7c, 0x71, 0xcc, 0x90, 0x06, 0xf7, 0x1c, 0xc2, 0x6a, 0xae, 0x69, 0x17, 0x99, 0x3a, 0x27, 0xd9, 0xeb, 0x2b, 0x22, 0xd2, 0xa9, 0x07, 0x33, 0x2d,
22、0x3c, 0x15, 0xc9, 0x87, 0xaa, 0x50, 0xa5, 0x03, 0x59, 0x09, 0x1a, 0x65, 0xd7, 0x84, 0xd0, 0x82, 0x29, 0x5a, 0x1e, 0x7b, 0xa8, 0x6d, 0x2c ;/ combined Xtimes3Sboxunsigned char Xtime3Sbox256 = 0xa5, 0x84, 0x99, 0x8d, 0x0d, 0xbd, 0xb1, 0x54, 0x50, 0x03, 0xa9, 0x7d, 0x19, 0x62, 0xe6, 0x9a, 0x45, 0x9d, 0x
23、40, 0x87, 0x15, 0xeb, 0xc9, 0x0b, 0xec, 0x67, 0xfd, 0xea, 0xbf, 0xf7, 0x96, 0x5b, 0xc2, 0x1c, 0xae, 0x6a, 0x5a, 0x41, 0x02, 0x4f, 0x5c, 0xf4, 0x34, 0x08, 0x93, 0x73, 0x53, 0x3f, 0x0c, 0x52, 0x65, 0x5e, 0x28, 0xa1, 0x0f, 0xb5, 0x09, 0x36, 0x9b, 0x3d, 0x26, 0x69, 0xcd, 0x9f, 0x1b, 0x9e, 0x74, 0x2e, 0x
24、2d, 0xb2, 0xee, 0xfb, 0xf6, 0x4d, 0x61, 0xce, 0x7b, 0x3e, 0x71, 0x97, 0xf5, 0x68, 0x00, 0x2c, 0x60, 0x1f, 0xc8, 0xed, 0xbe, 0x46, 0xd9, 0x4b, 0xde, 0xd4, 0xe8, 0x4a, 0x6b, 0x2a, 0xe5, 0x16, 0xc5, 0xd7, 0x55, 0x94, 0xcf, 0x10, 0x06, 0x81, 0xf0, 0x44, 0xba, 0xe3, 0xf3, 0xfe, 0xc0, 0x8a, 0xad, 0xbc, 0x
25、48, 0x04, 0xdf, 0xc1, 0x75, 0x63, 0x30, 0x1a, 0x0e, 0x6d, 0x4c, 0x14, 0x35, 0x2f, 0xe1, 0xa2, 0xcc, 0x39, 0x57, 0xf2, 0x82, 0x47, 0xac, 0xe7, 0x2b, 0x95, 0xa0, 0x98, 0xd1, 0x7f, 0x66, 0x7e, 0xab, 0x83, 0xca, 0x29, 0xd3, 0x3c, 0x79, 0xe2, 0x1d, 0x76, 0x3b, 0x56, 0x4e, 0x1e, 0xdb, 0x0a, 0x6c, 0xe4, 0x
26、5d, 0x6e, 0xef, 0xa6, 0xa8, 0xa4, 0x37, 0x8b, 0x32, 0x43, 0x59, 0xb7, 0x8c, 0x64, 0xd2, 0xe0, 0xb4, 0xfa, 0x07, 0x25, 0xaf, 0x8e, 0xe9, 0x18, 0xd5, 0x88, 0x6f, 0x72, 0x24, 0xf1, 0xc7, 0x51, 0x23, 0x7c, 0x9c, 0x21, 0xdd, 0xdc, 0x86, 0x85, 0x90, 0x42, 0xc4, 0xaa, 0xd8, 0x05, 0x01, 0x12, 0xa3, 0x5f, 0x
