专利名称：安全高效的椭圆曲线加解密参数的制作方法
技术领域：
本发明涉及数据加解密，特别是利用椭圆曲线参数的特征提高公钥密码计算效率和安全性的方法。
背景技术：
密码系统分对称密码系统和非对称密码系统。
对称密码也称传统密码算法，对称密码的加密密钥能够从解密密钥中推算出来，反之亦然。在大多数算法中，加密和解密使用的密钥是相同的。这类密码算法有时也称秘密密钥算法或单密钥算法，它要求发送者和接收者在安全通信之前，协商一个密钥。对称密码的安全性依赖于密钥的秘密性，泄漏密钥就意味着任何掌握密钥的人都可以对消息进行加密和解密。一般对称密码的运算速度很快，但如何把密钥安全地分发给合法使用者却是一个问题。
在专利“密码设备和方法”(“CRYPTOGRAPHIC APPARATUSAND METHOD”，专利号US4200770)中给出了一个可以在公开信道中交换密钥的方法，称为Diffie-Hellman密钥交换方法。该专利使得通信双方使用一个模幂函数协商和传递他们的秘密信息，攻击者要想获得传递的秘密信息，必须解决离散对数问题，而如果通信双方使用的参数足够大，则离散对数问题在计算上是不可解的。该专利奠定了公钥密码学的基本原理。
公钥密码，又称非对称密码，与只使用一个密钥的对称密码不同，它使用两个独立但又存在着某种数学联系的密钥公钥和私钥。通信的各方保密各自的私钥，公开其公钥，发送者使用接收者的公钥加密，接收者使用只有自己知道的私钥解密。公钥密码还可以解决数字签名的问题，签名者使用只有自己知道的私钥对消息签名，验证者使用签名者的公钥可以验证签名的合法性。
专利“密码通信系统和方法”(“CRYPTOGRAPHICCOMMNICATION SYSTEM AND METHOD”，专利号US4405829)提出了Rivest、Shamir和Adleman发明的一种公钥密码方法-RSA。RSA公钥密码方法的安全性基于大整数因子分解问题的难解性，伴随着应用对安全性要求的不断提高，RSA密钥的长度在不断增加。
椭圆曲线密码系统(Elliptic Curve Cryptosystems，简称ECC)自1985年由Neal Koblitz和Victor Miller提出以来，由于其相对于RSA的全方面的优势(更强的安全性、更高的实现效率、更省的实现代价)，吸引了大批密码学工作者就其安全性和实现方法作了大量的研究，并已逐渐被国际各大标准组织采纳做为公钥密码标准(IEEE P1363、ANSI X9、ISO/IEC、和IETF等)，成为主流应用的公钥密码之一。
ECC的安全性和实现性能，在很大程度上依赖于椭圆曲线参数的选取，包括基域的选取和基域上椭圆曲线方程的选取。
在ECC应用中，一般基域选择为二元扩域F2m或素域Fp(p为大于3的素数)当选择基域为F2m时，通过选择F2m中的模多项式为三项式或五项式以及用高斯正规基表示F2m中的元素等技术手段，可以很大程度上提高F2m上各种算术运算的性能，从而提高ECC的性能；当选择基域为Fp时，通过选择p为特殊的素数可以很大程度上提高Fp上各种算术运算的性能。
一般Fp上的椭圆曲线具有Weierstrass方程y2＝x3+ax+b，a、b∈Fp，选择特殊的a可以提高椭圆曲线点乘的运算效率。
椭圆曲线方程的选取决定了椭圆曲线的阶(即椭圆曲线上点的个数，记为n)，在ECC应用中，出于安全性的考虑一般要求n含有大素数因子，最佳选择是当基域为Fp时，n本身就是大素数。
发明内容
本发明提出一类ECC参数的选择方法及基于该方法的ECC参数，使得实现安全高效率的ECC软件和硬件更为可行。
根据本发明的一个方面，提供一种椭圆曲线加解密方法，其中加解密参数为选择椭圆曲线加解密的基域为素域Fp，设素数p的长度为32m比特，其中m为大于1的任意正整数，p满足p=232m+Σi=0m-1232iki,]]>ki∈{-1，0，1}.
