CN109462481B - 一种基于非对称双线性对的匿签密方法 - Google Patents

一种基于非对称双线性对的匿签密方法 Download PDF

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CN109462481B
CN109462481B CN201811403997.XA CN201811403997A CN109462481B CN 109462481 B CN109462481 B CN 109462481B CN 201811403997 A CN201811403997 A CN 201811403997A CN 109462481 B CN109462481 B CN 109462481B
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赵运磊
王红兵
黄兴忠
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Shanghai Humin Blockchain Technology Co ltd
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Abstract

本发明提供了一种非对称环境下基于身份的匿签密方法，包括：生成系统主私钥
Figure DDA0003315176390000011
在非对称双线性对类型‑1和类型‑2下，身份为
Figure DDA0003315176390000012
的匿签密发送方的私钥为
Figure DDA0003315176390000013
身份为
Figure DDA0003315176390000014
的匿签密验证方的私钥为
Figure DDA0003315176390000015
Figure DDA0003315176390000016
Figure DDA0003315176390000017
选取
Figure DDA0003315176390000018
计算
Figure DDA0003315176390000019
Figure DDA00033151763900000110
并将{X,C}发送给
Figure DDA00033151763900000111
其中
Figure DDA00033151763900000112
是双线性映射。在非对称双线性对类型‑3下，身份为
Figure DDA00033151763900000113
的匿签密发送方的私钥为
Figure DDA00033151763900000114
身份为
Figure DDA00033151763900000115
的匿签密验证方的私钥为
Figure DDA00033151763900000116
Figure DDA00033151763900000117
选取
Figure DDA00033151763900000118
计算
Figure DDA00033151763900000119
Figure DDA00033151763900000120
并将{X,C}发送给
Figure DDA00033151763900000121

Description

一种基于非对称双线性对的匿签密方法
技术领域
本发明涉及密码技术领域，具体地说，涉及一种基于非对称双线性对的身份基匿签密方法。
背景技术
数字签名和公钥加密是密码理论及应用的核心内容。签密是将数字签名和公钥加密的功能合二为一，既保证了加密内容的完整性和可验证性，又保证了加密消息的私密性，并且比简单地结合签名和加密的效率大为提升。与传统的公钥密码体制下相比，基于身份的签密将用户的身份作为公钥，可以简化公钥证书管理和发放的问题。但是，原有的基于身份签密方案均需公开传输用户的身份和公钥信息，并且效率较差。而在移动互联时代，设备的计算和存储能力受限，并且在很多应用中用户的身份信息往往属于敏感信息，需要保护。因此，发展高效的基于身份的身份匿藏签密方法(简记为“匿签密”)具有重要的理论及应用意义。
令G1、G2和GT是三个q阶循环群(q可以是素数,也可以是合数,如RSA模数)。为了描述方便起见，我们记G1、G2和GT为乘法群(所有本发明中描述的方案均在G1、G2和GT记为加法群时同样工作)。一般而言，一个双线性对
Figure GDA0003462521140000016
就是一个从G1×G2到GT的双线性映射,并满足下面性质:
(1)双线性:设g1∈G1，g2∈G2，x,y∈Zq，有
Figure GDA0003462521140000011
(2)非退化性：对于每一个
Figure GDA0003462521140000012
总存在一个g2∈G2，使得
Figure GDA0003462521140000013
其中，
Figure GDA0003462521140000014
是G1的单位元，
Figure GDA0003462521140000015
是GT的单位元；
(3)双线性映射可以有效计算。
双线性对有下面三种类型:
Type-1(类型1)：G1→G2有一个可有效计算的同构，这时一般记为G1＝G2(通常用G表示)。这类双线性对一般可以用超奇异椭圆曲线或超椭圆曲线来实现。
Type 2(类型2)：有一个有效计算群同态G2→G1,但无从G1到G2的有效同态。这类双线性对一般用素数域上的一般椭圆曲线实现,G1是基域上椭圆曲线群,G2是扩域上椭圆曲线子群,G2→G1的同态一般取迹映射。
Type 3(类型3)：没有任何G2→G1或G1→G2的有效可计算的同态(同态甚至同构一定是存在的,这里是指没有有效计算的同构)。这类双线性对也是用素域上的一般曲线来构造,G2一般取迹映射的核。
