技术领域Technical Field
本发明属于通信技术领域，特别涉及一种基于动态参数表的DFMA系统的密钥分发方法及系统。The present invention belongs to the field of communication technology, and in particular relates to a key distribution method and system of a DFMA system based on a dynamic parameter table.
背景技术Background Art
随着高清视频、虚拟现实VR，5G前传等技术的发展，现代社会对传输速率和带宽提出了越来越高的要求。PON网络因其比特率高，资源分配灵活，综合建设成本低等特点，很好的满足了这些要求的。其中，数字滤波多址接入无源光网络凭借其满足未来宽带接入网对高度动态、可重构的需求、以及具备灵活的带宽分配方案等优势，成为下一代接入网的核心技术之一。但是，由于PON网络一般采用广播形式向下行传输数据，这也就意味着网络中的没一个ONU都可以接收来自OLT发送的所有数据，某些非法ONU就会伪装成合法的OUN窃取来自OLT的信息，这种由于广播形式传送数据也是造成PON网络安全性问题的主要原因。With the development of technologies such as high-definition video, virtual reality VR, and 5G fronthaul, modern society has put forward higher and higher requirements for transmission rate and bandwidth. PON network meets these requirements well due to its high bit rate, flexible resource allocation, and low comprehensive construction cost. Among them, digital filtering multiple access passive optical network has become one of the core technologies of the next generation access network by virtue of its advantages such as meeting the highly dynamic and reconfigurable requirements of future broadband access networks and having flexible bandwidth allocation schemes. However, since PON networks generally use broadcasting to transmit data downstream, this means that no ONU in the network can receive all data sent from the OLT. Some illegal ONUs will disguise themselves as legitimate OUNs to steal information from the OLT. This transmission of data in broadcasting form is also the main cause of PON network security problems.
混沌加密应用在PON网络中也是一个研究的热点，目前混沌加密在PON网络中的应用主要有两个方面，一个是激光混沌，一个是数字混沌。激光混沌因其需要发送方和接收方的激光器高度同步，导致对设备要求很高，经济效益低。而目前的PON网络中的数字混沌加密主要集中在加密层面，通过各种改进加密算法来提高安全性，但是混沌加密作为对称加密的一种，密钥分发往往被人忽视，并且常见的密钥分发过程和数据传输是分开的，作为两个步骤进行密钥分发的过程也会降低对称加密的加解密的效率。The application of chaotic encryption in PON networks is also a hot topic of research. At present, there are two main aspects of the application of chaotic encryption in PON networks, one is laser chaos and the other is digital chaos. Laser chaos requires high synchronization of the lasers of the sender and the receiver, which leads to high requirements for equipment and low economic benefits. The current digital chaotic encryption in PON networks mainly focuses on the encryption level, and improves security through various improved encryption algorithms. However, as a type of symmetric encryption, key distribution of chaotic encryption is often overlooked, and the common key distribution process is separated from data transmission. The key distribution process as a two-step process will also reduce the efficiency of encryption and decryption of symmetric encryption.
此外，目前的混沌通过选取不同参数的方法实现混沌同步，基本都是在参数表不变的情况下，在参数表中选取静态参数和动态参数，这种方式存在两个问题，一个是混沌同步的效率极低，每次都需要通过大量的混沌迭代计算，接收端引入较大的DSP延迟，另一个则是由于是固定参数表，短时间可以抵抗铭文选择性攻击，但是进过长时间发送了大量的信息肯定会有重复的参数被选择，相同的参数作为混沌初值并且按照固定的参数产生的同步序列和密钥也是相同的，这样长此以往很容易遭到非法攻击者的窃取。In addition, the current chaos synchronization is achieved by selecting different parameters. Basically, static parameters and dynamic parameters are selected in the parameter table without changing the parameter table. There are two problems with this method. One is that the efficiency of chaos synchronization is extremely low. A large number of chaotic iterative calculations are required each time, and a large DSP delay is introduced at the receiving end. The other is that due to the fixed parameter table, it can resist the selective attack of inscriptions in a short time, but if a large amount of information is sent for a long time, repeated parameters will definitely be selected. The same parameters are used as the chaos initial values, and the synchronization sequence and key generated according to the fixed parameters are also the same. In this way, it is easy to be stolen by illegal attackers in the long run.