根据本发明的一个实施例，在素域fp上的椭圆曲线具有Weierstrass方程y2＝x3+ax+b，a、b∈Fp，选择椭圆曲线方程参数a满足a≡-3mod p，任意选取整数b满足(4a3+27b2)mod p≠0，同时选取的b使得椭圆曲线的阶n为素数。
具体实施例方式
以下将对本发明进行详细说明1、参数选择根据本发明的椭圆曲线加解密方法，其中加解密参数选择为选择椭圆曲线加解密的基域为素域Fp，设素p的长度为32m比特，其中m为大于1的任意正整数，p满足p=232m+Σi=0m-1232iki,]]>ki∈{-1，0，1}，p所具备的特点使得对p取模运算可以通过为数不多的加法和减法操作完成，从而可以设计高效的模乘软件和硬件实现算法。
在素域Fp上的椭圆曲线具有Weierstrass方程y2＝x3+ax+b，a、b∈Fp，为提高椭圆曲线点乘效率，本发明选取的椭圆曲线方程参数a满足a≡-3mod p，任意选取整数b满足(4a3+27b2)mod p≠0，同时为满足安全性本发明选取的b使得椭圆曲线的阶n为素数。
根据本发明的椭圆曲线加解密方法，其中素数p具体可选择为以下其中的一个当m＝6时素数p为如下其中的一个p＝0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFp＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001当m＝8时素数p为如下其中的一个p＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001p＝0xFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFF0000000000000001p＝0xFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF00000000FFFFFFFEFFFFFFFFFFFFFFFFp＝0xFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF00000000FFFFFFFEFFFFFFFFp＝0xFFFFFFFFFFFFFFFF00000000FFFFFFFEFFFFFFFFFFFFFFFF0000000100000001p＝0xFFFFFFFFFFFFFFFEFFFFFFFF00000000FFFFFFFFFFFFFFFF0000000100000001p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF
p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFEFFFFFFFF00000001p＝0xFFFFFFFF00000000000000010000000100000001000000000000000000000001p＝0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFFp＝0xFFFFFFFF00000000FFFFFFFFFFFFFFFF0000000100000000FFFFFFFFFFFFFFFFp＝0xFFFFFFFF0000000100000000FFFFFFFEFFFFFFFEFFFFFFFF0000000100000001p＝0xFFFFFFFF00000000FFFFFFFF00000000FFFFFFFF000000000000000000000001p＝0xFFFFFFFF00000000FFFFFFFEFFFFFFFEFFFFFFFF0000000100000000FFFFFFFFp＝0xFFFFFFFEFFFFFFFF0000000000000000FFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFp＝0xFFFFFFFEFFFFFFFEFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF00000001p＝0xFFFFFFFEFFFFFFFF00000000FFFFFFFFFFFFFFFFFFFFFFFF0000000100000001p＝0xFFFFFFFEFFFFFFFF00000000FFFFFFFF00000000FFFFFFFF00000000FFFFFFFFp＝0xFFFFFFFEFFFFFFFEFFFFFFFF00000000FFFFFFFF000000000000000000000001p＝0xFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFF00000000FFFFFFFF0000000100000001根据本发明的椭圆曲线加解密方法，其中加解密参数具体可选择为以下各组中的一组当m＝6时，素域Fp上192位ECC参数可以是p＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x9FCABCD826AE1D60CE5068C4FEAB2854C11A1D5652D7A1Fn＝0xFFFFFFFF0000000000000000E4E8DFB4D59E58D97F26D5D7p＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x7ABE825463428724FBFFA6CAF1CC2B77756B40A93A83BDD2n＝0xFFFFFFFEFFFFFFFFFFFFFFFE564CBA1EC2AA664CB2B7E94Fp＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFE
b＝0xD0AC1463B5B7B0BEE817774BCD6E874B1585B0A6409E3B1Cn＝0xFFFFFFFF00000000000000007A563BC26E67D4BBAAA6347Fp＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x9AA18BB42495DD0DA5B635AE3843ADFE7D122191EDBAF170n＝0xFFFFFFFEFFFFFFFFFFFFFFFD84DE30358151E8EF7CA28249p＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x5C197F2F0AA07D87DA3B5C5823317BAF7949A660E010F6A7n＝0xFFFFFFFEFFFFFFFFFFFFFFFF7940B371E3581580460208FBp＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x23113DA07BB09BAA0A839379D8128C814AC3F0E6BBADB7B7n＝0xFFFFFFFF00000000000000001D6C4190C18A77FB0537FD85当m＝8时，素域Fp上256位ECC参数可以是p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0xA50B198D9FFA965FF7FB955C27ABE0CCC0F1E0748025ACCCA8C627388D088B19n＝0xFFFFFFFF000000000000000000000001EF6CA6269CB9360D98D9CBA4991B1CD5p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0xCCB51F034BA3FB7DBCF6C1C958E9F4157ED877C18B6143FDBE64339BFD6D47D4n＝0xFFFFFFFF000000000000000000000000AAAD130A161E5BF1B5BFC69E2F46A4C9p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC
b＝0x65F1CFCEB2378CB0E69DA6027F9287E1480C2DB1C8BE08255CDE3526C29EBD12n＝0xFFFFFFFF00000000000000000000000027A414BDD1317369D27251D2D9C061A3p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0x28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93n＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0x6C50029623EFC02DE2DA4DAAB0F4777EF5DB537C8BB0635AE99B2EC9DB6A8AA7n＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFEA4552FEB7DFDDD5CF51F6FDF47B67CC5p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0xE0F0EBB116CB9ECB51225941D0EBE70A5B8BC5E0B9F35252717FC7F1B8AC2F4Fn＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFEDFD42527EE682EBDACB4A158AE8EB9A5p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0xD7CFCE0160025A8B21B418CC5241ADDD92B8ABC980588128230771EBCE6B332Cn＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF586382EEABF94C5477490C545ECF904Bp＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFF
FFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0x8F3225CE7BF40B648A27DE5BB759A299BAAC8172811C1A41E47E76D9C39DE2F5n＝0xFFFFFFFF00000000000000000000000051B2847C1330D064F01F1CDA5D8E5509p＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0x481A15C879B8B61EB350AA9AB999F8C61CEF1220D03A723245B3247774395399n＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001851FADA977F600C3EA76C6B18D12A3F1p＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0x5E40E5F0872E95ED70A3F25EB2EAA3D5F2D06A7B585E387004B3C091CCBD3FF2n＝0xFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF488387B29148034CFC98A7D9D5E0EEA7p＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0x5E979587965D3FAD8946BA907A76C43C386678A355F9E83D7C287957CC11A3D2n＝0xFFFFFFFFFFFFFFFFFFFFFFFF000000000D3F4C196169FD138A2C7299249E471Fp＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0xE560C0A6BFBC6984FD3772D150F3192FDFF1E04B6E2B143625B1D521E6800C56n＝0xFFFFFFFFFFFFFFFFFFFFFFFF000000026DFA64C67491708A16AF7865
25CDDB1Dp＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0x70C013C24D52626CD0114E242B8076D774A184FB22077BF10998022A8C2A688En＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001DD5339A0B680627F4D339E00BF3E97BB本发明的素数均通过确定性素性检测。为保证椭圆曲线系统安全性，本发明选取的n和p通过MOV判断条件。
权利要求
1.一种椭圆曲线加解密方法，椭圆曲线加解密基域为素域Fp，设素数p的长度为32m比特，其中m为大于1的任意正整数，p满足p=232n+Σi=0m-1232iki,]]>Ki∈{-1，0，1}。
2.如权利要求1的椭圆曲线加解密方法，在素域Fp上的椭圆曲线具有Weierstrass方程y2＝x3+ax+b，a、b∈Fp，选择椭圆曲线方程参数a满足a≡-3 mod p，任意选取整数b满足(4a3+27b2)mod p≠0，同时选取的b使得椭圆曲线的阶n为素数。
3.如权利要求1的椭圆曲线加解密方法，当m＝6时素数p为如下其中的一个p＝0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFp＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001
4.如权利要求1的椭圆曲线加解密方法，当m＝8时素数p为如下其中的一个p＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001p＝0xFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFF0000000000000001p＝0xFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF00000000FFFFFFFEFFFFFFFFFFFFFFFFp＝0xFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF00000000FFFFFFFEFFFFFFFFp＝0xFFFFFFFFFFFFFFFF00000000FFFFFFFEFFFFFFFFFFFFFFFF0000000100000001p＝0xFFFFFFFFFFFFFFFEFFFFFFFF00000000FFFFFFFFFFFFFFFF0000000100000001p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFp＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFEFFFFFFFF00000001p＝0xFFFFFFFF00000000000000010000000100000001000000000000000000000001p＝0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFFp＝0xFFFFFFFF00000000FFFFFFFFFFFFFFFF0000000100000000FFFFFFFFFFFFFFFFp＝0xFFFFFFFF0000000100000000FFFFFFFEFFFFFFFEFFFFFFFF0000000100000001p＝0xFFFFFFFF00000000FFFFFFFF00000000FFFFFFFF000000000000000000000001p＝0xFFFFFFFF00000000FFFFFFFEFFFFFFFEFFFFFFFF0000000100000000FFFFFFFFp＝0xFFFFFFFEFFFFFFFF0000000000000000FFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFp＝0xFFFFFFFEFFFFFFFEFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF00000001p＝0xFFFFFFFEFFFFFFFF00000000FFFFFFFFFFFFFFFFFFFFFFFF0000000100000001p＝0xFFFFFFFEFFFFFFFF00000000FFFFFFFF00000000FFFFFFFF00000000FFFFFFFFp＝0xFFFFFFFEFFFFFFFEFFFFFFFF00000000FFFFFFFF000000000000000000000001p＝0xFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFF00000000FFFFFFFF0000000100000001
