CN103986575B - 一种计算非对称的共享密钥建立方法 - Google Patents
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
- H04L9/0841—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these involving Diffie-Hellman or related key agreement protocols
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0852—Quantum cryptography
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Abstract
本发明公开了一种计算非对称的共享密钥建立方法,属于信息安全技术领域;本发明在张量问题和遍历矩阵问题基础上构造出新的困难问题,在此困难问题基础上给出了一种计算非对称的共享密钥建立方法,该技术具有实现效率高、不需要密码算法协处理器、高度安全性、可应用到计算能力非对称的场景中,抗量子计算机攻击等优点,在物联网,云计算等安全领域中服务器与移动设备之间等比传统密钥交换协议如Diffie‑Hellman密钥交换协议等有优势,在电子环境和未来的量子环境下均可使用。本发明提供的方法可广泛应用于网络安全、电子商务等信息安全***领域。
Description
技术领域
本发明属于信息安全技术领域,尤其涉及一种计算非对称的共享密钥建立方法。
背景技术
针对对称密码体制中密钥管理复杂的难题,1976年Diffie和Hellman开创性地提出了“公钥密码体制”的概念,指出可以在***道上传递秘密信息。与对称密码相比,公钥密码***中加解密运算一般比较复杂、实现效率低,因而并不适合直接加密大量数据。通常的做法是:使用公钥密码技术(密钥建立协议)来建立一个共享会话密钥;然后,用会话密钥作为对称密码的密钥来加密大量明文信息。
Diffie-Hellman交换协议于1976年被给出,从而开辟了公钥密码学的新领域,Diffie-Hellman交换协议是离散对数困难问题为基础的,特点是双方在一个对等的环境下且计算为对称的(计算对称即双方做的运算是相同的)。而随着信息技术产业的不断发展,密钥交换协议的应用场景也不断在发生改变,原有的密钥交换协议在有的场合下以不太适用,如云计算,物联网中,服务器和终端之间,服务器和移动设备之间的密钥交换协议,由于双方存在计算资源和能力的差异,因此它们需要使用非对称计算的密钥交换协议。
目前,量子计算机已经出现。如果量子计算机进一步发展,将对Diffie-Hellman密钥交换协议构成严重威胁。现有的许多协议是在Diffie-Hellman密钥交换协议的基础上改进而成的,例如MQV协议已成为IEEE P1363标准。但是这些协议大都是基于离散对数或椭圆曲线离散对数,不能抵御量子计算的攻击。因此,人们需要能够抵抗量子计算机攻击的密钥交换协议。为此,1999年Anshel等提出了基于一般非交换群的密钥交换协议,2001年他们又基于辫群提出了一个双方密钥交换协议,这两个协议后来被证明是不安全的。2000年美密会上Ko等提出了所谓的Diffie-Hellman类型的共轭问题(DHCP),并基于此问题的困难性假设,提出了一个Diffie-Hellman型的双方密钥交换协议,然而,2003年Cheon等给出了求解这个问题的多项式时间算法,2005年Myasnikon等给出一个更高效的求解方法。2010年Boucher等在PQCrypto2010会议上基于一种特殊非交换乘法多项式提出了一种双方密钥交换协议,这个协议随后被Dubois等攻破。
发明内容
针对上述存在的技术问题,本发明的目的是提供一种在电子计算和量子计算环境下都安全的计算非对称的共享密钥协议。
为达到上述目的,本发明采用如下的技术方案:一种计算非对称的共享密钥建立方法,其特征在于:
(I)***建立:给定遍历矩阵随机均匀选取和在中计算和作为公开参数,其中两两不互逆,两两不互逆;
(II)假设通信双方是B和A,通信双方建立密钥共享的过程包括以下步骤:
步骤1:A随机均匀选取将r做为自己的私钥,然后计算和
步骤2:B随机均匀选取和并将k,l,M做为私钥,
计算
步骤3:A发送给B;
步骤4:B发送给A;
步骤5:A用自己的私钥计算出共享密钥
步骤6:B用自己的私钥计算出共享密钥
(III)通过密钥协商协议,A和B协商出共同的密钥
其中,符号表示有限域上的张量积。
本发明具有以下优点和积极效果:
(1)本发明是一种安全性很高的密钥交换协议。其安全性性能主要基于张量问题和遍历矩阵问题,这两个问题已被证明为NPC问题,另外,本发明所基于的问题满足非交换下,因而从计算复杂性角度和代数结构角度考虑,本发明具有抵抗量子计算机攻击的潜力;
(2)本发明是一种高效的密钥交换协议,其运算主要为有限域上的乘法运算,如果我们选择较小的域参数如则乘法可采用查表,效率较高,本方案可广泛应用于计算能力有限的嵌入式设备中;
(3)本发明是一种非对称计算的密钥交换协议,而随着物联网云计算等新型信息技术的发展,很多场合需要非对称计算的密钥交换协议,本发明不但可以用于计算能力对等的应用场景中,也可应用到计算能力非对等的应用场景中。
附图说明
图1:是本发明实施例提供的量子计算环境下的共享密钥建立方法。
具体实施方式
为了便于本领域普通技术人员理解和实施本发明,下面结合附图及实施例对本发明作进一步的详细描述,应当理解,此处所描述的实施示例仅用于说明和解释本发明,并不用于限定本发明。
请见图1,本发明所采用的技术方案是:一种计算非对称的共享密钥建立方法,
(I)***建立:
选择参数为q=3,n=3,m=3.给定有限域F3上的遍历矩阵
选择x1=3、x2=4、x3=5、x4=1∈F8, 计算 和 将他们作为公共参数.
(II)假设通信双方是A和B,通信双方建立密钥共享的过程包括以下步骤:
步骤1:A随机均匀选取r=(1,0,1,0)4,计算and
步骤2:B随机均匀选取和计算
步骤3:A发送给B。
步骤4:B发送给
A
步骤5:A计算
步骤6:B计算
通过交互A和B可以得到共同的密钥
通过交互A和B可以得到共同的密钥,它是27行27列的,在不影响安全性和说明的条件下,为了更节空间,我们只给出共享密钥的部分。
应当理解的是,本说明书未详细阐述的部分均属于现有技术。
应当理解的是,上述针对较佳实施例的描述较为详细,并不能因此而认为是对本发明专利保护范围的限制,本领域的普通技术人员在本发明的启示下,在不脱离本发明权利要求所保护的范围情况下,还可以做出替换或变形,均落入本发明的保护范围之内,本发明的请求保护范围应以所附权利要求为准。
Claims (1)
1.一种计算非对称的共享密钥建立方法,其特征在于:
(I)***建立:给定遍历矩阵随机均匀选取和 在 中计算 和 作为公开参数,其中 两两不互逆, 两两不互逆;
(II)假设通信双方是A和B,通信双方建立密钥共享的过程包括以下步骤:
步骤1:A随机均匀选取将r做为自己的私钥,然后计算和
步骤2:B随机均匀选取和并将k,l,M做为私钥,
计算
步骤3:A发送给B;
步骤4:B发送给A;
步骤5:A用自己的私钥计算出共享密钥
步骤6:B用自己的私钥计算出共享密钥
(III)通过密钥协商协议,A和B协商出共同的密钥
其中,符号表示有限域上的张量积。
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US14/724,809 US9548860B2 (en) | 2014-06-05 | 2015-05-29 | Asymmetric-computing type shared key establishing method suitable for cloud computing and IoT |
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