CN107682150B - 一种适用于计算资源非对称领域的共享密钥建立方法 - Google Patents

一种适用于计算资源非对称领域的共享密钥建立方法 Download PDF

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CN107682150B
CN107682150B CN201711024800.7A CN201711024800A CN107682150B CN 107682150 B CN107682150 B CN 107682150B CN 201711024800 A CN201711024800 A CN 201711024800A CN 107682150 B CN107682150 B CN 107682150B
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王后珍
张焕国
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Wuhan University WHU
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    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • 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
    • H04L9/0819—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s)
    • H04L9/0825—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s) using asymmetric-key encryption or public key infrastructure [PKI], e.g. key signature or public key certificates
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • 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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Abstract

本发明公开了一种适用于计算资源非对称领域的共享密钥建立方法，采用背包问题和离散对数问题(包括椭圆曲线离散对数问题)给出了一种共享密钥的建立方法，其特点是协议双方实现过程中所需的计算资源不对称，极大地提高了协议一方的实现效率。特别适用于物联网，云计算等安全领域中服务器与移动终端计算资源非对称应用领域，在这些领域比传统密钥交换协议如Diffie‑Hellman密钥交换协议等有优势。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

一种适用于计算资源非对称领域的共享密钥建立方法
技术领域
本发明属于信息安全技术领域，尤其涉及一种适用于计算资源非对称领域的共享密钥建立方法。
背景技术
针对对称密码算法中密钥管理复杂的问题，1976年Diffie和Hellman提出了“公钥密码体制”的思想，并提出了Diffie-Hellman密钥交换(密钥建立)协议，解决了***道密钥的传输难题。
传统公钥密码体制存在两个缺陷：
(1)与对称密码相比，公钥密码体制大多基于数学困难问题而设计、实现效率低；
(2)算法本身没有考虑实现环境的差异，例如，对于经典的Diffie-Hellman密钥交换协议，协议双方在实现协议的过程中消耗的计算资源是相同的，亦即，均需执行两次大整数模幂运算。
然而，目前很多应用领域如物联网、云计算等往往呈现计算资源非对称的特点，即服务器一端计算资源强，终端计算资源弱。
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适用于计算资源非对称领域的共享密钥建立方法。
本发明所采用的技术方案是：一种适用于计算资源非对称领域的共享密钥建立方法，假设通信双方是Bob和Alice，则通信双方建立密钥共享包括以下步骤：
步骤1：建立***；
首先选定循环群
Figure GDA0002238255290000011
然后随机选取n个值
Figure GDA0002238255290000012
则***的公开参数为
Figure GDA0002238255290000013
步骤2：Alice随机选取集合
Figure GDA0002238255290000014
将S做为自己的临时私钥，然后计算KA＝Πi∈S yi；
步骤3：Alice通过***道发送KA给Bob；
步骤4：Bob随机选取
Figure GDA0002238255290000015
并依次计算
Figure GDA0002238255290000016
步骤5：Bob通过***道发送
Figure GDA0002238255290000017
给Alice；
步骤6：Alice收到KB后，用自己的私钥S计算出共享密钥
Figure GDA0002238255290000021
步骤7：Bob收到KA后，用自己的私钥b计算出共享密钥KAB＝(Πi∈S yi)b；
其中步骤2、步骤4、步骤6、步骤7中的运算均在循环群
Figure GDA0002238255290000023
中进行。
本发明具有以下优点和积极效果：协议双方实现过程中所需的计算资源不对称，极大地提高了协议一方的实现效率。特别适用于物联网，云计算等安全领域中服务器与移动终端计算资源非对称应用领域，在这些领域比传统密钥交换协议如Diffie-Hellman密钥交换协议等有优势。
附图说明
图1是本发明实施例的流程图。
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，本发明提供的一种适用于计算资源非对称领域的共享密钥建立方法，假设通信双方是Bob和Alice，则通信双方建立密钥共享包括以下步骤：
步骤1：建立***；
首先选定循环群
Figure GDA0002238255290000024
然后随机选取n个值
Figure GDA0002238255290000025
则***的公开参数为
Figure GDA0002238255290000026
步骤2：Alice随机选取集合
Figure GDA0002238255290000027
将S做为自己的临时私钥，然后计算KA＝Πi∈S yi；
步骤3：Alice通过***道发送KA给Bob；
步骤4：Bob随机选取
Figure GDA0002238255290000028
并依次计算
Figure GDA0002238255290000029
步骤5：Bob通过***道发送
Figure GDA00022382552900000210
给Alice；
步骤6：Alice收到KB后，用自己的私钥S计算出共享密钥
Figure GDA00022382552900000211
步骤7：Bob收到KA后，用自己的私钥b计算出共享密钥KAB＝(Πi∈S yi)b；
其中步骤2、步骤4、步骤6、步骤7中的运算均在循环群
Figure GDA00022382552900000213
中进行。
本发明还提供了一种适用于计算资源非对称领域的共享密钥建立方法，假设通信双方是Bob和Alice，则通信双方建立密钥共享包括以下步骤：
步骤1：建立***；
选定椭圆曲线上点集组成的循环群
Figure GDA0002238255290000031
然后随机选取n个点
Figure GDA0002238255290000032
则***的公开参数为
Figure GDA0002238255290000033
步骤2：Alice随机选取集合
Figure GDA0002238255290000034
将S做为自己的临时私钥，然后计算KA＝∑i∈S(xi，yi)；
步骤3：Alice通过***道发送KA给Bob；
步骤4：Bob随机选取
Figure GDA0002238255290000036
并计算b(x1，y1)，…，b(xn，yn)，其中b(xi，yi)表示椭圆曲线的点乘运算；
步骤5：Bob通过***道发送KB＝{b(x1，y1)，…，b(xn，yn)}给Alice；
步骤6：Alice收到KB后，用自己的私钥S计算出共享密钥KBA＝∑i∈S b(xi，yi)；
步骤7：Bob收到KA后，用自己的私钥b计算出共享密钥KAB＝b∑i∈S(xi，yi)；
其中步骤2、步骤4、步骤6、步骤7中的运算均在循环群
Figure GDA0002238255290000035
中进行。
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 (2)

