CN103346875A

CN103346875A - Method for generating digital chaos code in chaotic secure communication system

Info

Publication number: CN103346875A
Application number: CN2013101680347A
Authority: CN
Inventors: 黄洪斌; 邱灿灿
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2013-05-08
Filing date: 2013-05-08
Publication date: 2013-10-09
Anticipated expiration: 2033-05-08
Also published as: CN103346875B

Abstract

A method for generating digital chaos ciphers in a chaotic secure communication system. The digital chaotic secure communication system includes 1) a channel for communication between information sending end A and information receiving end B, and 2) a digital chaotic network connected to the channel for generating chaotic digital numbers , from the codes generated by the digital chaotic network, select a certain length of chaotic codes and transform them into chaotic codes k ₁ (t) through the password generation function g ₁ of chaotic codes, k ₁ (t)=g ₁ (X,p) ; The two complex chaotic networks of sending and receiving adopt exactly the same method to calculate and obtain the chaotic synchronous digital number; Generate or decrypt the chaotic password from the digital chaotic network by the chaotic password generation and the chaotic encryption or decryption module of the plain text in the following way: the length of the password k ₁ It is one to many digits, select a certain number of p numbers randomly or regularly from the chaotic numbers generated by the chaotic network to construct the password k ₁ =g ₁ [X,p], p≤q; for all the original data generated by the complex network A series of function b _i operations are performed on the number to generate one.

Description

The Generation Method of Digital Chaos Cipher in Chaos Security Communication System

一、技术领域：1. Technical field:

本发明涉及电子信息保密技术领域，尤其是涉及保密通信系统和方法。The invention relates to the technical field of electronic information security, in particular to a security communication system and method.

二、背景技术：2. Background technology:

近年来，基于混沌同步的保密通信引起了国际上的极大研究兴趣。人们对混沌保密通信进行了大量的理论和实验研究，并在商业光纤通信网中进行了高速远距离（120km）实验。在混沌保密通信方案中，传送信息在发送端被混沌信号掩盖，而在接收端利用混沌同步将混沌信号去掉而解密。由于混沌动力学对系统的初值条件和系统的动力学参数极其敏感，使得混沌动力学的重建和再现极其困难，因而窃密者很难解密窃密信号，而混沌同步技术却可使合法信息接收者去掉混沌信号而解密。然而到目前为止的理论和实验研究中存在如下问题：In recent years, secure communication based on chaos synchronization has aroused great international research interest. People have done a lot of theoretical and experimental research on chaotic secure communication, and carried out high-speed long-distance (120km) experiments in commercial optical fiber communication networks. In the chaotic secure communication scheme, the transmitted information is covered by the chaotic signal at the sending end, and the chaotic signal is removed and decrypted at the receiving end by using chaos synchronization. Because the chaotic dynamics is extremely sensitive to the initial value conditions of the system and the dynamic parameters of the system, it is extremely difficult to reconstruct and reproduce the chaotic dynamics, so it is difficult for the stealer to decipher the stolen signal, but the chaotic synchronization technology can make the legitimate information receiver Decrypt by removing the chaotic signal. However, the following problems exist in the theoretical and experimental research so far:

(1)、通信中所用混沌信号多为低维混沌系统（单个混沌激光器或单个混沌电路）产生，这使得窃密者有可能利用延迟坐标等方法重建混沌动力学进而破密。因而产生高维随机混沌信号并在信道中利用是必需的。(1) Most of the chaotic signals used in communication are generated by low-dimensional chaotic systems (single chaotic laser or single chaotic circuit), which makes it possible for stealers to use delay coordinates and other methods to reconstruct chaotic dynamics and then break the secret. Therefore, it is necessary to generate high-dimensional random chaotic signals and use them in channels.

(2)、在目前的混沌保密研究中，信道中传输的是混沌波，因混沌波对噪声等外界因素及其敏感，所以在远距离信息传输中利用混沌同步进行信息解密技术还未解决。混沌信号的数字化是解决这一问题的有效方案。(2) In the current chaotic security research, chaotic waves are transmitted in the channel. Because chaotic waves are extremely sensitive to external factors such as noise, the technology of using chaos synchronization for information decryption in long-distance information transmission has not yet been resolved. Digitization of chaotic signals is an effective solution to this problem.

（3）、利用数字化的混沌信号对数字信息进行加密并利用混沌同步技术解密的保密通信方案和技术还未出现。特别是与现代数字信息技术兼容并获得应用的数字混沌保密技术还未见报道.(3) The secure communication scheme and technology that uses digital chaotic signals to encrypt digital information and decrypts them using chaotic synchronization technology has not yet appeared. In particular, the digital chaos security technology that is compatible with modern digital information technology and has been applied has not been reported yet.

（4）、有效产生复杂且实用的数字混沌密码方法和技术还未见报道。(4), effective generation complex and practical digital chaos encryption methods and techniques have not been reported yet.

目前主要是用传统算法产生的密码对信息进行加密，主要有对称加密算法（如DES,AES等）和非对称加密算法(如RSA,ECC等)。但由于传统算法密码不是一次性密码，因而被破解的风险很大，实际上已有一些传统算法密码被破解。At present, the passwords generated by traditional algorithms are mainly used to encrypt information, mainly including symmetric encryption algorithms (such as DES, AES, etc.) and asymmetric encryption algorithms (such as RSA, ECC, etc.). However, because traditional algorithm passwords are not one-time passwords, there is a high risk of being cracked. In fact, some traditional algorithm passwords have been cracked.

三、发明内容：3. Contents of the invention:

本发明目的是，提出一种基于数字混沌编码算法的混沌保密通信系统，包括一种复杂数字混沌保密系统中产生数字混沌密码的复杂混沌网络的混沌编码算法和技术。本发明通过复杂混沌网络产生复杂数字混沌密码，该混沌密码是一次性密码，密码空间远大于基于传统算法的密码空间，信息的解密是基于混沌同步。The object of the present invention is to propose a chaotic security communication system based on a digital chaotic coding algorithm, including a chaotic coding algorithm and technology of a complex chaotic network that generates a digital chaotic password in a complex digital chaotic security system. The invention generates a complex digital chaotic password through a complex chaotic network, the chaotic password is a one-time password, the password space is much larger than that based on a traditional algorithm, and the decryption of information is based on the chaos synchronization.

本发明的技术方案是，基于数字混沌编码算法的数字混沌保密通信系统，包括：The technical scheme of the present invention is, the digital chaos secure communication system based on the digital chaos coding algorithm, comprising:

1）、一个信息发送端A和信息接收端B进行通信的信道，1), a communication channel between information sending end A and information receiving end B,

2）、一个与信道连接的用于产生混沌数字数码的数字混沌网络，从该数字混沌网络所产生的数码中按选取一定长度的混沌数码经混沌编码的密码生成函数g₁转变成混沌密码k₁(t)，k₁(t)=g₁(X,p)2) A digital chaotic network connected to the channel for generating chaotic digital numbers, from the numbers generated by the digital chaotic network, a certain length of chaotic numbers is selected and converted into a chaotic code k by the password generation function _g1 of the chaotic code ₁ (t), k ₁ (t)=g ₁ (X,p)

其中X为数字混沌网络所产生的数字数码，p为t时刻从数字混沌网络所选数码长度；信息发送端A将要在信道中传输的信息M由密码k₁经加密函数F加密变成密文C以在所述信道中传输：C(t)=F[M(t),k₁(t)]Among them, X is the digital code generated by the digital chaotic network, and p is the digital length selected from the digital chaotic network at time t; the information M to be transmitted in the channel by the information sender A is encrypted by the password k ₁ through the encryption function F to become ciphertext C to transmit in said channel: C(t)=F[M(t),k ₁ (t)]