发明内容Summary of the invention
为了更加有效地抵抗选择明文攻击，并提高了接收方的解密速率，本发明提出一种基于动态参数表的DFMA系统的密钥分发方法，发送端和接收端采用相同的混沌系统和参数寄存器，参数寄存器中存储下次加密所需的索引值，混沌系统中还设置有一个动态参数表和一个静态参数表，每一个索引值对应一个动态参数表中的位置和一个静态参数表中的位置，进行秘钥分发的过程具体包括以下步骤：In order to more effectively resist chosen plaintext attacks and improve the decryption rate of the receiver, the present invention proposes a key distribution method for a DFMA system based on a dynamic parameter table. The sending end and the receiving end use the same chaotic system and parameter register. The parameter register stores the index value required for the next encryption. A dynamic parameter table and a static parameter table are also provided in the chaotic system. Each index value corresponds to a position in a dynamic parameter table and a position in a static parameter table. The process of key distribution specifically includes the following steps:
发送方从参数寄存器中取出索引值作为本次使用索引值Pi，并通过随机数的方式产生一个随机索引Pi+1覆盖寄存器中的索引值；The sender takes the index value from the parameter register as the index valuePi for this use, and generates a random indexPi+1 by random number to overwrite the index value in the register;
发送方根据索引值Pi对应的动态参数和静态参数作用于混沌系统，经过迭代与量化产生二进制混沌序列Bi，从Bi中第1位开始截取N位的二进制序列作为同步序列L；The sender acts on the chaotic system according to the dynamic parameters and static parameters corresponding to the index valuePi , generates a binary chaotic sequenceBi through iteration and quantization, and intercepts the N-bit binary sequence from the first bit ofBi as the synchronization sequence L;
从Bi的第N+1位开始截取和发送数据相同长度的二进制序列作为密钥，对待发送的数据以及索引值的二进制序列进行异或加密，将加密后的数据以及同步序列一起发送给接收方；From the N+1th bit ofBi, a binary sequence of the same length as the transmitted data is intercepted as the key, the data to be transmitted and the binary sequence of the index value are XOR-encrypted, and the encrypted data and the synchronization sequence are sent to the receiver together;
发送方混沌系统Y端输出序列的最后两位参数替换索引值Pi对应动态参数表中的值；The last two parameters of the output sequence of the chaotic system Y at the sender replace the index valuePi with the value in the dynamic parameter table;
接收方接收到数据后，接收方参数存储器中存储的索引值产生同步序列L’，判断同步序列L’与同步序列L的相关度是否大于设定阈值；After the receiver receives the data, the index value stored in the receiver parameter memory generates a synchronization sequence L', and determines whether the correlation between the synchronization sequence L' and the synchronization sequence L is greater than a set threshold;
若同步序列L’与同步序列L的相关度不大于设定阈值，则接收端遍历所有索引值对应的静态参数和动态参数，直到同步序列L’与同步序列L的相关度大于设定阈值，获取此时的动态参数和静态参数；If the correlation between the synchronization sequence L' and the synchronization sequence L is not greater than the set threshold, the receiving end traverses the static parameters and dynamic parameters corresponding to all index values until the correlation between the synchronization sequence L' and the synchronization sequence L is greater than the set threshold, and obtains the dynamic parameters and static parameters at this time;
若大于则根据接收方参数存储器中存储的索引值对应的动态参数和静态参数作用于混沌系统产生密钥，利用密钥对接收的加密数据进行解密；If it is greater than, the dynamic parameters and static parameters corresponding to the index value stored in the parameter memory of the receiver are used to generate a key on the chaotic system, and the key is used to decrypt the received encrypted data;
利用混沌系统Y端输出的两个参数替换索引值Pi对应的动态参数；The two parameters output from the chaotic system Y terminal are used to replace the dynamic parameters corresponding to the index valuePi ;
利用接收端解密得到的索引值替换接收端参数寄存器中存储的索引值。The index value obtained by decryption at the receiving end is used to replace the index value stored in the parameter register at the receiving end.
进一步的，发送端和接收端进行初始化时，发送端随机选择两个索引值，将其中一个作为下一次使用的索引值存储在其本地的参数寄存器中，将接收端本地的参数寄存器初始化为零。Furthermore, when the sending end and the receiving end are initialized, the sending end randomly selects two index values, stores one of them as the index value to be used next time in its local parameter register, and initializes the local parameter register of the receiving end to zero.
进一步的，两个同步序列之间的相关度的计算表示为：Furthermore, the calculation of the correlation between two synchronization sequences is expressed as:
其中，ρvu表示同步序列V与同步序列U之间的相关性参数，当ρvu大于设定阈值时同步序列V与同步序列U相关。Wherein, ρvu represents the correlation parameter between the synchronization sequence V and the synchronization sequence U. When ρvu is greater than a set threshold, the synchronization sequence V is correlated with the synchronization sequence U.
进一步的，接收端和发送端采用二维改进型logistics混沌系统产生混沌信号，二维改进型logistics混沌系统表示为：Furthermore, the receiving end and the transmitting end use a two-dimensional improved logistics chaotic system to generate chaotic signals. The two-dimensional improved logistics chaotic system is expressed as:
其中，Xn+1表示混沌系统第n+1次迭代X端产生的信号，Yn+1表示混沌系统第n+1次迭代Y端产生的信号；a为混沌系统的静态参数，a的取值范围为(0,1)；X0和Y0为混沌系统的动态参数，取值范围为(0,1)。Wherein, Xn+1 represents the signal generated at the X end of the chaotic system at the n+1th iteration, Yn+1 represents the signal generated at the Y end of the chaotic system at the n+1th iteration; a is the static parameter of the chaotic system, and the value range of a is (0,1);X0 andY0 are the dynamic parameters of the chaotic system, and the value range is (0,1).
进一步的，二维改进型logistics混沌系统总共叠加n+2次，将X端产生的信号进行预处理和量化后作为混沌序列Bi；利用Y端最后两次迭代输出的值更新本次使用索引值Pi对应动态参数表中两个动态参数的值。Furthermore, the two-dimensional improved logistics chaotic system is superimposed n+2 times in total, and the signal generated by the X end is preprocessed and quantized as the chaotic sequenceBi ; the values of the two dynamic parameters in the dynamic parameter table corresponding to the index valuePi used this time are updated using the values output from the last two iterations of the Y end.