本发明所描述的方法可以在上述三种类型双线性对任一类型上都可以工作，区别在于：对于类型1双线性对，G1＝G2；对于类型2双线性对，系统公开参数中需要有一个可有效计算的同构ψ:G1→G2，即ψ为将G1中元素映射到G2的可有效计算的同构；对于类型3双线性对，系统公开参数中不需要有一个可有效计算的同构ψ:G1→G2，但每个用户的私钥由一个增加到两个，分别用于签密和验证签密。在下述的发明方案描述中，基于类型-2和类型-3来描述，当应用到类型-1双线性对时则有G1＝G2。
发明内容
为解决上述问题，本发明提供了一种非对称环境下高效的基于身份的匿签密方法，包括：私钥生成器生成系统主私钥
Figure GDA0003462521140000021
在非对称双线性对类型-1和类型-2下，身份为
Figure GDA0003462521140000022
的匿签密发送方的私钥为
Figure GDA0003462521140000023
身份为
Figure GDA0003462521140000024
的匿签密验证方的私钥为
Figure GDA0003462521140000025
选取
Figure GDA0003462521140000026
计算
Figure GDA0003462521140000027
Figure GDA0003462521140000028
并将{X,C}发送给
Figure GDA0003462521140000029
其中
Figure GDA00034625211400000210
是双线性映射。
Figure GDA00034625211400000211
计算
Figure GDA00034625211400000212
Figure GDA00034625211400000213
且
Figure GDA00034625211400000214
则接受匿签密信息M。在非对称双线性对类型-3下，身份为
Figure GDA00034625211400000215
的匿签密发送方的私钥为
Figure GDA00034625211400000216
Figure GDA00034625211400000217
身份为
Figure GDA00034625211400000218
的匿签密验证方的私钥为
Figure GDA00034625211400000219
Figure GDA00034625211400000220
选取
Figure GDA00034625211400000221
计算
Figure GDA00034625211400000222
Figure GDA00034625211400000223
并将{X,C}发送给
Figure GDA00034625211400000224
其中
Figure GDA00034625211400000225
是双线性映射。
Figure GDA00034625211400000226
计算
Figure GDA00034625211400000227
Figure GDA00034625211400000228
且
Figure GDA00034625211400000229
则接受匿签密信息M。
附图说明
图1是发明方法一个实例(非对称双线性配对类型-2)实现的流程图。
图2是发明方法一个实例(非对称双线性配对类型-3)实现的流程图。
具体实施方式
图1是发明方法一个实例(非对称双线性配对类型-2)实现的流程图；其中，令G1≠G2,
Figure GDA0003462521140000031
auxM为空，
Figure GDA0003462521140000032
为群GT的单位元，H:{0,1}*→G1是哈希函数，D是与加密函数E对应的解密函数，
Figure GDA0003462521140000033
指的是利用密钥K对密文C进行解密得到
Figure GDA0003462521140000034
表示的是x从
Figure GDA0003462521140000035
中随机选取。
图2是发明方法一个实例(非对称双线性配对类型-3)实现的流程图；其中，令G1≠G2,
Figure GDA0003462521140000036
auxM为空，
Figure GDA0003462521140000037
为群GT的单位元，H1:{0,1}*→G1,H2:{0,1}*→G2是两个哈希函数，D是与加密函数E对应的解密函数，
Figure GDA0003462521140000038
指的是利用密钥K对密文C进行解密得到
Figure GDA0003462521140000039
表示的是x从
Figure GDA00034625211400000310
中随机选取。
本发明提供了一种基于非对称双线性对的匿签密方法，现举例给出具体实施方式：
系统建立：生成系统公开参数，一个安全参数n取128，双线性对
Figure GDA00034625211400000311