信息接收端B从所述信道中接收到密文C，然后将密文C由混沌密码k′₁经混沌解密函数F^-1解密：M′(t)=F^-1[C(t),k′₁(t)]=M(t)The information receiving end B receives the ciphertext C from the channel, and then decrypts the ciphertext C by the chaotic code k′ ₁ through the chaotic decryption function F ⁻¹ : M′(t)=F ⁻¹ [C(t), k′ ₁ (t)]=M(t)

混沌密码k′₁由信息接收端混沌密码产生系统产生，该密码产生系统由产生数码的并与所述信道相连的数字混沌网络及密码生成函数g₁构成，g₁将与接收端相同的方式从数字混沌网络选取的数码变成混沌密码k′₁(t-τ)=g₁[Y(t-τ),p]The chaotic password _k'1 is generated by the chaotic password generating system of the information receiving end, and the password generating system is composed of a digital chaotic network and a password generating function _g1 that generate digital numbers and are connected to the channel, _g1 will be in the same way as the receiving end The number selected from the digital chaotic network becomes the chaotic password k′ ₁ (t-τ)=g ₁ [Y(t-τ),p]

其中Y为信息接收端混沌网络所产生的数字数码，p为t时刻从复杂混沌网络所选数码长度。且信息接收端的混沌密码k′₁与信息发送端的混沌密码k₁混沌同步：Among them, Y is the digital code generated by the chaotic network at the information receiving end, and p is the digital length selected from the complex chaotic network at time t. And the chaotic password k′ ₁ at the information receiving end is chaotically synchronized with the chaotic password k ₁ at the information sending end:

$\underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} [[{k k}_{11}^{' '} ((t t - - τ τ)) - - {k k}_{11} ((t t))]] &RightArrow; &Right Arrow; 00 . .$

数字混沌网络指复杂的数字混沌网络。Digital chaotic network refers to complex digital chaotic network.

编解码方法可以采用微分动力学方程或单向耦合环状迭代（ＯＣＲＭＬ）非线性系统产生混沌信号，并对混沌信号进行截断处理而产生的混沌伪随机序列或经典的Logistic映射作为混沌信号发生模型。The encoding and decoding method can use differential dynamic equations or one-way coupled ring iterative (OCRML) nonlinear systems to generate chaotic signals, and truncate the chaotic signals to generate chaotic pseudo-random sequences or classical Logistic mapping as chaotic signal generation models. .

本发明的全双工双向数字混沌保密通信系统。信息发送方和接收方各有两个（相同或不同的）混沌网络分别用于混沌加密和混沌解密，一方的加密和解密密码由不同混沌网络产生，但双方对应的一对（如图1中14和17及15和16）加密和解密混沌网络要有相同的拓扑结构和动力学结构。加密函数F_i(i=1,2)满足F_iF_i ^-1=I。数字信息M由混沌密码经F函数运算加密的密文C经信道（可含数字复接器、调制器、解调器、数字分接器及其它数字信号处理器等）传输到接收端后经反函数F_i ^-1运算利用混沌同步解密获得传送信息M。对远距离通信，接收信息要进行信息处理（放大，信号处理等）。The full-duplex two-way digital chaos security communication system of the present invention. The information sender and the receiver each have two (same or different) chaotic networks for chaotic encryption and chaotic decryption. The encryption and decryption passwords of one party are generated by different chaotic networks, but the corresponding pair of both parties (as shown in Figure 1 14 and 17 and 15 and 16) Encryption and decryption chaotic networks must have the same topology and dynamics. The encryption function F _i (i=1,2) satisfies F _i F _i ^-1 =I. The digital information M is encrypted by the chaotic cipher through the F function operation and the ciphertext C is transmitted to the receiving end through the channel (including digital multiplexer, modulator, demodulator, digital splitter and other digital signal processors, etc.) The operation of the inverse function F _i ^-1 uses chaotic synchronous decryption to obtain the transmission information M. For long-distance communication, receiving information requires information processing (amplification, signal processing, etc.).

信息发送端A与所述信道相连的数字混沌网络与信息接收端B与所述信道相连的数字混沌网络具有如下特征：The digital chaotic network in which the information sending end A is connected to the channel and the digital chaotic network in which the information receiving end B is connected to the channel has the following characteristics:

（1）、具有相同的拓扑和动力学结构，受共同信号驱动且二者处于混沌同步态，数字混沌网络可由单个或多个网络上混沌振子构成，混沌振子（节点）i的选取要使混沌网络形成复杂斑图混沌动力学，既时空混沌动力学。在保证二网络斑图混沌动力学同步的条件下，复杂混沌网络是任意拓扑结构结构，如正规网络，随机网络，小世界网络，标度自由网络和模块网络等，(1) With the same topology and dynamic structure, driven by a common signal and both are in a chaotic synchronous state, the digital chaotic network can be composed of a single or multiple chaotic oscillators on the network, and the selection of the chaotic oscillator (node) i should make the chaotic The network forms complex pattern chaotic dynamics, namely spatiotemporal chaotic dynamics. Under the condition that the chaotic dynamics of the two network patterns are synchronized, the complex chaotic network is an arbitrary topological structure, such as regular network, random network, small world network, scale free network and modular network, etc.

（2）、信息发送端A用于产生混沌数字数码的复杂混沌网络动力学方程由微分动力学方程描写(2) The complex chaotic network dynamics equation used by the information sending terminal A to generate chaotic digital numbers is described by the differential dynamics equation

${\overset{\cdot &Center Dot;}{x x}}_{i i} = = {f f}_{i i} (({x x}_{i i},, {a a}_{i i})) + + {Σ Σ}_{j j = = 11}^{n no} {G G}_{ij ij} {H h}_{j j} (({x x}_{j j})) + + \underset{j j}{Σ Σ} {α α}_{ij ij} {h h}_{j j} [[D D. (({C C}_{A A})),, {x x}_{j j}]]$

或由迭代动力学方程描写or described by the iterative dynamics equation

${x x}_{l l}^{n no + + 11} = = {g g}_{l l} (({x x}_{l l}^{n no},, {b b}_{l l})) + + {Σ Σ}_{k k = = 11}^{n no} {U u}_{lk lk} {W W}_{k k} (({x x}_{k k}^{n no},, {x x}_{l l})) + + \underset{k k}{Σ Σ} {β β}_{lk lk} {w w}_{k k} [[D D. (({C C}_{A A})),, {x x}_{k k}^{n no}]]$

或由微分动力学方程和迭代动力学方程共同描写，Or it is described jointly by differential dynamics equation and iterative dynamics equation,

${\overset{\cdot &Center Dot;}{z z}}_{i i} = = {f f}_{i i} (({z z}_{i i},, {a a}_{i i})) + + {Σ Σ}_{j j = = 11}^{n no} {G G}_{ij ij} {H h}_{j j} (({z z}_{j j},, {x x}_{j j}^{n no})) + + \underset{j j}{Σ Σ} {α α}_{ij ij} {h h}_{j j} [[D D. (({C C}_{A A})),, {z z}_{j j},, {x x}_{j j}^{n no}]]$

${x x}_{l l}^{n no + + 11} = = {g g}_{l l} (({x x}_{l l}^{n no},, {b b}_{l l})) + + {Σ Σ}_{k k = = 11}^{n no} {U u}_{lk lk} {W W}_{k k} (({x x}_{k k}^{n no},, {x x}_{l l})) + + \underset{k k}{Σ Σ} {β β}_{lk lk} {w w}_{k k} [[D D. (({C C}_{A A})),, {x x}_{k k}^{n no},, {z z}_{k k}]]$

其中:in:

${\overset{\cdot &Center Dot;}{z z}}_{i i} = = {f f}_{i i} (({z z}_{i i},, {a a}_{i i})),, {z z}_{i i} &Element; &Element; {R R}^{mi mi},, {f f}_{i i} : : {R R}^{mi mi} &RightArrow; &Right Arrow; {R R}^{mi mi},, {H h}_{i i} : : {R R}^{mi mi} &RightArrow; &Right Arrow; {R R}^{mi mi}$

$x_{l}^{n + 1} = g_{l} (x_{l}^{n}, b_{l}), x_{l}^{n} &Element; R^{ml}, g_{l} : R^{ml} &RightArrow; R^{ml}, W_{l} : R^{ml} &RightArrow; R^{ml}$ 是第i及第l个网络节点的孤立振子m_i维混沌动力学方程（非耦合方程）， $x_{l}^{no + 1} = g_{l} (x_{l}^{no}, b_{l}), x_{l}^{no} &Element; R^{ml}, g_{l} : R^{ml} &Right Arrow; R^{ml}, W_{l} : R^{ml} &Right Arrow; R^{ml}$ is the i _- dimensional chaotic dynamics equation (uncoupled equation) of the isolated oscillator m of the i-th and l-th network nodes,

x_i上面的一点表示x_i对时间的微分，a_i及b_l是孤立振子方程的动力学参数，H_j及W_j网络节点间的耦合函数，G_ij及U_ij是节点间的耦合矩阵元，h_j及w_j是混沌网络的驱动函数，驱动函数D(C_A)是传送密文C_A的函数，α_ij及β_ij是耦合系数,网络混沌节点的数目n≥1,信息接收端B的混沌网络动力学方程与信息发送端A的混沌网络动力学方程完全相同；The point above _xi represents the differential of _xi with respect to time, a _i and b _l are the dynamic parameters of the isolated oscillator equation, H _j and W _j are the coupling functions between network nodes, G _ij and U _ij are the coupling matrices between nodes element, h _j and w _j are the driving functions of the chaotic network, the driving function D(C _A ) is the function of transmitting the ciphertext C _A , α _ij and β _ij are the coupling coefficients, the number of chaotic nodes in the network is n≥1, and the information receiving The chaotic network dynamics equation of terminal B is exactly the same as the chaotic network dynamics equation of information sending terminal A;

（3）、信息发送端A及信息接收端B与所述信道相连的数字混沌网络设有将上述方程数字化的模块、或将由上述复杂混沌网络动力学方程所描述的模拟电路产生的混沌信号用模-数转换器转变成数字混沌信号的产生模块，(3) The digital chaotic network connected to the channel between the information sending end A and the information receiving end B is equipped with a module for digitizing the above equation, or using the chaotic signal generated by the analog circuit described by the above complex chaotic network dynamics equation The analog-to-digital converter is converted into a digital chaotic signal generation module,

（4）、在（3）中信息发送端A与所述信道相连的数字复杂混沌网络与信息接收端B与所述信道相连的数字混沌网络是数字电子混沌网络或是模拟电子混沌网络，数字电子混沌网络由逻辑芯片（如FPGA等）上实现，也可由一定的语言在数字信号处理器（如DSP等）上实现，还可由计算机程序实现，另外也可制成专用数字芯片；模拟电子混沌网络可经模-数转换器转变成数字混沌网络，或将模拟电子混沌网络产生的许多混沌信号经模-数转换器转变成数字混沌信号，(4), in (3), the digital complex chaotic network connected to the channel at the information sending end A and the digital chaotic network connected to the channel at the information receiving end B are digital electronic chaotic networks or analog electronic chaotic networks, digital The electronic chaotic network can be realized by a logic chip (such as FPGA, etc.), can also be realized by a certain language on a digital signal processor (such as DSP, etc.), can also be realized by a computer program, and can also be made into a dedicated digital chip; analog electronic chaos The network can be converted into a digital chaotic network through an analog-to-digital converter, or many chaotic signals generated by an analog electronic chaotic network can be converted into a digital chaotic signal through an analog-to-digital converter.

（5）、数字混沌网络任意两节点i、j间的耦合可以是两变量直接耦合，也可以选取各节点变量x_i的部分数码与变量x_j的部分数码进行耦合，在混沌网络的耦合中可以全部采取这种数码耦合，也可以部分采取这种数码耦合；(5) The coupling between any two nodes i and j in the digital chaotic network can be the direct coupling of two variables, or select part of the numbers of the variable x _i of each node and part of the numbers of the variable x _j to couple, in the coupling of the chaotic network This kind of digital coupling can be adopted entirely or partly;

（6）、在（5）中，可以对x_i和x_j选取的数码进行编码后再耦合，混沌网络可全部或部分采用这种编码耦合；(6) In (5), the codes selected by x _i and x _j can be encoded and then coupled, and the chaotic network can adopt this encoding coupling in whole or in part;

进一步的，在（5）和（6）中，x_i和x_j的表示数码在混沌网络生成的所有数码中按一定方式选取，如随机选取方式等，因此复杂混沌网络变量间的耦合是网络所生成的所有数码间按一定规律的耦合，混沌网络可全部或部分采用这种选码及编码耦合。Furthermore, in (5) and (6), the representation numbers of x _i and x _j are selected in a certain way among all the numbers generated by the chaotic network, such as random selection, so the coupling between the variables of the complex chaotic network is the network All the generated codes are coupled according to a certain law, and the chaotic network can adopt this code selection and coding coupling in whole or in part.

进一步的，复杂混沌网络可由其所生成的数码按一定的耦合方式耦合而成，如随机耦合、标度自由耦合方式等，即混沌网络某一变量的数码可部分或全部选自网络其它变量的数码，因此数码是复杂混沌网络耦合的基本单元，数码耦合是一种全新的网络耦合方式，混沌网络可全部或部分采用数码耦合。Furthermore, the complex chaotic network can be formed by coupling the generated numbers according to a certain coupling method, such as random coupling, scale-free coupling, etc., that is, the number of a certain variable in the chaotic network can be partially or completely selected from other variables in the network. Digital, therefore, digital is the basic unit of complex chaotic network coupling, digital coupling is a brand-new network coupling method, and chaotic network can adopt digital coupling in whole or in part.

进一步的，混沌网络可由数码耦合、选码及编码耦合和变量耦合共同形成。Furthermore, the chaotic network can be formed by digital coupling, code selection and coding coupling and variable coupling.

进一步的，与信道相连的复杂混沌网络动力学方程的参数是时间的函数。Furthermore, the parameters of the dynamic equations of the complex chaotic network connected to the channel are functions of time.

进一步的，信息发送方和信息接收方的数字混沌网络的共同驱动函数D(C)保证发送方和接收方两个网络混沌同步；混沌网络的共同驱动函数D(C)是密文数码的编码函数，不同的共同驱动函数D(C)给出不同的混沌网络动力学运算，也将得到不同的混沌密码k；共同驱动函数是时间的函数,即在不同的信息加密时段用不同的共同驱动函数。Further, the common driving function D(C) of the digital chaotic network of the information sender and the information receiver ensures that the two networks of the sender and the receiver are chaotically synchronized; the common driving function D(C) of the chaotic network is the code of the ciphertext number function, different common driving functions D(C) give different chaotic network dynamics operations, and will also obtain different chaotic passwords k; the common driving function is a function of time, that is, different common driving functions are used in different information encryption periods. function.

进一步的，信息发送方和信息接收方与信道相连的用于生成数字数码的混沌网络的驱动函数D(C)用来驱动混沌网络的部分或全部变量，见上述混沌网络的动力学方程，也可选取D(C)的部分数码驱动混沌网络的部分或全部变量，D(C)的部分数码与某一被驱动变量的耦合是将D(C)的部分数码与该被驱动变量的部分数码重新编码，该编码或其某种函数用来驱动该变量。Further, the driving function D(C) of the chaotic network used to generate digital numbers connected to the channel between the information sender and the information receiver is used to drive some or all of the variables of the chaotic network, see the dynamic equation of the above-mentioned chaotic network, and also Partial numbers of D(C) can be selected to drive part or all of the variables of the chaotic network. The coupling of part numbers of D(C) and a driven variable is to combine part numbers of D(C) with part numbers of the driven variable. Recode, the code or some function of it is used to drive the variable.