进一步的，为了增强二进制中的0与1统计特性，对每次混沌系统输出的序列进行预处理，包括：Furthermore, in order to enhance the statistical characteristics of 0 and 1 in binary, the sequence output by each chaotic system is preprocessed, including:
Xi＝106Xi-floor(106Xi)Xi =106 Xi -floor (106 Xi )
Yi＝106Yi-floor(106Yi)Yi =106 Yi -floor (106 Yi )
其中，(Xi，Yi)为混沌系统第i次迭代X端、Y端输出的序列；floor(·)为向下取整函数。Wherein, (Xi , Yii ) is the sequence of the X-end and Y-end outputs of the chaotic system at the i-th iteration; floor(·) is the floor rounding function.
进一步的，进过迭代输出混沌序列(Xi，Yi)，对X端输出进行量化操作，将量化后得到的序列作为：Furthermore, the chaotic sequence (Xi ,Yi ) is iteratively output, and the output of the X terminal is quantized, and the sequence obtained after quantization is used as:
其中，Bi表示混沌序列经过量化后的二进制序列。Among them,Bi represents the binary sequence after the chaotic sequence is quantized.
进一步的，二进制序列Bi的长度为n，n为同步序列长度、待发送的数据以及索引值的二进制序列之和。Furthermore, the length of the binary sequenceBi is n, where n is the sum of the length of the synchronization sequence, the data to be sent, and the binary sequence of the index value.
进一步的，每个索引值中包括一个静态参数表中的行、列位置索引和两个动态参数表中的行、列位置索引，将所有位置每个索引位置转换为二进制参数后进行加密。Furthermore, each index value includes a row and column position index in a static parameter table and a row and column position index in two dynamic parameter tables, and each index position of all positions is converted into a binary parameter and then encrypted.
本发明还提出一种基于动态参数表的DFMA系统的密钥分发系统，用于实现一种基于动态参数表的DFMA系统的密钥分发方法，包括混沌信号产生模块、参数索引寄存器、参数表寄存器、相关系数判断器，其中：The present invention also proposes a key distribution system of a DFMA system based on a dynamic parameter table, which is used to implement a key distribution method of a DFMA system based on a dynamic parameter table, including a chaotic signal generation module, a parameter index register, a parameter table register, and a correlation coefficient judgement device, wherein:
参数索引寄存器，用于存储混沌信号产生模块下一次使用所需静态参数和动态参数的索引值；The parameter index register is used to store the index values of static parameters and dynamic parameters required for the next use of the chaotic signal generating module;
混沌信号产生模块，用于根据静态参数和动态参数产生混沌序列，并根据混沌序列获取同步序列以及根据混沌序列更新参数表寄存器中索引值对应的动态参数；A chaotic signal generating module is used to generate a chaotic sequence according to static parameters and dynamic parameters, obtain a synchronization sequence according to the chaotic sequence, and update the dynamic parameters corresponding to the index values in the parameter table register according to the chaotic sequence;
参数表寄存器，用于根据索引值存储动态参数和静态参数；Parameter table registers, used to store dynamic parameters and static parameters according to index values;
相关系数判断器，用于判断两个同步序列的相关系数是否大于设定阈值。The correlation coefficient determiner is used to determine whether the correlation coefficient of two synchronization sequences is greater than a set threshold.
通过在发送方和接送方增加一个参数寄存器，这个参数寄存器中存储着相同的索引值，即下一次加解密所需的参数组索引，并且将下一次加解密所需的索引插入到传输数据的后面并进行加密，再将同步序列插入到索引的后面，一起传送到发送方，提高了加解密的效率，同时利用混沌系统Y端的输出参数对使用过的动态参数进行替代，使得参数表实时更新，每次使用的参数都是唯一的，每次加密的密钥也是不同的，达到一种类一次一密的效果，这样可以更加有效地抵抗选择明文攻击。By adding a parameter register to the sender and the receiver, the parameter register stores the same index value, that is, the parameter group index required for the next encryption and decryption, and inserting the index required for the next encryption and decryption after the transmission data and encrypting it, and then inserting the synchronization sequence after the index and transmitting it to the sender together, the efficiency of encryption and decryption is improved. At the same time, the output parameters of the Y end of the chaotic system are used to replace the used dynamic parameters, so that the parameter table is updated in real time. The parameters used each time are unique, and the encryption key is different each time, achieving a one-time one-key effect, which can more effectively resist chosen plaintext attacks.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明实施例的基于动态参数表的DFMA系统的密钥分发方案在DFMA-PON系统的加密过程的传输结构示意图；1 is a schematic diagram of the transmission structure of the encryption process of the key distribution scheme of the DFMA system based on the dynamic parameter table in the DFMA-PON system according to an embodiment of the present invention;
图2本发明加解密过程的详细流程图；FIG2 is a detailed flow chart of the encryption and decryption process of the present invention;
图3为混沌初始值敏感性特点的折线图；Figure 3 is a line graph showing the sensitivity characteristics of the chaos initial value;
图4为混沌系统中混沌序列相关系数和自相关系数的关系，其中(a)为混沌系统产生的混沌序列之间的相关系数与时间的关系；(b)为混沌系统产生的混沌序列的自相关系数与时间的关系；Figure 4 shows the relationship between the correlation coefficient and the autocorrelation coefficient of the chaotic sequence in the chaotic system, where (a) is the relationship between the correlation coefficient and time of the chaotic sequence generated by the chaotic system; (b) is the relationship between the autocorrelation coefficient and time of the chaotic sequence generated by the chaotic system;
图5为相关系数与误码率之间的关系曲线图；FIG5 is a graph showing the relationship between the correlation coefficient and the bit error rate;
图6为本发明实施例的加密信号与原始信号，非法ONU经过25km光纤传输的误码率对比示意图；6 is a schematic diagram comparing the bit error rate of the encrypted signal and the original signal of the embodiment of the present invention, and the illegal ONU transmitted through a 25km optical fiber;
图7为本发明中未加寄存器和添加寄存器实现混沌同步，所需时间随着参数表中参数个数变化带来影响的曲线图FIG. 7 is a graph showing the effect of the number of parameters in the parameter table on the time required to achieve chaotic synchronization without and with registers in the present invention.