G1×G2→GT，其中G1、G2和GT是三个q阶循环群，整数q取3594707740912722592580264824659245374581620005772120566140827390747490618210732713776201829166921179104690985316170865403357128018053115705235365035756944666781840271151398486024508905819032066430042870294016997308232041571009239026199854058373227102211040396565230117801219598111998342507534997235192001889，q的二进制长度(记为|q|)为n的多项式；两个哈希函数：H1:{0,1}*→G1，H2:{0,1}*→G2，分别采用MD5和SHA-1函数；密钥导出函数KDF:{0,1}*→{0,1}n采用Openssl的AES算法内置KDF；g1为G1的生成元，取值72026754027934651490995918212523766243371000525971101339334699885320636543746077563483364060839557244370694227487917252409638191550569389028359389164974323853180025346237445763293422583856014029352597479177910324941936807527651378495009235344516904490274731975063077229612562360754643102255089897348148780690，g2∈G2为G2的生成元，取值77706302561608440010618368313478656108503343589089519700566055587018553414302968551516717115506698339473642981470868826042443741805044287846666289451133627751364843226483789350336451089265057408624982566636736744757835440696623220350219622426665921578454579853475107616688094007335536946549349101096432348567，
Figure GDA0003462521140000041
为群GT的单位元；E采用对称加密函数AES；系统公开参数包括：
Figure GDA0003462521140000042
系统公开参数可以由系统内的用户协商决定，或由可信第三方给定；PKG生成系统主密钥
Figure GDA0003462521140000043
msk取315541380177942662356417812076875991665600114430；
用户私钥提取：具有身份ID∈{0,1}*的用户在PKG注册，PKG为其生成私钥：
Figure GDA0003462521140000044
为了描述方便起见，下述的方法描述中签密的生成方的身份记为
Figure GDA0003462521140000045
令
Figure GDA0003462521140000046
计算签密和验证签密私钥分别
Figure GDA0003462521140000047
Figure GDA0003462521140000048
Figure GDA0003462521140000049
签密验证方记为
Figure GDA00034625211400000410
令
Figure GDA00034625211400000411
签密和验证签密私钥分别为
Figure GDA00034625211400000412
Figure GDA00034625211400000413
Figure GDA0003462521140000051
匿签密生成：令M∈{0,1}*为匿签密的信息，M取值2MMMMMMMMMMMMMMMMmmmmmmMMMMMMMMMMMMMMMMMMMMM；用户
Figure GDA0003462521140000052
选取x＝272228183584204209780836865847286436217086609891，计算
Figure GDA0003462521140000053
Figure GDA0003462521140000054
Figure GDA0003462521140000055
若采用类型-3双线性对，计算
Figure GDA0003462521140000056
Figure GDA0003462521140000057
Figure GDA0003462521140000058
(若采用类型-2双线性对，计算
Figure GDA0003462521140000059
)若
Figure GDA00034625211400000510
(否则重新选取x，重新计算PS)，计算K＝KDF(PS,auxK)＝KDF(PS,auxK)＝{rounds＝10；rd_key＝4216471528 24692937404275299365 3296311078 2466021090 3720210055 17518228831838784427 10530547351329698917}iv＝a45978c5a2726072，
Figure GDA00034625211400000511
计算
Figure GDA00034625211400000512
Figure GDA00034625211400000513
得667afc15fc776f81b5f74e9028723c7236f804cf40491f86cbcc70a1ef3b5976e1343fe5cdedd30ad1da70fbfd61cf53a1a7ab57d004c56799351dd3afa32cdf13506dc5e10af7cd39fc3ca426cb7b7fd091c5d70454517841a01412e48d2b43；最后，用户
Figure GDA00034625211400000514
将{X,C}发送给用户