进一步的，在混沌网络的动力学计算中，所有混沌网络动力学变量或部分动力学变量的每一步或几步数值计算后，对变量重新进行编码，然后进行下一步或下几部的计算，这种编码计算和对变量的选取是任意的，对变量重新编码规律可以是时间的函数。Further, in the dynamic calculation of the chaotic network, after each step or several steps of numerical calculation of all the dynamic variables of the chaotic network or part of the dynamic variables, the variables are recoded, and then the next step or the next few steps of calculation are performed, This coding calculation and selection of variables are arbitrary, and the recoding law of variables can be a function of time.

进一步的，在混沌网络的动力学运算过程中的某些计算步按一定规律对部分网络动力学变量或全部网络动力学变量按一定方式编码，其中某一个动力学变量的数码可按一定规律从网络动力学变量所生成的所有数码中按一定方式选取，某一个动力学变量的数码长度（矢量长度）可定义在一定范围内，这叫做混沌网络的分布式混沌编码计算法和分布式混沌编码耦合法。一定方式指随机方式或规则方式，或小世界方式等。Furthermore, some calculation steps in the dynamics operation process of the chaotic network encode part of the network dynamics variables or all the network dynamics variables in a certain way according to a certain law, and the number of a certain dynamic variable can be changed from All numbers generated by network dynamic variables are selected in a certain way, and the digital length (vector length) of a certain dynamic variable can be defined within a certain range. This is called the distributed chaos coding algorithm and distributed chaos coding of chaotic network coupling method. A certain method refers to a random method, a regular method, or a small world method, etc.

进一步的，对混沌网络动力学计算过程中的部分变量或全部变量在某些计算步或全部计算步作某种函数运算，如重新编码运算、不同变量间的异或等逻辑运算等，也可将该函数与引进的某些函数作某种函数运算，如逻辑运算等。Furthermore, it is also possible to perform certain functional operations on some or all variables in the calculation process of chaotic network dynamics in some or all calculation steps, such as recoding operations, logical operations such as exclusive OR between different variables, etc. Perform certain functional operations, such as logical operations, on this function and some imported functions.

进一步的，混沌网络动力学的计算可采用并行算法及其它快速算法，混沌网络的参数及动力学变量可采用整数型或实数型数据，这些数据可采用二进制等不同的进制表示，信息发送端的复杂混沌网络与信息接收端的复杂混沌网络采用完全相同的算法。Further, the calculation of chaotic network dynamics can use parallel algorithms and other fast algorithms. The parameters and dynamic variables of chaotic networks can use integer or real data, and these data can be expressed in different binary systems such as binary. The complex chaotic network and the complex chaotic network at the information receiving end use exactly the same algorithm.

进一步的，计算所得混沌网络从计算开始时刻到取码时刻的所有数码或部分数码可储存在存储器中以备取码所用。可对混沌网络计算中所得混沌数字数码作某种函数运算。Furthermore, all or part of the numbers of the calculated chaotic network from the calculation start time to the code retrieval time can be stored in the memory for code retrieval. Some kind of function operation can be performed on the chaotic digital numbers obtained in the chaotic network calculation.

进一步的，用于生成数字混沌网络的驱动函数D(C)要保证这发收的两个网络混沌同步。混沌网络的共同驱动函数D(C)是数字密文C或部分数字密文C的数码的某种排列组合的驱动函数D(C)，即D(C)是密文数码的编码函数，不同的共同驱动函数D(C)将给出不同的混沌网络动力学，也将得到不同的混沌密码k，共同驱动函数可以是时间的函数,即在不同的信息加密时段用不同的共同驱动函数。Further, the driving function D(C) used to generate the digital chaotic network should ensure the chaotic synchronization of the two sending and receiving networks. The common driving function D(C) of the chaotic network is the driving function D(C) of a certain permutation and combination of digital ciphertext C or part of the digital ciphertext C, that is, D(C) is the encoding function of the ciphertext number, different The common driving function D(C) of D(C) will give different chaotic network dynamics, and will also obtain different chaotic password k. The common driving function can be a function of time, that is, different common driving functions are used in different information encryption periods.

进一步的，信息发送方和信息接收方与信道相连的用于生成数字数码的混沌网络的驱动函数D(C)可用来驱动混沌网络的部分或全部变量，也可选取D(C)的部分数码驱动混沌网络的部分或全部变量，D(C)的部分数码与某一被驱动变量的耦合是将D(C)的部分数码与该被驱动变量的部分数码重新编码，该编码或其某种函数用来驱动该变量。Further, the driving function D(C) of the chaotic network used to generate digital numbers connected to the channel between the information sender and the information receiver can be used to drive some or all of the variables of the chaotic network, and some digital numbers of D(C) can also be selected. Part or all of the variables that drive the chaotic network, the coupling of some codes of D (C) and a certain driven variable is to recode some codes of D (C) and some codes of the driven variable. A function is used to drive this variable.

混沌保密通信系统中数字混沌密码的产生方法，其特征是基于数字混沌编码算法的混沌保密通信系统中：信息发送端A与所述信道相连的数字混沌网络与信息接收端B与所述信道相连的数字混沌网络具有如下特征：The generation method of the digital chaos password in the chaos security communication system is characterized in that in the chaos security communication system based on the digital chaos coding algorithm: the digital chaos network where the information sending end A is connected to the channel and the information receiving end B is connected to the channel The digital chaotic network has the following characteristics:

1）具有相同的拓扑和动力学结构，受共同信号驱动且二者处于混沌同步态，保证二网络斑图混沌动力学同步的条件下，数字混沌网络包括复杂混沌网络，复杂混沌网络是任意拓扑结构结构，包括正规网络，随机网络，小世界网络，标度自由网络和模块网络；1) With the same topology and dynamic structure, driven by a common signal and the two are in a chaotic synchronous state, under the condition that the chaotic dynamics of the two network patterns are synchronized, the digital chaotic network includes a complex chaotic network, and a complex chaotic network is an arbitrary topology Structural structures, including regular networks, random networks, small-world networks, scale-free networks, and modular networks;

2）信息发送端A用于产生混沌数字数码的复杂混沌网络动力学方程由微分动力学方程描写、由迭代动力学方程描写或由微分动力学方程和迭代动力学方程共同描写；2) The complex chaotic network dynamics equation used by information sending terminal A to generate chaotic digital numbers is described by differential dynamics equations, iterative dynamics equations, or both differential dynamics equations and iterative dynamics equations;

收发两端复杂混沌网络采用完全相同的方法进行计算以获得混沌同步数字数码；用如下方法通过混沌密码生成及明文的混沌加密或解密模块从数字混沌网络产生或解密混沌密码：The complex chaotic network at the sending and receiving ends adopts exactly the same method for calculation to obtain chaotic synchronous digital numbers; use the following method to generate or decrypt the chaotic code from the digital chaotic network through the chaotic code generation and the chaotic encryption or decryption module of the plaintext:

(1)密码k₁的长度是一位至多位，数字网络所产生的所有原始数码B共有Nq个,其中N是复杂混沌网络方程的项数，q是方程变量数字化的位数；若只利用原始数码，则密码k₁最长为k₁=Nq；一般情况下，从混沌网络产生的混沌数码中按随机、规则等方式选取一定数量p的数码构造密码k₁=g₁[X,p]，p≤q；(1) The length of the password k ₁ is one to many digits, and all the original digital Bs produced by the digital network have Nq in total, where N is the number of items of the complex chaotic network equation, and q is the number of digits of the equation variable digitization; if only using The original number, the longest password k ₁ is k ₁ =Nq; in general, a certain number of p numbers are selected randomly and regularly from the chaotic numbers generated by the chaotic network to construct the password k ₁ =g ₁ [X,p ], p≤q;