具体实施方式DETAILED DESCRIPTION
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
本发明提出一种基于动态参数表的DFMA系统的密钥分发方法，发送端和接收端采用相同的混沌系统和参数寄存器，参数寄存器中存储下次加密所需的索引值，混沌系统中还设置有一个动态参数表和一个静态参数表，每一个索引值对应一个动态参数表中的位置和一个静态参数表中的位置，进行秘钥分发的过程具体包括以下步骤：The present invention proposes a key distribution method for a DFMA system based on a dynamic parameter table. The transmitting end and the receiving end use the same chaotic system and parameter register. The parameter register stores the index value required for the next encryption. A dynamic parameter table and a static parameter table are also provided in the chaotic system. Each index value corresponds to a position in the dynamic parameter table and a position in the static parameter table. The process of key distribution specifically includes the following steps:
发送方从参数寄存器中取出索引值作为本次使用索引值Pi，并通过随机数的方式产生一个随机索引Pi+1覆盖寄存器中的索引值；The sender takes the index value from the parameter register as the index valuePi for this use, and generates a random indexPi+1 by random number to overwrite the index value in the register;
发送方根据索引值Pi对应的动态参数和静态参数作用于混沌系统，经过迭代与量化产生二进制混沌序列Bi，从Bi中第1位开始截取N位的二进制序列作为同步序列L；The sender acts on the chaotic system according to the dynamic parameters and static parameters corresponding to the index valuePi , generates a binary chaotic sequenceBi through iteration and quantization, and intercepts the N-bit binary sequence from the first bit ofBi as the synchronization sequence L;
从Bi的第N+1位开始截取和发送数据相同长度的二进制序列作为密钥，对待发送的数据以及索引值的二进制序列进行异或加密，将加密后的数据以及同步序列一起发送给接收方；From the N+1th bit ofBi, a binary sequence of the same length as the transmitted data is intercepted as the key, the data to be transmitted and the binary sequence of the index value are XOR-encrypted, and the encrypted data and the synchronization sequence are sent to the receiver together;
发送方混沌系统Y端输出序列的最后两位参数替换索引值Pi对应动态参数表中的值；The last two parameters of the output sequence of the chaotic system Y at the sender replace the index valuePi with the value in the dynamic parameter table;
接收方接收到数据后，接收方参数存储器中存储的索引值产生同步序列L’，判断同步序列L’与同步序列L的相关度是否大于设定阈值；After the receiver receives the data, the index value stored in the receiver parameter memory generates a synchronization sequence L', and determines whether the correlation between the synchronization sequence L' and the synchronization sequence L is greater than a set threshold;
若同步序列L’与同步序列L的相关度不大于设定阈值，则接收端遍历所有索引值对应的静态参数和动态参数，直到同步序列L’与同步序列L的相关度大于设定阈值，获取此时的动态参数和静态参数；If the correlation between the synchronization sequence L' and the synchronization sequence L is not greater than the set threshold, the receiving end traverses the static parameters and dynamic parameters corresponding to all index values until the correlation between the synchronization sequence L' and the synchronization sequence L is greater than the set threshold, and obtains the dynamic parameters and static parameters at this time;
若大于则根据接收方参数存储器中存储的索引值对应的动态参数和静态参数作用于混沌系统产生密钥，利用密钥对接收的加密数据进行解密；If it is greater than, the dynamic parameters and static parameters corresponding to the index value stored in the parameter memory of the receiver are used to generate a key on the chaotic system, and the key is used to decrypt the received encrypted data;
利用混沌系统Y端输出的两个参数替换索引值Pi对应的动态参数；The two parameters output from the chaotic system Y terminal are used to replace the dynamic parameters corresponding to the index valuePi ;
利用接收端解密得到的索引值替换接收端参数寄存器中存储的索引值。The index value obtained by decryption at the receiving end is used to replace the index value stored in the parameter register at the receiving end.