Figure GDA00034625211400000515
匿签密验证：用户
Figure GDA00034625211400000516
接收到{X,C}后，若采用类型-3双线性对，计算
Figure GDA00034625211400000517
Figure GDA00034625211400000518
Figure GDA00034625211400000519
(若采用类型-1双线性对，计算
Figure GDA00034625211400000520
若采用类型-2双线性对，计算
Figure GDA00034625211400000521
Figure GDA00034625211400000522
)；若
Figure GDA00034625211400000523
计算K＝KDF(PS,auxK)＝{rounds＝10；rd_key＝4216471528 24692937404275299365 3296311078 2466021090 3720210055 17518228831838784427 10530547351329698917}iv＝a45978c5a2726072，
Figure GDA0003462521140000061
利用K对C解密得到
Figure GDA0003462521140000067
且
Figure GDA0003462521140000064
Figure GDA0003462521140000065
Figure GDA0003462521140000066
与传输密文相等，验证成功，接受匿签密信息M。
本发明的其它特征和优点将在随后的说明书中阐述，并且，部分地从说明书中变得显而易见，或者通过实施本发明而了解。本发明的目的和其他优点可通过在说明书、权利要求书以及附图中所特别指出的结构来实现和获得。
应该理解的是，本发明所公开的实施例不限于这里所公开的特定处理步骤，而应当延伸到相关领域的普通技术人员所理解的这些特征的等同替代。还应当理解的是，在此使用的术语仅用于描述特定实施例的目的，而并不意味着限制。
说明书中提到的“两个实施例”或“实施例”意指结合实施例描述的特定特征、结构或特性包括在本发明的至少两个实施例中。因此，说明书通篇各个地方出现的短语“两个实施例”或“实施例”并不一定均指同一实施例。
虽然上述示例用于说明本发明在一个或多个应用中的原理，但对于本领域的技术人员来说，在不背离本发明的原理和思想的情况下，明显可以在形式上、用法及实施的细节上作各种修改而不用付出创造性劳动。因此，本发明由所附的权利要求书来限定。

Claims (1)

1.一种基于非对称双线性对的身份基匿签密方法，所述方法包括：
系统建立：生成系统公开参数，包括：一个安全参数n，双线性对
Figure FDA00034625211300000132
Figure FDA00034625211300000133
整数q，其中G1、G2和GT是三个q阶循环群，q的二进制长度记为|q|，其为n的多项式；两个哈希函数：H1:{0,1}*→G1，H2:{0,1}*→G2，一个可有效计算的同构ψ:G1→G2，一个密钥导出函数KDF:{0,1}*→{0,1}n；令g1∈G1为G1的生成元，g2∈G2为G2的生成元，1GT为群GT的单位元；E为一个对称加密函数；系统公开参数记为：
Figure FDA0003462521130000011
系统公开参数可以由系统内的用户协商决定，或由可信第三方给定；私钥生成器PKG，生成用户主密钥msk，且
Figure FDA0003462521130000012
即msk从
Figure FDA0003462521130000013
中随机选取，其中
Figure FDA0003462521130000014
的取值范围为1到q-1中的整数，且q为一个大素数；公开发布SysPar，保密保存msk；
用户私钥生成：具有身份ID∈{0,1}*的用户在PKG注册，PKG根据主密钥msk和用户身份生成用户私钥：
Figure FDA0003462521130000015
其中
Figure FDA0003462521130000016
用来签密，
Figure FDA0003462521130000017
用来验证签密；签密生成方记为
Figure FDA0003462521130000018
签密和验证签密私钥分别为
Figure FDA0003462521130000019
签密验证方记为
Figure FDA00034625211300000110
签密和验证签密私钥分别为
Figure FDA00034625211300000111
匿签密生成：令M∈{0,1}*为匿签密的信息；
构造方法一，基于Type 1双线性对：用户
Figure FDA00034625211300000112
选取
Figure FDA00034625211300000113
计算
Figure FDA00034625211300000114
Figure FDA00034625211300000115
计算
Figure FDA00034625211300000116
若
Figure FDA00034625211300000117
计算K＝KDF(PS,auxK)；计算
Figure FDA00034625211300000118
即：将K作为对称加密函数E的密钥对
Figure FDA00034625211300000119
按照规定或约定编码方式进行加密，其中auxM是可为空或包含一个时间戳信息的集合；群G1和G2可以相等，其记为G，即基于Type1的双线性配对的构造如构造方法一；q为素数或合数；从
Figure FDA00034625211300000120