27、f9, 0xd0, 0x91, 0x58, 0x27, 0xb9, 0x38, 0x13, 0xb3, 0x33, 0xbb, 0x70, 0x89, 0xa7, 0xb6, 0x22, 0x92, 0x20, 0x49, 0xff, 0x78, 0x7a, 0x8f, 0xf8, 0x80, 0x17, 0xda, 0x31, 0xc6, 0xb8, 0xc3, 0xb0, 0x77, 0x11, 0xcb, 0xfc, 0xd6, 0x3a ;unsigned char Xtime2256 = 0x00, 0x02, 0x04, 0x06, 0x08, 0x0a, 0x0c, 0x0e,
28、0x10, 0x12, 0x14, 0x16, 0x18, 0x1a, 0x1c, 0x1e, 0x20, 0x22, 0x24, 0x26, 0x28, 0x2a, 0x2c, 0x2e, 0x30, 0x32, 0x34, 0x36, 0x38, 0x3a, 0x3c, 0x3e, 0x40, 0x42, 0x44, 0x46, 0x48, 0x4a, 0x4c, 0x4e, 0x50, 0x52, 0x54, 0x56, 0x58, 0x5a, 0x5c, 0x5e, 0x60, 0x62, 0x64, 0x66, 0x68, 0x6a, 0x6c, 0x6e, 0x70, 0x72,
29、0x74, 0x76, 0x78, 0x7a, 0x7c, 0x7e, 0x80, 0x82, 0x84, 0x86, 0x88, 0x8a, 0x8c, 0x8e, 0x90, 0x92, 0x94, 0x96, 0x98, 0x9a, 0x9c, 0x9e, 0xa0, 0xa2, 0xa4, 0xa6, 0xa8, 0xaa, 0xac, 0xae, 0xb0, 0xb2, 0xb4, 0xb6, 0xb8, 0xba, 0xbc, 0xbe, 0xc0, 0xc2, 0xc4, 0xc6, 0xc8, 0xca, 0xcc, 0xce, 0xd0, 0xd2, 0xd4, 0xd6,
30、0xd8, 0xda, 0xdc, 0xde, 0xe0, 0xe2, 0xe4, 0xe6, 0xe8, 0xea, 0xec, 0xee, 0xf0, 0xf2, 0xf4, 0xf6, 0xf8, 0xfa, 0xfc, 0xfe, 0x1b, 0x19, 0x1f, 0x1d, 0x13, 0x11, 0x17, 0x15, 0x0b, 0x09, 0x0f, 0x0d, 0x03, 0x01, 0x07, 0x05, 0x3b, 0x39, 0x3f, 0x3d, 0x33, 0x31, 0x37, 0x35, 0x2b, 0x29, 0x2f, 0x2d, 0x23, 0x21,
31、0x27, 0x25, 0x5b, 0x59, 0x5f, 0x5d, 0x53, 0x51, 0x57, 0x55, 0x4b, 0x49, 0x4f, 0x4d, 0x43, 0x41, 0x47, 0x45, 0x7b, 0x79, 0x7f, 0x7d, 0x73, 0x71, 0x77, 0x75, 0x6b, 0x69, 0x6f, 0x6d, 0x63, 0x61, 0x67, 0x65, 0x9b, 0x99, 0x9f, 0x9d, 0x93, 0x91, 0x97, 0x95, 0x8b, 0x89, 0x8f, 0x8d, 0x83, 0x81, 0x87, 0x85,
32、0xbb, 0xb9, 0xbf, 0xbd, 0xb3, 0xb1, 0xb7, 0xb5, 0xab, 0xa9, 0xaf, 0xad, 0xa3, 0xa1, 0xa7, 0xa5, 0xdb, 0xd9, 0xdf, 0xdd, 0xd3, 0xd1, 0xd7, 0xd5, 0xcb, 0xc9, 0xcf, 0xcd, 0xc3, 0xc1, 0xc7, 0xc5, 0xfb, 0xf9, 0xff, 0xfd, 0xf3, 0xf1, 0xf7, 0xf5, 0xeb, 0xe9, 0xef, 0xed, 0xe3, 0xe1, 0xe7, 0xe5; unsigned char Xtime9256 = 0x00, 0x09, 0
copyright@ 2008-2022 冰豆网网站版权所有
经营许可证编号:鄂ICP备2022015515号-1