本发明基于基于动态参数表的DFMA系统的密钥分发方案的加密方法，过程如图1和图2所示，该系统包括二维改进型logistics混沌信号产生模块、信号发生模块、光传输模块、信号接收模块、参数索引寄存器、参数表寄存器，进行加密的过程具体包括：The present invention is based on an encryption method of a key distribution scheme of a DFMA system based on a dynamic parameter table. The process is shown in Figures 1 and 2. The system includes a two-dimensional improved logistics chaotic signal generation module, a signal generation module, an optical transmission module, a signal receiving module, a parameter index register, and a parameter table register. The encryption process specifically includes:
logistic映射是一维离散混沌系统，运算速度快，方程反复迭代可以产生较好的混沌序列。为了增强DFMA-PON抵抗攻击的能力，针对传统logistics混沌密钥空间小、结构简单等问题，本发明选择了一种二维改进型logistics混沌系统为本系统产生混沌信号，该混沌系统在原有传统logistics混沌系统基础上添加正弦项及新的变量，构造改进的二维logistics混沌系统。该系统能够增大密钥空间，且结构简单，生成的混沌序列伪随机性强，将其作为密钥能够提高加密算法的安全性。下面是改进后的混沌系统公式：The logistic map is a one-dimensional discrete chaotic system with fast operation speed. Repeated iteration of the equation can generate a better chaotic sequence. In order to enhance the ability of DFMA-PON to resist attacks, the present invention selects a two-dimensional improved logistics chaotic system to generate chaotic signals for this system, aiming at the problems of small key space and simple structure of traditional logistics chaotic system. The chaotic system adds sine terms and new variables on the basis of the original traditional logistics chaotic system to construct an improved two-dimensional logistics chaotic system. The system can increase the key space, and has a simple structure. The generated chaotic sequence has strong pseudo-randomness. Using it as a key can improve the security of the encryption algorithm. The following is the formula of the improved chaotic system:
其中，Xn+1表示混沌系统第n+1次迭代X端产生的信号，Yn+1表示混沌系统第n+1次迭代Y端产生的信号；a为混沌系统的静态参数，a的取值范围为(0,1)；X0、Y0为混沌系统的动态参数，取值范围为(0,1)；当所有取值属于范围内时，该混沌系统才处于混沌状态。Among them, Xn+1 represents the signal generated at the X end of the chaotic system at the n+1th iteration, and Yn+1 represents the signal generated at the Y end of the chaotic system at the n+1th iteration; a is the static parameter of the chaotic system, and the value range of a is (0,1);X0 andY0 are the dynamic parameters of the chaotic system, and the value range is (0,1); when all values are within the range, the chaotic system is in a chaotic state.
混沌的输出序列为(Xi，Yi)，为了增强二进制中的0与1统计特性，对输出序列(Xi，Yi)进行如下处理：The chaotic output sequence is (Xi ,Yi ). In order to enhance the statistical characteristics of 0 and 1 in binary, the output sequence (Xi ,Yi ) is processed as follows:
Xi＝106Xi-floor(106Xi)Xi =106 Xi -floor (106 Xi )
Yi＝106Yi-floor(106Yi)Yi =106 Yi -floor (106 Yi )
其中，(Xi，Yi)为混沌系统第i次迭代X端、Y端输出的序列；floor(...)为向下取整函数。Wherein, (Xi , Yii ) is the sequence of the X-end and Y-end outputs of the chaotic system at the i-th iteration; floor(...) is the floor rounding function.
进过迭代输出混沌序列(Xi，Yi)，对Xi输出进行量化操作：After iteratively outputting the chaotic sequence (Xi ,Yi ), theXi output is quantized:
本发明采用的混沌系统能够增大密钥空间，且结构简单，生成的混沌序列伪随机性强，将其作为密钥能够提高加密算法的安全性；通过分析，二维改进型logistic混沌系统三个参数的取值范围皆为0～1且不包含0和1，本发明的计算精度为10-15(即小数点后15位)，密钥空间为1015×1015×1015≈2150>2100,说明该混沌可以有效地抵抗穷举攻击。The chaotic system adopted by the present invention can increase the key space, and has a simple structure. The generated chaotic sequence has strong pseudo-randomness, and using it as a key can improve the security of the encryption algorithm. Through analysis, the value ranges of the three parameters of the two-dimensional improved logistic chaotic system are all 0-1 and do not include 0 and 1. The calculation accuracy of the present invention is10-15 (i.e., 15 decimal places), and the key space is1015 ×1015×1015≈2150>2100 , which shows that the chaos can effectively resist exhaustive attacks.
第一次通讯中，发送方和接收方寄存器中存储的索引值是空的，发送方和接收方进行密钥同步的过程包括：In the first communication, the index values stored in the registers of the sender and the receiver are empty. The process of key synchronization between the sender and the receiver includes:
发送方从寄存器中的参数表选取两组静态参数和动态参数，将其中一组的索引值记为Pi，另外一组索引值记为Pi+1，将Pi+1存储在寄存器中作为下一次的索引值，我们利用Pi在参数表中选取参数作用于混沌产生一定长度的二进制序列(本实施例中产生400bit长度的二进制序列)，将发送端产生的同步序列称为同步序列L。The sender selects two groups of static parameters and dynamic parameters from the parameter table in the register, records the index value of one group asPi , and records the index value of the other group asPi+1 , and stores Pi+1 in the register as the next index value. We usePi to select parameters in the parameter table to act on chaos to generate a binary sequence of a certain length (a binary sequence of 400 bits in length is generated in this embodiment), and the synchronization sequence generated by the sender is called the synchronization sequence L.