（2）对复杂网络所产生的所有原始数码作一系列函数b_i运算产生一系列新的数字函数，(2) Perform a series of function b _i operations on all the original numbers generated by the complex network to generate a series of new digital functions,

b₁(X,p₁),b₂(X,p₂),…,b_m(X,p_m)，其中b_i是多项式函数等，然后从这一系列数字函数中按随机等方式选取数码通过函数g₁构造密码:k₁=g₁[b₁(X,p₁),b₂(X,p₂),…b_m(X,p_m)，p]，其中g₁是随机、规则等编码函数；b ₁ (X,p ₁ ),b ₂ (X,p ₂ ),…,b _m (X,p _m ), where b _i is a polynomial function, etc., and then randomly selected from this series of digital functions The code constructs a password through the function g ₁ : k ₁ =g ₁ [b ₁ (X,p ₁ ),b ₂ (X,p ₂ ),…b _m (X,p _m ),p], where g ₁ is random , rules and other encoding functions;

（3）密码k₁也由复杂混沌网络所生成的数码B的某中函数F(B)生成：k₁=g₁[F(B)]；(3) The password k ₁ is also generated by a certain function F(B) of the digital B generated by the complex chaotic network: k ₁ =g ₁ [F(B)];

(4)产生的混沌密码要符合一定的密码分布，如噪声分布等，密码功率谱要掩盖信息的功率谱；(4) The generated chaotic code must conform to a certain code distribution, such as noise distribution, etc., and the power spectrum of the code should cover the power spectrum of the information;

（5）在信息接收端，解密密码k′₁的产生方式与信息发送端加密码k₁的产生方式完全一样；(5) At the information receiving end, the generation method of the decryption code k′ ₁ is exactly the same as the generation method of the encryption code k ₁ at the information sending end;

（6）从数字复杂网络或其函数组选取数码是指数码选择器连续不断的选取数码以产生密码。(6) Selecting numbers from a digital complex network or its function group means that the number selector continuously selects numbers to generate a password.

进一步的，从信息发送端复杂混沌网络所产生的混沌数码中按相同或不同方式选取不同的方式选取数码，按相同或不同方式产生混沌密码k₁,k₂,…,k_i,…，从信息接受端复杂混沌网络所产生的混沌数码中按与信息发送端相同的规则选取数码和产生解密的混沌数码…k′_i,…k′₂,k′₁，其中k′_i-k_i=0。Further, from the chaotic codes generated by the complex chaotic network at the information sending end, the codes are selected in the same or different ways, and the chaotic codes k ₁ , k ₂ ,...,k _i ,... are generated in the same or different ways, from From the chaotic codes generated by the complex chaotic network at the information receiving end, select the codes according to the same rules as the information sending end and generate the decrypted chaotic codes...k′ _i ,...k′ ₂ ,k′ ₁ , where k′ _i -k _i = 0.

进一步的，从复杂混沌网络选取数码构造密码的选取器、密码的生成器、信息的加密器及网络的驱动函数器都由数字集成电路实现，包括用硬件描述语言在逻辑芯片或专用集成芯片上实现，或在信号处理器上用计算机程序实现。Further, the selector, the generator of the password, the encryptor of the information and the driving function of the network are all realized by digital integrated circuits, including hardware description language on logic chips or ASICs. implemented, or implemented with a computer program on a signal processor.

进一步的，在混沌密码生成及明文的混沌加密模块中，包含：Further, in the chaotic password generation and plaintext chaotic encryption module, it includes:

第一个寄存器用于接受和储存生成的用于信息M加密的混沌密码k₁，The first register is used to accept and store the generated chaotic password k ₁ for encrypting the information M,

第二个寄存器用于接受和储存将被加密的信息M，The second register is used to accept and store the information M to be encrypted,

第三个寄存器用于接受和储存混沌加密信息C，The third register is used to accept and store chaotic encrypted information C,

还由一个寄存器用于存储计算所得混沌网络的所有或部分数码，A register is also used to store all or part of the numbers of the calculated chaotic network,

至少一个选择器用于从从复杂混沌网络选取数码用于构造密码，At least one selector is used to select numbers from the complex chaotic network for constructing passwords,

至少一个加密函数生成器，即信息加密函数运算器，at least one encryption function generator, i.e. information encryption function operator,

至少一个生成混沌密码k₁的密码生成函数运算器，用于将从复杂混沌网络选取的数码变成混沌密码k₁。At least one password generating function operator for generating chaotic password k ₁ is used to convert the numbers selected from the complex chaotic network into chaotic password k ₁ .

进一步的，信息接收端混沌解密密码的生成及密文C的解密模块中，包含：Further, the generation of chaotic decryption code at the information receiving end and the decryption module of ciphertext C include:

第一个寄存器用于接受和储存生成的用于解密密文C的混沌密码，The first register is used to accept and store the generated chaotic password for decrypting ciphertext C,

第二个寄存器用于接受和储存将被解密的密文C，The second register is used to accept and store the ciphertext C to be decrypted,

第三个寄存器用于接受和储存混沌解密信息M，The third register is used to accept and store chaos decryption information M,

至少一个选择器用于从从复杂混沌网络选取数码用于解密密码，At least one selector is used to select codes from the complex chaotic network for decrypting the code,

至少一个解密函数生成器，既密文解密函数运算器，At least one decryption function generator, that is, a ciphertext decryption function operator,

至少一个生成混沌密码k′₁的密码生成函数运算器，用于将从复杂混沌网络选取的数码变成混沌密码k′₁。At least one password generating function operator for generating chaotic password k′ ₁ is used to change the number selected from the complex chaotic network into chaotic password k′ ₁ .

进一步的，信息发送方和信息接收方分别包含m个数码函数b₁(X,p₁),b₂(X,p₂),…b_m(X,p_m)的生成模块及相应的函数寄存器。Further, the information sender and the information receiver respectively include m generation modules of digital functions b ₁ (X,p ₁ ), b ₂ (X,p ₂ ),…b _m (X,p _m ) and corresponding functions register.

进一步的，信息发送方和信息接收方分别包含复杂混沌网络的驱动函数生成器和相应的驱动函数寄存器。Further, the information sender and the information receiver respectively include a driving function generator and a corresponding driving function register of the complex chaotic network.

进一步的，从数字混沌网络中选择数码以产生混沌密码的方式可以是以随机方式从数字混沌网络中选取，也可以是规则、标度自由、小世界网络等方式，混沌密码生成函数g₁可以是网络选码的随即编码及规则编码等函数，也可以是对网络选码先作如多项式等函数运算，再进行编码。Further, the way of selecting numbers from the digital chaotic network to generate the chaotic password can be randomly selected from the digital chaotic network, or it can be in the form of rules, scale freedom, small-world network, etc. The chaotic password generation function g ₁ can be It is a function such as random coding and regular coding of the network code selection, and it can also perform function operations such as polynomials on the network code selection first, and then perform coding.

进一步的，从数字混沌网络中选择数码以产生混沌密码的方式g₁是数字混沌网络所产生的所有数码的函数。Further, the way g ₁ of selecting numbers from the digital chaotic network to generate the chaotic code is a function of all the numbers generated by the digital chaotic network.