5.如权利要求2的椭圆曲线加解密方法，当m＝6时，素域Fp上192位ECC参数为下列各组中的一组p＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x9FCABCD826AE1D60CE5068C4FEAB2854C11A1D5652D7A1Fn＝0xFFFFFFFF0000000000000000E4E8DFB4D59E58D97F26D5D7p＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x7ABE825463428724FBFFA6CAF1CC2B77756B40A93A83BDD2n＝0xFFFFFFFEFFFFFFFFFFFFFFFE564CBA1EC2AA664CB2B7E94Fp＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0xD0AC1463B5B7B0BEE817774BCD6E874B1585B0A6409E3B1Cn＝0xFFFFFFFF00000000000000007A563BC26E67D4BBAAA6347Fp＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x9AA18BB42495DD0DA5B635AE3843ADFE7D122191EDBAF170n＝0xFFFFFFFEFFFFFFFFFFFFFFFD84DE30358151E8EF7CA28249p＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x5C197F2F0AA07D87DA3B5C5823317BAF7949A660E010F6A7n＝0xFFFFFFFEFFFFFFFFFFFFFFFF7940B371E3581580460208FBp＝0xFFFFFFFEFFFFFFFFFFFFFFFF000000010000000100000001a＝0xFFFFFFFEFFFFFFFFFFFFFFFF0000000100000000FFFFFFFEb＝0x23113DA07BB09BAA0A839379D8128C814AC3F0E6BBADB7B7n＝0xFFFFFFFF00000000000000001D6C4190C18A77FB0537FD85
6.如权利要求2的椭圆曲线加解密方法，当m＝8时，素域Fp上256位ECC参数为下列各组中的一组p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0xA50B198D9FFA965FF7FB955C27ABE0CCC0F1E0748025ACCCA8C627388D088B19n＝0xFFFFFFFF000000000000000000000001EF6CA6269CB9360D98D9CBA4991B1CD5p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0xCCB51F034BA3FB7DBCF6C1C958E9F4157ED877C18B6143FDBE64339BFD6D47D4n＝0xFFFFFFFF000000000000000000000000AAAD130A161E5BF1B5BFC69E2F46A4C9p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0x65F1CFCEB2378CB0E69DA6027F9287E1480C2DB1C8BE08255CDE3526C29EBD12n＝0xFFFFFFFF00000000000000000000000027A414BDD1317369D27251D2D9C061A3p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0x28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93n＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0x6C50029623EFC02DE2DA4DAAB0F4777EF5DB537C8BB0635AE99B2EC9DB6A8AA7n＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFEA4552FEB7DFDDD5CF51F6FDF47B67CC5p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0xE0F0EBB116CB9ECB51225941D0EBE70A5B8BC5E0B9F35252717FC7F1B8AC2F4Fn＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFEDFD42527EE682EBDACB4A158AE8EB9A5p＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0xD7CFCE0160025A8B21B418CC5241ADDD92B8ABC980588128230771EBCE6B332Cn＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF586382EEABF94C5477490C545ECF904Bp＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFFa＝0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFCb＝0x8F3225CE7BF40B648A27DE5BB759A299BAAC8172811C1A41E47E76D9C39DE2F5n＝0xFFFFFFFF00000000000000000000000051B2847C1330D064F01F1CDA5D8E5509p＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0x481A15C879B8B61EB350AA9AB999F8C61CEF1220D03A723245B3247774395399n＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001851FADA977F600C3EA76C6B18D12A3F1p＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0x5E40E5F0872E95ED70A3F25EB2EAA3D5F2D06A7B585E387004B3C091CCBD3FF2n＝0xFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF488387B29148034CFC98A7D9D5E0EEA7p＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0x5E979587965D3FAD8946BA907A76C43C386678A355F9E83D7C287957CC11A3D2n＝0xFFFFFFFFFFFFFFFFFFFFFFFF000000000D3F4C196169FD138A2C7299249E471Fp＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0xE560C0A6BFBC6984FD3772D150F3192FDFF1E04B6E2B143625B1D521E6800C56n＝0xFFFFFFFFFFFFFFFFFFFFFFFF000000026DFA64C67491708A16AF786525CDDB1Dp＝0xFFFFFFFFFFFFFFFFFFFFFFFF0000000100000001000000000000000100000001a＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001000000010000000000000000FFFFFFFEb＝0x70C013C24D52626CD0114E242B8076D774A184FB22077BF10998022A8C2A688En＝0xFFFFFFFFFFFFFFFFFFFFFFFF00000001DD5339A0B680627F4D339E00BF3E97BB
全文摘要
本发明提出一类ECC参数的选择方法及基于该方法的ECC参数，使得实现安全高效率的ECC软件和硬件更为可行。本发明的椭圆曲线加解密方法中加解密参数为选择椭圆曲线加解密的基域为素域F
文档编号H04L9/30GK1885767SQ200610101868
公开日2006年12月27日 申请日期2006年7月12日 优先权日2006年7月12日
发明者陈建华, 汪朝晖, 胡进, 胡志金, 孙金龙, 张家宏, 阳凌怡, 张丽娜, 何德彪, 汪玉 申请人:北京华大信安科技有限公司