获得同步序列后，将Pi+1转化为二进制序列Di+1并插入到待发送数据的后面，将同步序列插入到Di+1的后面，然后我们将发送数据、同步序列、Di+1三个部分作为一个整体数据，再次利用该混沌产生密钥C，密钥C与发送数据和Di+1总长度相同，我们利用密钥C对发送数据和Di+1两个部分进行异或加密，然后将加密后的整体数据发通过信道送到到接收方。其中加密过程为：After obtaining the synchronization sequence, Pi+1 is converted into a binary sequence Di+1 and inserted behind the data to be sent, and the synchronization sequence is inserted behind Di+1 . Then we take the three parts of the sent data, synchronization sequence, and Di+1 as a whole data, and use the chaos again to generate the key C. The key C has the same total length as the sent data and Di+1 . We use the key C to XOR encrypt the two parts of the sent data and Di+1 , and then send the encrypted whole data through the channel to the receiver. The encryption process is:
其中，C为密钥，Q为待发送二进制数据，S为加密后产生的密文，Di+1为Pi+1对应的二进制序列，Pi+1包括三组索引，即一个静态参数的坐标索引以及两个动态参数的坐标索引，若其中一个坐标为(3,4)，表示该组参数是动态参数表或者静态参数表中第3行、第4列中存储的参数值，则该坐标二进制记为100011，为异或运算。Where C is the key, Q is the binary data to be sent, S is the ciphertext generated after encryption, Di+1 is the binary sequence corresponding to Pi+1 , Pi+1 includes three groups of indexes, namely the coordinate index of a static parameter and the coordinate index of two dynamic parameters. If one of the coordinates is (3,4), it means that the group of parameters is the parameter value stored in the 3rd row and 4th column in the dynamic parameter table or the static parameter table, then the coordinate is recorded as 100011 in binary. It is an XOR operation.
发送方在完成发送后，将使用Y端输出的Yn+1和Yn+2替换动态参数表中使用过的动态参数，这样就可以保证使得动态参数只被使用一次，不会被重复使用，每次用于加密的密钥不会出现重复的结果，达到一种类一次一密的效果，更加有效地抵抗选择明文攻击。After completing the transmission, the sender will use Yn+1 andYn+2 output by the Y terminal to replace the dynamic parameters used in the dynamic parameter table. This ensures that the dynamic parameters are used only once and will not be reused. The key used for encryption each time will not have repeated results, achieving a one-time-one-key effect and more effectively resisting chosen-plaintext attacks.
接收方接收到这个传输数据后，由于第一次本地存储器中参数为空，接收方遍历自己的参数集从中选取不同的静态参数和动态参数，作用于混沌系统接产生同步序列L'，计算L和L'之间的相关系数，相关系数公式定义如下：After the receiver receives the transmission data, since the parameters in the local memory are empty for the first time, the receiver traverses its own parameter set and selects different static parameters and dynamic parameters from them, acts on the chaotic system to generate the synchronization sequence L', and calculates the correlation coefficient between L and L'. The correlation coefficient formula is defined as follows:
其中，ρvu表示同步序列V与同步序列U之间的相关性参数；cov(V,U)表示同步序列V与同步序列U之间的协方差函数，D(V)表示同步序列V的方差，D(U)表示同步序列U的方差，cov(V,U)记为σvu，记为σv，记为σu。Wherein, ρvu represents the correlation parameter between synchronization sequence V and synchronization sequence U; cov(V,U) represents the covariance function between synchronization sequence V and synchronization sequence U, D(V) represents the variance of synchronization sequence V, D(U) represents the variance of synchronization sequence U, and cov(V,U) is denoted as σvu , Denoted as σv , Denoted as σu .
由于混沌的初始值敏感的特性，发送方的参数和接收方的参数若不相同，L与L'之间的相关系数会很小，若他们相同，则L与L'是一摸一样的，也就意味着他们的相关系数为1，考虑到同步序列在传输过程中可能会产生误码，所以本发明中设置一个阈值(该阈值在本实施例中取0.3，本领域技术人员可以根据实际情况或者经验选择)，L当与L'之间的相关系数大于阈值的时候，就认为接收端的参数与发送端的参数是一样的，也就是实现了混沌的同步，接着用同步后的混沌同步系统产生密钥对接收的数据S进行解密，提取其中的Di+1并转化为Pi+1，在获取下次解密所Y需的Pi+1后，就会将其存储在自己的参数寄存器中。同时接收方将使用Y端输出的Yn+1和Yn+2替换动态参数表中使用过的动态参数，保证发送方和接收方的参数表保持统一。Due to the sensitive characteristics of the initial value of chaos, if the parameters of the sender and the receiver are different, the correlation coefficient between L and L' will be very small. If they are the same, L and L' are exactly the same, which means that their correlation coefficient is 1. Considering that the synchronization sequence may generate errors during transmission, a threshold is set in the present invention (the threshold is 0.3 in this embodiment, and those skilled in the art can choose according to actual conditions or experience). When the correlation coefficient between L and L' is greater than the threshold, it is considered that the parameters of the receiving end are the same as the parameters of the sending end, that is, the synchronization of chaos is achieved. Then, the synchronized chaotic synchronization system is used to generate a key to decrypt the received data S, extract Di+1 therein and convert it into Pi+1 , and after obtaining Pi+1 required for the next decryption, it will be stored in its own parameter register. At the same time, the receiver will useYn+1 andYn+2 output by the Y terminal to replace the dynamic parameters used in the dynamic parameter table, ensuring that the parameter tables of the sender and the receiver remain unified.