本发明是一种复杂数字混沌保密系统中产生数字混沌密码的复杂混沌网络的混沌编码算法和技术。在信息发送端用混沌密码采用适当的加密函数运算加密传送信息（明文M），该数字混沌加密信息（密文C）经信道传输到信息接收端，信息接收端采用反函数运算利用混沌同步将密文C解密获得传送明文M′=M。信息发送端的混沌密码由发送端的复杂混沌网络产生。信息接收端的混沌解密密码由信息接收端的复杂混沌网络产生且与信息发送端加密密码混沌同步。接收端和发送端的复杂混沌网络可由变量耦合、选码及编码耦合或数码耦合形成，也可由这些耦合共同形成。The invention relates to a chaotic coding algorithm and technology for a complex chaotic network generating digital chaotic codes in a complex digital chaotic security system. At the information sending end, the chaotic cipher is used to encrypt and transmit the information (plaintext M) with an appropriate encryption function operation. The digital chaotic encrypted information (ciphertext C) is transmitted to the information receiving end through the channel. The information receiving end adopts the inverse function operation and uses chaos synchronization to The ciphertext C is decrypted to obtain the transmitted plaintext M'=M. The chaotic password at the information sending end is generated by the complex chaotic network at the sending end. The chaotic decryption code at the information receiving end is generated by the complex chaotic network at the information receiving end and is synchronized with the encryption code at the information sending end. The complex chaotic network at the receiving end and the sending end can be formed by variable coupling, code selection and coding coupling or digital coupling, and can also be formed by these couplings.

接收端和发送端的复杂混沌网络具有相同的拓扑及动力学结构。采用共同驱动技术驱动接收端和发送端的复杂混沌网络使它们处于混沌同步态，驱动函数是密文的函数。在混沌网络的动力学计算中，网络中的全部或部分动力学变量在计算过程中可按一定的规律进行编码，某些或全部网络动力学变量的数字表示数码可在所有网络动力学变量或网络函数生成的数码中按一定方式选取。The complex chaotic network at the receiving end and the sending end have the same topology and dynamic structure. The complex chaotic network at the receiving end and the sending end is driven by common driving technology to make them in a chaotic synchronous state, and the driving function is a function of the ciphertext. In the dynamic calculation of chaotic network, all or part of the dynamic variables in the network can be coded according to certain rules during the calculation process, and the digital representation of some or all network dynamic variables can be used in all network dynamic variables or The numbers generated by the network function are selected in a certain way.

本发明有益效果是：通过从复杂混沌网络产生复杂数字混沌密码，该混沌密码是一次性密码，密码空间远大于基于传统算法的密码空间，信息的解密是基于混沌同步，特别是该发明技术可获得复杂、实用且高速的混沌密码，该发明技术是与现代信息技术兼容的数字混沌保密技术，该数字混沌保密技术可应用于现代数字通信中,如有线、无线数字通信；信息存储；计算机互联网等。The beneficial effects of the present invention are: by generating complex digital chaotic passwords from complex chaotic networks, the chaotic passwords are one-time passwords, the password space is much larger than that based on traditional algorithms, and the decryption of information is based on chaotic synchronization, especially the inventive technology can Obtain complex, practical and high-speed chaotic ciphers. This invention is a digital chaotic security technology compatible with modern information technology. This digital chaotic security technology can be applied to modern digital communications, such as wired and wireless digital communications; information storage; computer Internet wait.

四、附图说明4. Description of drawings

图1为全双工双向数字混沌保密通信系统图；Fig. 1 is a full-duplex two-way digital chaos secure communication system diagram;

图2为半双工双向数字混沌保密通信系统图Figure 2 is a half-duplex two-way digital chaos secure communication system diagram

图3为单向数字混沌保密通信系统图；Fig. 3 is a one-way digital chaos secure communication system diagram;

图4为单向数字签名混沌保密通信系统图；Fig. 4 is a diagram of a one-way digital signature chaotic secure communication system;

图5为复杂混沌网络及混沌加密图；Fig. 5 is complex chaotic network and chaotic encryption diagram;

图6为复杂混沌网络及混沌解密图；Fig. 6 is a complex chaotic network and a chaotic decryption diagram;

图7发送端和接收端产生混沌网络的复杂混沌网络图；The complex chaotic network diagram of the chaotic network generated by the sending end and the receiving end of Fig. 7;

图8为全双工双向数字签名混沌保密通信系统图；Fig. 8 is a full-duplex two-way digital signature chaos security communication system diagram;

图9为半双工双向数字签名混沌保密通信系统图；Fig. 9 is a half-duplex two-way digital signature chaos security communication system diagram;

图10为多终端单向数字混沌保密通信系统图；Fig. 10 is a multi-terminal one-way digital chaos secure communication system diagram;

图11为另一种多终端单向数字混沌保密通信系统图；Fig. 11 is another kind of multi-terminal one-way digital chaos secure communication system diagram;

图12为由8个子复杂混沌网络的复杂混沌网络图。Fig. 12 is a diagram of a complex chaotic network consisting of 8 sub-complex chaotic networks.

五、具体实施方式5. Specific implementation

为了更清楚的描述该数字混沌保密技术，然后图详细介绍数字混沌保密技术原理和方法。In order to describe the digital chaos security technology more clearly, then the figure introduces the principle and method of the digital chaos security technology in detail.

图1是该发明技术的全双工双向数字混沌保密通信系统。信息发送方和接收方各有两个（相同或不同的）混沌网络分别用于混沌加密和混沌解密，一方的加密和解密密码由不同混沌网络产生，但双方对应的一对（如图1中14和17及15和16）加密和解密混沌网络要有相同的拓扑结构和动力学结构。加密函数F_i(i=1,2)满足F_iF_i ^-1=I。数字信息M由混沌密码经F函数运算加密的密文C经信道（可含数字复接器、调制器、解调器、数字分接器及其它数字信号处理器等）传输到接收端后经反函数F_i ^-1运算利用混沌同步解密获得传送信息M。对远距离通信，接收信息要进行信息处理（放大，信号处理等）。Fig. 1 is the full-duplex two-way digital chaos secure communication system of this invention technology. The information sender and the receiver each have two (same or different) chaotic networks for chaotic encryption and chaotic decryption. The encryption and decryption passwords of one party are generated by different chaotic networks, but the corresponding pair of both parties (as shown in Figure 1 14 and 17 and 15 and 16) Encryption and decryption chaotic networks must have the same topology and dynamics. The encryption function F _i (i=1,2) satisfies F _i F _i ^-1 =I. The digital information M is encrypted by the chaotic cipher through the F function operation and the ciphertext C is transmitted to the receiving end through the channel (including digital multiplexer, modulator, demodulator, digital splitter and other digital signal processors, etc.) The operation of the inverse function F _i ^-1 uses chaotic synchronous decryption to obtain the transmission information M. For long-distance communication, receiving information requires information processing (amplification, signal processing, etc.).

图2是该发明技术的半双工双向数字混沌保密通信系统。与图1全双工双向通信系统不同的是，信息发送方和接收方各有一个混沌网络即用于混沌加密和也用于混沌解密，对双终端通信，加密函数F满足FF^-1=I，对多终端通信，加密函数F_i满足F_i ²=F_i ^-2=I。Fig. 2 is the half-duplex two-way digital chaos secure communication system of the invention technology. Different from the full-duplex two-way communication system in Figure 1, the information sender and receiver each have a chaotic network for chaotic encryption and chaotic decryption. For two-terminal communication, the encryption function F satisfies FF ^-1 =I , for multi-terminal communication, the encryption function F _i satisfies F _i ² =F _i ^-2 =I.

图3是单向数字混沌保密通信系统。可用于混沌加密信息的存储和提取，身份识别。Fig. 3 is a one-way digital chaos secure communication system. It can be used for storage and extraction of chaotically encrypted information and identification.