中随机选取，或在ZQ∩{0,1}l中随机选取，其中，1≤l≤|q|；
Figure FDA00034625211300000121
或
Figure FDA00034625211300000122
Figure FDA00034625211300000123
E是一个认证加密函数或者带有辅助输入的认证加密函数；最后，用户
Figure FDA00034625211300000124
将{X,C}发送给用户
Figure FDA00034625211300000125
构造方法二，基于Type 2双线性对：用户
Figure FDA00034625211300000126
选取
Figure FDA00034625211300000127
计算
Figure FDA00034625211300000128
Figure FDA00034625211300000129
计算
Figure FDA00034625211300000130
若
Figure FDA00034625211300000131
计算K＝KDF(PS,auxK)，auxK或为空，或为
Figure FDA0003462521130000021
的一个子集；计算
Figure FDA0003462521130000022
即：将K作为对称加密函数E的密钥对
Figure FDA0003462521130000023
按照规定或约定编码方式进行加密，其中auxM是可为空或包含一个时间戳信息的集合；G1≠G2；H1＝H2:{0,1}*→G1，记为H:{0,1}*→G1，此时有
Figure FDA0003462521130000024
对于Type 2双线性对，且其构造方法不需要哈希函数H2:{0,1}*→G2；最后，用户
Figure FDA0003462521130000025
将{X,C}发送给用户
Figure FDA0003462521130000026
构造方法三，基于Type 3双线性对：用户
Figure FDA0003462521130000027
选取
Figure FDA0003462521130000028
计算
Figure FDA0003462521130000029
Figure FDA00034625211300000210
计算
Figure FDA00034625211300000211
若
Figure FDA00034625211300000212
计算K＝KDF(PS,auxK)，auxK或为空，或为
Figure FDA00034625211300000213
的一个子集，这里，哈希函数H1将
Figure FDA00034625211300000214
的身份映射到群G1，哈希函数H2将
Figure FDA00034625211300000215
的身份映射到群G2，且
Figure FDA00034625211300000216
计算
Figure FDA00034625211300000217
Figure FDA00034625211300000218
即：将K作为对称加密函数E的密钥对
Figure FDA00034625211300000219
按照规定或约定编码方式进行加密，其中auxM是可为空或包含一个时间戳信息的集合；G1≠G2；且其构造方法不需要一个可有效计算的同构ψ:G1→G2；最后，用户
Figure FDA00034625211300000220
将{X,C}发送给用户
Figure FDA00034625211300000221
匿签密验证：用户
Figure FDA00034625211300000222
接收到{X,C}后，针对如上的三种匿签密算法分别做如下解密及验证：
验证方法一，基于Type 1双线性对：计算
Figure FDA00034625211300000223
若
Figure FDA00034625211300000224
返回无效字符，表明匿签密无效；否则，计算K＝KDF(PS,auxK)，利用K对C解密得到
Figure FDA00034625211300000225
若
Figure FDA00034625211300000226
且
Figure FDA00034625211300000227
且auxM有效，则接受匿签密信息M，否则拒绝接受；
验证方法二，基于Type 2双线性对：计算
Figure FDA00034625211300000228
若
Figure FDA00034625211300000229
Figure FDA00034625211300000230
返回无效字符，表明匿签密无效；否则，计算K＝KDF(PS,auxK)，利用K对C解密得到
Figure FDA00034625211300000231
若
Figure FDA00034625211300000232
且
Figure FDA00034625211300000233
且auxM有效，则接受匿签密信息M，否则拒绝接受；
验证方法三，基于Type 3双线性对：计算
Figure FDA00034625211300000234
若
Figure FDA00034625211300000235
返回无效字符，表明匿签密无效；否则，计算K＝KDF(PS,auxK)，利用K对C解密得到
Figure FDA00034625211300000236
若
Figure FDA00034625211300000237
且
Figure FDA00034625211300000238
且auxM有效，则接受匿签密信息M，否则拒绝接受。
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