接下来的通信就会简单很多，本发明将发送方存储器中的上次产生的Pi+1取出，在参数表选取对应的动态参数和静态参数作用于混沌系统产生同步序列，同时产生一组新的索引值Pi+1存替换储在寄存器中，将新的Pi+1转化为二进制序列Di+1并插入到发送数据的尾部，同样地将同步序列插入到Di+1的后面一起发送到接送方，由于接收方在上次通信中已经获得解密所需的Pi(上次通信中的Pi+1)，并存储在本地寄存器中，接收方收到数据后直接从自己的寄存器中取出索引值Pi，直接作用于混沌产生同步序列L'，然后将L与L'计算相关系数R，若R>阈值，就认为寄存器中存储的Pi是正确的。当然接收方寄存器Pi也就是上次通信的Pi+1在上次通信中可能发生误码或者丢失，导致本次通信中接收方寄存器存储的Pi是错误的，表现出的就是相关系数<阈值，当相关系数<阈值时，接收端就像刚开始那样通过接收方遍历参数集产生同步序列L'直到相关系数>阈值，然后再用选择的参数产生密钥用于解密，保证通信地正常进行，解密完成后，同样提取其中的Di+1并转化为Pi+1，在获取下次解密所需的Pi+1后，就会将其存储在自己的参数寄存器中。The subsequent communication will be much simpler. The present invention takes out the Pi+1 generated last time in the memory of the sender, selects the corresponding dynamic parameters and static parameters in the parameter table to act on the chaotic system to generate a synchronization sequence, and at the same time generates a set of new index values Pi+1 to store in the register, converts the new Pi+1 into a binary sequence Di+1 and inserts it to the end of the transmitted data. Similarly, the synchronization sequence is inserted after Di+1 and sent to the receiver. Since the receiver has obtained thePi (Pi+1 in the last communication) required for decryption in the last communication and stored it in the local register, the receiver directly takes out the index valuePi from its own register after receiving the data, and directly acts on the chaos to generate a synchronization sequence L', and then calculates the correlation coefficient R between L and L'. If R>threshold, it is considered that thePi stored in the register is correct. Of course, the receiver's registerPi, which is Pi+1 of the last communication, may have errors or be lost in the last communication, resulting in thePi stored in the receiver's register in this communication being wrong, which is manifested as the correlation coefficient < threshold. When the correlation coefficient < threshold, the receiver traverses the parameter set to generate a synchronization sequence L' as at the beginning until the correlation coefficient > threshold, and then uses the selected parameters to generate a key for decryption to ensure normal communication. After decryption is completed, Di+1 is also extracted and converted into Pi+1 . After obtaining the Pi+1 required for the next decryption, it will be stored in its own parameter register.
最后，发送方和接收方采用同样的方式，产生对应的混沌值Yn+1和Yn+2替换动态参数表中的使用过的参数。Finally, the sender and the receiver use the same method to generate corresponding chaotic values Yn+1 and Yn+2 to replace the used parameters in the dynamic parameter table.
一般情况下攻击者暂时获得加密系统的使用权，因此攻击者能加密任意的明文，并获得相对应的密文，攻击者再将加密生成的密文与截获的密文一一对比，以此破译出全部或部分明文。而在本文发明中，通过采用动态参数和动态参数表的方式，使得每次加密所需的密钥和其对应的同步序列都不相同，有效地抵抗了选择明文攻击。Generally, the attacker temporarily obtains the right to use the encryption system, so the attacker can encrypt any plaintext and obtain the corresponding ciphertext. The attacker then compares the encrypted ciphertext with the intercepted ciphertext one by one to decipher all or part of the plaintext. In the invention of this article, by adopting the method of dynamic parameters and dynamic parameter tables, the key required for each encryption and its corresponding synchronization sequence are different, which effectively resists the chosen plaintext attack.
本发明还提出一种基于动态参数表的DFMA系统的密钥分发系统，用于实现一种基于动态参数表的DFMA系统的密钥分发方法，包括混沌信号产生模块、参数索引寄存器、参数表寄存器、相关系数判断器，其中：The present invention also proposes a key distribution system of a DFMA system based on a dynamic parameter table, which is used to implement a key distribution method of a DFMA system based on a dynamic parameter table, including a chaotic signal generation module, a parameter index register, a parameter table register, and a correlation coefficient judgement device, wherein:
参数索引寄存器，用于存储混沌信号产生模块下一次使用所需静态参数和动态参数的索引值；The parameter index register is used to store the index values of static parameters and dynamic parameters required for the next use of the chaotic signal generating module;
混沌信号产生模块，用于根据静态参数和动态参数产生混沌序列，并根据混沌序列获取同步序列以及根据混沌序列更新参数表寄存器中索引值对应的动态参数；混沌信号产生模块进行n+2次迭代，X端和Y端两个端口分别输出n+2个混沌参数，将X端产生的混沌参数中的前n个混沌参数进行预处理和量化，形成二进制序列，将该二进制序列的前N位作为同步序列，第N到n个作为加密待发送的数据以及索引值的二进制序列的密钥，该密钥的长度与待发送的数据以及索引值的二进制序列的长度之和相同，并将Y端最后两次迭代的数据对当前索引值对应的两个动态参数的位置中保存值进行更新，保证下一次使用该索引位置时动态参数的值与本次使用时不同；A chaotic signal generating module is used to generate a chaotic sequence according to static parameters and dynamic parameters, obtain a synchronization sequence according to the chaotic sequence, and update the dynamic parameters corresponding to the index value in the parameter table register according to the chaotic sequence; the chaotic signal generating module performs n+2 iterations, and the two ports of the X end and the Y end respectively output n+2 chaotic parameters, and the first n chaotic parameters of the chaotic parameters generated by the X end are preprocessed and quantized to form a binary sequence, and the first N bits of the binary sequence are used as the synchronization sequence, and the Nth to nth bits are used as the key for encrypting the binary sequence of the data to be sent and the index value, and the length of the key is the same as the sum of the lengths of the binary sequence of the data to be sent and the index value, and the data of the last two iterations of the Y end are used to update the values stored in the positions of the two dynamic parameters corresponding to the current index value, so as to ensure that the value of the dynamic parameter when the index position is used next time is different from that when it is used this time;
参数表寄存器，用于根据索引值存储动态参数和静态参数，在该寄存器中每个表包括多个行和列，每一个行、列作为一个索引位置，每个位置中存储一个参数值，其中静态参数的值固定不变，但是动态参数中每次使用的索引位置的值在使用完后需要进行更新；A parameter table register is used to store dynamic parameters and static parameters according to index values. In this register, each table includes multiple rows and columns. Each row and column is used as an index position. A parameter value is stored in each position. The value of the static parameter is fixed, but the value of the index position used each time in the dynamic parameter needs to be updated after use.