1.一种适用于计算资源非对称领域的共享密钥建立方法，其特征在于：假设通信双方是Bob和Alice，则通信双方建立密钥共享包括以下步骤：
步骤1：建立***；
首先选定循环群
Figure FDA0002238255280000011
然后随机选取n个值
Figure FDA0002238255280000012
则***的公开参数为
Figure FDA0002238255280000013
步骤2：Alice随机选取集合
Figure FDA0002238255280000014
将S做为自己的临时私钥，然后计算KA＝Πi∈Syi；
步骤3：Alice通过***道发送KA给Bob；
步骤4：Bob随机选取
Figure FDA0002238255280000015
并依次计算
Figure FDA0002238255280000016
步骤5：Bob通过***道发送
Figure FDA0002238255280000017
给Alice；
步骤6：Alice收到KB后，用自己的私钥S计算出共享密钥
Figure FDA0002238255280000018
步骤7：Bob收到KA后，用自己的私钥b计算出共享密钥KAB＝(Πi∈Syi)b；
其中步骤2、步骤4、步骤6、步骤7中的运算均在循环群
Figure FDA0002238255280000019
中进行。
2.一种适用于计算资源非对称领域的共享密钥建立方法，其特征在于：假设通信双方是Bob和Alice，则通信双方建立密钥共享包括以下步骤：
步骤1：建立***；
选定椭圆曲线上点集组成的循环群
Figure FDA00022382552800000115
然后随机选取n个点
Figure FDA00022382552800000110
则***的公开参数为
Figure FDA00022382552800000111
步骤2：Alice随机选取集合
Figure FDA00022382552800000112
将S做为自己的临时私钥，然后计算KA＝∑i∈S(xi，yi)；
步骤3：Alice通过***道发送KA给Bob；
步骤4：Bob随机选取
Figure FDA00022382552800000113
并依次计算b(x1，y1)，…，b(xn，yn)，其中b(xi，yi)表示椭圆曲线的点乘运算；
步骤5：Bob通过***道发送KB＝{b(x1，y1)，…，b(xn，yn)}给Alice；
步骤6：Alice收到KB后，用自己的私钥S计算出共享密钥KBA＝∑i∈Sb(xi，yi)；
步骤7：Bob收到KA后，用自己的私钥b计算出共享密钥KAB＝b∑i∈S(xi，yi)；
其中步骤2、步骤4、步骤6、步骤7中的运算均在循环群
Figure FDA00022382552800000114
中进行。
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