相关系数判断器，用于判断两个同步序列的相关系数是否大于设定阈值，若大于则判定接收端和发送端的混沌系统已经对齐，可以直接使用参数寄存器中的参数进行密钥同步，若不大于设定阈值，则需要遍历参数寄存器中的参数，直到产生的同步序列与接收到的同步序列的相关系数大于设定阈值，将满足该条件的参数产生的密钥作为同步的密钥。The correlation coefficient judger is used to judge whether the correlation coefficient of two synchronization sequences is greater than the set threshold. If it is greater, it is determined that the chaotic systems of the receiving end and the sending end have been aligned, and the parameters in the parameter register can be directly used for key synchronization. If it is not greater than the set threshold, it is necessary to traverse the parameters in the parameter register until the correlation coefficient of the generated synchronization sequence and the received synchronization sequence is greater than the set threshold, and the key generated by the parameters that meet this condition is used as the synchronization key.
通过图3，可以更加深入地理解混沌的初始值敏感性，该图中有两条折线，这两条折线上的点基本不重合，而这两条折线分别是两个不同初值经过混沌迭代产生的结果，而这两个初值仅仅相差10-15。而图4(a)则表示的是不同初值产生的混沌序列经过量化形成二进制的相关系数，可以得出结论，由于混沌的初值敏感性特点，不同初值产生的混沌序列之间的相关性很小，他们的相关系数也是一个接近于0的数值。Figure 3 provides a deeper understanding of the initial value sensitivity of chaos. There are two broken lines in the figure. The points on these two broken lines are basically non-coincident. These two broken lines are the results of two different initial values after chaotic iteration, and the difference between these two initial values is only10-15 . Figure 4 (a) shows the correlation coefficient of the chaotic sequence generated by different initial values after quantization to form binary. It can be concluded that due to the initial value sensitivity of chaos, the correlation between chaotic sequences generated by different initial values is very small, and their correlation coefficient is also a value close to 0.
图6为加密信号与原始信号经过25km标准单模光纤传输后的误码率对比图，图中原始信号相比加密信号的BER有稍许下降。这主要是由于该方案增加了系统的复杂度，但是由于该方案只是对原始数据进行变动，并未引入额外的调制等操作，所以他们之间的差距几乎可以忽略。Figure 6 is a comparison of the bit error rates of the encrypted signal and the original signal after being transmitted over a 25km standard single-mode optical fiber. In the figure, the BER of the original signal is slightly lower than that of the encrypted signal. This is mainly because the scheme increases the complexity of the system, but since the scheme only changes the original data and does not introduce additional modulation operations, the difference between them is almost negligible.
从图7中可以看出，在光纤信道传输正常的情况下，采用本发明的基于动态参数表的DFMA系统的密钥分发方案可以极大提升接收端实现混沌同步的效率，并且解决了物理层加密方案普遍存在的无法抗选择明文攻击，密钥单一固定等问题。此外，该加密系统操作简单，占用空间小，具备实时、高速加密信号的能力，可以很好地为DFMA-PON提供物理层加密。As can be seen from Figure 7, under the condition of normal transmission of the optical fiber channel, the key distribution scheme of the DFMA system based on the dynamic parameter table of the present invention can greatly improve the efficiency of the receiving end to achieve chaotic synchronization, and solve the problems that the physical layer encryption scheme is generally unable to resist the chosen plaintext attack and the key is fixed. In addition, the encryption system is simple to operate, occupies a small space, has the ability to encrypt signals in real time and at high speed, and can provide physical layer encryption for DFMA-PON.
尽管已经示出和描述了本发明的实施例，对于本领域的普通技术人员而言，可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由所附权利要求及其等同物限定。Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.
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| CN111600661A (en)* | 2020-05-14 | 2020-08-28 | 浙江大学 | Three-dimensional encrypted OFDM optical system based on real-time update chaotic key distribution |
| CN117082502A (en)* | 2023-10-17 | 2023-11-17 | 南京华飞数据技术有限公司 | Data acquisition and signal identification method based on data information encryption method |
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| CN114418823B (en)* | 2022-01-25 | 2025-04-25 | 安徽大学 | A chaotic image encryption method based on logistic large key space bit scrambling |
| CN117155532A (en)* | 2023-08-29 | 2023-12-01 | 重庆大学 | Integrated circuit system, method and medium based on combined chaotic encryption algorithm |
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111600661A (en)* | 2020-05-14 | 2020-08-28 | 浙江大学 | Three-dimensional encrypted OFDM optical system based on real-time update chaotic key distribution |
| CN117082502A (en)* | 2023-10-17 | 2023-11-17 | 南京华飞数据技术有限公司 | Data acquisition and signal identification method based on data information encryption method |
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