图5是该发明技术中信息发送端用于产生混沌密码（用与加密信息）的复杂混沌网络，其中黑点表示网络的混沌节点（如数字混沌电路，由硬件或软件实现）。网络中每个节点产生的混沌态都不一样，应用中可用适当的方式选取数字复杂混沌网络产生的数字数码经密码产生函数g产生所需的混沌密码，信息发送端和接收端复杂网络产生密码的方式，如图1中6和13（10和9），要一样。混沌网络的节点越多，产生密码的方式也就越多。Figure 5 is a complex chaotic network used by the information sending end to generate chaotic codes (used to encrypt information) in the technology of the invention, where the black dots represent the chaotic nodes of the network (such as digital chaotic circuits, implemented by hardware or software). The chaotic state generated by each node in the network is different. In the application, the digital number generated by the digital complex chaotic network can be selected in an appropriate way through the password generation function g to generate the required chaotic password, and the complex network at the information sending end and the receiving end generates the password. The way of 6 and 13 (10 and 9) in Fig. 1 should be the same. The more nodes in the chaotic network, the more ways to generate passwords.

图6是该发明技术中信息接收端用于产生混沌密码（用于解密信息）的复杂混沌网络，与发送端对应的混沌网络有相同的拓扑结构和动力学结构。图5和图6中的混沌网络由信道5中的密文信号C共同驱动，图1和图2中回路7和12是驱动线路。Fig. 6 is a complex chaotic network used by the information receiving end to generate chaotic codes (for decrypting information) in the technology of the invention, which has the same topological structure and dynamic structure as the corresponding chaotic network of the sending end. The chaotic network in Fig. 5 and Fig. 6 is jointly driven by the ciphertext signal C in the channel 5, and the loops 7 and 12 in Fig. 1 and Fig. 2 are driving lines.

图7是信息系统发送端和接收端的复杂混沌网络，两个复杂非线性网络具有完全相同的动力学拓扑结构，两网络的最大Lyapunov指数λ_max应大于0以保证稳定的网络混沌态。两网络间的最大横向Lyapunov指数λ_⊥应小于0以保证两网络间的稳定混沌同步。在这些条件下，两网络间产生延迟混沌斑图同步，因而可产生混沌同步的加密密码和解密密码。Figure 7 shows the complex chaotic network at the sending end and receiving end of the information system. The two complex nonlinear networks have exactly the same dynamic topology. The maximum Lyapunov exponent λ _max of the two networks should be greater than 0 to ensure a stable network chaotic state. The maximum horizontal Lyapunov exponent λ _⊥ between the two networks should be less than 0 to ensure the stable chaos synchronization between the two networks. Under these conditions, a delayed chaotic pattern synchronization is generated between the two networks, and thus a chaotic synchronous encryption cipher and decryption cipher can be generated.

在图1-4中，信道中传输的是数字混沌加密信息C,这保证了混沌同步的鲁棒性。In Figure 1-4, the digital chaos encrypted information C is transmitted in the channel, which ensures the robustness of chaos synchronization.

图10是多终端单向数字混沌保密通信系统，可设计成全双工和半双工双向数字混沌保密通信系统。Figure 10 is a multi-terminal one-way digital chaos secure communication system, which can be designed as a full-duplex and half-duplex two-way digital chaos secure communication system.

图11是多终端单向数字签名混沌保密通信系统，与图8和图9类似，可设计成全双工和半双工双向数字签名混沌保密通信系统。Figure 11 is a multi-terminal one-way digital signature chaos security communication system, which is similar to Figure 8 and Figure 9, and can be designed as a full-duplex and half-duplex two-way digital signature chaos security communication system.

图12是一个模块混沌网络，由8个子混沌网络构成。可置于某一混沌保密通信终端用于产生不同的混沌密码。模块混沌网络的这一功能也可由一非模块复杂混沌网络（如正规网络，小世界网络，标度自由网络等任意复杂结构网络）代替。因此图1、图4、图8和图9中某一终端的多个混沌网络可用一个复杂混沌网络代替。Figure 12 is a modular chaotic network consisting of 8 sub-chaotic networks. It can be placed in a chaotic secure communication terminal to generate different chaotic ciphers. This function of a modular chaotic network can also be replaced by a non-modular complex chaotic network (such as a regular network, a small-world network, a scale-free network, and any other complex structure network). Therefore, multiple chaotic networks of a certain terminal in Fig. 1, Fig. 4, Fig. 8 and Fig. 9 can be replaced by one complex chaotic network.

数字混沌加密技术的详细描述：Detailed description of digital chaos encryption technology:

图1描述与该发明技术相关的双向数字混沌保密通信系统。A终端发送数字信息M_A由混沌密码k₁经加密函数F₁加密变成数字密文C_A=F₁(M_A,k₁)，该密文通过信道5传送给B终端，B终端经解密函数F₁ ^-1和密码混沌同步k′₁=k₁解密获得传送数字信息M′_A=F₁ ^-1（C_A,k′₁）=M_A。B终端也可以同样的方法将信息安全传送给A终端。对远距离信息传送，信道5可包含调制器、解调器、放大器及信号处理系统等。图1中14和17分别是信息发送端和接收端的复杂混沌网络（16和15也是）用于产生加密和解密混沌密码，混沌网络14和17具有相同的拓扑和动力学结构。信息发送端A的混沌网络14共有n节点，第i个节点的动力学变量为x_i，混沌网络14动力学变量由X描写： $X (t) = {[x_{1} (t), x_{2} (t), . . ., x_{n} (t)]}^{T}, x_{i} = {(x_{i 1}, x_{i 2}, . . ., x_{{im}_{i}})}^{T}$ Fig. 1 describes the two-way digital chaos secure communication system related to the technology of this invention. The digital information M _A sent by the A terminal is encrypted by the chaotic code k ₁ through the encryption function F ₁ to become a digital ciphertext C _A =F ₁ (M _A ,k ₁ ), and the ciphertext is transmitted to the B terminal through the channel 5, and the B terminal passes through The decryption function F ₁ ^-1 and cryptographic chaos synchronization k′ ₁ =k ₁ are decrypted to obtain the transmitted digital information M′ _A =F ₁ ^-1 (C _A ,k′ ₁ )=M _A . Terminal B can also safely transmit information to terminal A in the same way. For long-distance information transmission, channel 5 may include modulators, demodulators, amplifiers, and signal processing systems. In Fig. 1, 14 and 17 are the complex chaotic networks (16 and 15) of the information sending end and the receiving end respectively, which are used to generate encryption and decryption chaotic ciphers, and the chaotic networks 14 and 17 have the same topology and dynamic structure. The chaotic network 14 of the information sending end A has n nodes in total, the dynamic variable of the i-th node is x _i , and the dynamic variable of the chaotic network 14 is described by X: $x (t) = {[x_{1} (t), x_{2} (t), . . ., x_{no} (t)]}^{T}, x_{i} = {(x_{i 1}, x_{i 2}, . . ., x_{{im}_{i}})}^{T}$

混沌网络14的网络动力学方程为：The network dynamics equation of chaotic network 14 is:

${\overset{\cdot \cdot}{x x}}_{i i} = = {f f}_{i i} (({x x}_{i i},, {a a}_{i i})) + + {Σ Σ}_{j j = = 11}^{n no} {G G}_{ij ij} {H h}_{j j} (({x x}_{j j})) + + \underset{j j}{Σ Σ} {α α}_{ij ij} {h h}_{j j} [[D D. (({C C}_{A A})),, {x x}_{j j}]]$

或：or:

$\overset{\cdot &Center Dot;}{X x} ((t t)) = = F f ((X x,, a a,, G G,, α α))$

其中:in:

${\overset{\cdot \cdot}{x x}}_{i i} = = {f f}_{i i} (({x x}_{i i},, {a a}_{i i})),,$ ${x x}_{i i} &Element; &Element; {R R}^{{m m}_{i i}},,$ ${f f}_{i i} : : {R R}^{{m m}_{i i}} &RightArrow; &Right Arrow; {R R}^{{m m}_{i i}},,$ ${H h}_{i i} : : {R R}^{{m m}_{i i}} &RightArrow; &Right Arrow; {R R}^{{m m}_{i i}}$

是第i个网络节点的孤立振子m_i维混沌动力学方程（非耦合方程），x_i上面的一点表示x_i对时间的微分，a_i是孤立振子方程的动力学参数，H_j(x_j)网络节点间的耦合函数，G_ij是节点间的耦合矩阵元，h_j[D(C_A),x_j]是混沌网络的耦合驱动函数，驱动函数D(C_A)是C_A的函数，α_ij是耦合系数。网络14的所有可能的参数{a_i,G_ij,α_ij}构成连续的参数空间：is the isolated oscillator m _i- dimensional chaotic dynamics equation (uncoupled equation) of the i-th network node, a point above x _i represents the differential of x _i with respect to time, a _i is the dynamic parameter of the isolated oscillator equation, H _j (x _j ) The coupling function between network nodes, G _ij is the coupling matrix element between nodes, h _j [D(C _A ), x _j ] is the coupling driving function of the chaotic network, and the driving function D(C _A ) is _the function, α _ij is the coupling coefficient. All possible parameters {a _i ,G _ij ,α _ij } of the network 14 form a continuous parameter space:

ω_X={{a_i}:{G_ij:i,j=1,2,...,n}:{α_ij:i,j=1,2,...,n}}ω _X ={{a _i }:{G _ij :i,j=1,2,...,n}:{α _ij :i,j=1,2,...,n}}

而网络的几何结构由n×n耦合矩阵G的矩阵元G_ij的个数和分布（网络14的节点间的连接数及连接分布）及H(x)和h[D(C_A),x]描写。令G¹为网络14的连接矩阵，即：The geometric structure of the network consists of the number and distribution of the matrix elements G _ij of the n×n coupling matrix G (the number and distribution of connections between the nodes of the network 14) and H(x) and h[D(C _A ),x ]description. Let ^G1 be the connectivity matrix of network 14, namely:

{G¹}≡{G:{G_ij=1:i,j=1,2,..,n}}{G ¹ }≡{G:{G _ij =1:i,j=1,2,..,n}}

这是一个由n×n矩阵G¹构成的矩阵空间。网络14的驱动矩阵为This is a matrix space consisting of n×n matrices ^G1 . The driving matrix of network 14 is

{α¹}≡{α:{α_ij=1;i,j=1,2,..,n}}{α ¹ }≡{α:{α _ij =1;i,j=1,2,..,n}}

所有n×n矩阵G¹和α¹形成网络的几何结构空间：All n×n matrices ^G1 and ^α1 form the geometric structure space of the network:

因而在n个网络节点选定的情形下，网络14的动力学空间是网络的参数空间和几何结构空间的直积：Therefore, when n network nodes are selected, the dynamic space of the network 14 is the direct product of the parameter space and the geometric structure space of the network:

下面的方程与上面的方程一样（作代换：x_i→y_i），用于描写信息接收端B的混沌网络17的动力学。The following equation is the same as the above equation (substitution: x _i →y _i ), and is used to describe the dynamics of the chaotic network 17 at the information receiving end B.

$Y Y ((t t)) = = {[[{y the y}_{11} ((t t)),, {y the y}_{22} ((t t)),, . . . . . .,, {y the y}_{n no} ((t t))]]}^{T T},, {y the y}_{i i} = = {(({y the y}_{i i 11},, {y the y}_{i i 22},, . . . . . .,, {y the y}_{{im im}_{i i}}))}^{T T}$

${\overset{\cdot \cdot}{y the y}}_{i i} = = {f f}_{i i} (({y the y}_{i i},, {a a}_{i i})) + + {Σ Σ}_{j j = = 11}^{n no} {G G}_{ij ij} {H h}_{j j} (({y the y}_{j j})) + + \underset{j j}{Σ Σ} {α α}_{ij ij} {h h}_{j j} [[D D. (({C C}_{A A})),, {x x}_{j j}]]$

或 $\overset{\cdot}{Y} (t) = F (Y, a, G, α)$ or $\overset{&Center Dot;}{Y} (t) = f (Y, a, G, α)$

其中 ${\overset{\cdot}{y}}_{i} = f_{i} (y_{i}, a_{i}),$ $y_{i} &Element; R^{m_{i}},$ $f_{i} : R^{m_{i}} &RightArrow; R^{m_{i}},$ $H_{i} : R^{m_{i}} &RightArrow; R^{m_{i}}$ in ${\overset{&Center Dot;}{the y}}_{i} = f_{i} ({the y}_{i}, a_{i}),$ ${the y}_{i} &Element; R^{m_{i}},$ $f_{i} : R^{m_{i}} &Right Arrow; R^{m_{i}},$ $h_{i} : R^{m_{i}} &Right Arrow; R^{m_{i}}$

混沌保密通信的安全性由网络节点的混沌动力学{f_i(x_i,a_i)}、复杂混沌网络的拓扑结构、复杂混沌网络的动力学结构、网络动力学方程的参数ω(ω_X和ω_Y)及网络的驱动函数D(C_A)决定（另外一个安全因素是由混沌网络产生混沌密码的方式，见后面的介绍。）。在实际构造混沌保密通信系统时，每个通信终端用于产生混沌密码的网络动力学方程应是保密的，这样窃密者很难从信道中窃取的信息重建网络动力学方程，也就无法产生信道中用于加密和解密的混沌密码。The security of chaotic secure communication is determined by the chaotic dynamics {f _i ( _xi ,a _i )} of network nodes, the topology structure of complex chaotic network, the dynamic structure of complex chaotic network, and the parameter ω(ω _X and ω _Y ) and the driving function D(C _A ) of the network (another security factor is the way the chaotic network generates the chaotic password, see the introduction later.). In the actual construction of a chaotic secure communication system, the network dynamic equations used by each communication terminal to generate chaotic ciphers should be kept secret, so that it is difficult for the stealer to reconstruct the network dynamic equations from the information stolen from the channel, and the channel cannot be generated. Chaotic ciphers for encryption and decryption in .

为了产生稳定的混沌密码，网络14和网络17的最大Lyapunov指数λ_max必须大于零：In order to produce a stable chaotic cipher, the maximum Lyapunov exponent _λmax of network 14 and network 17 must be greater than zero:

${λ λ}_{max max} = = \underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} \frac{11}{t t} ln ln ((\frac{| | δX δX ((t t)) | |}{| | δX δX ((00)) | |})) = = \underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} \frac{11}{t t} ln ln ((\frac{| | δY δY ((t t)) | |}{| | δY δY ((00)) | |})) > > 00$

其中t是时间，δX(t)是X(t)的变分。选取适当的网络振子{f_i：i=1,2,…,n}及适当的耦合函数H_j(x_j)和h_j[D(C_A),x_j]并调整网络参数where t is time and δX(t) is the variation of X(t). Select an appropriate network oscillator {f _i : i=1,2,…,n} and an appropriate coupling function H _j (x _j ) and h _j [D(C _A ),x _j ] and adjust the network parameters

ω_Y={{a_i};{G_ij:i,j=1,2,...,n};{α_ij:i.j=1,2,...,n}}=ω_X ω _Y ={{a _i };{G _ij :i,j=1,2,...,n};{α _ij :ij=1,2,...,n}}=ω _X

可使最大Lyapunov指数λ_max大于大于零：The maximum Lyapunov exponent λ _max can be made greater than or greater than zero:

λ_max》0λ _max 》0

为了利用混沌同步解密，网络14和网络17间的最大横向Lyapunov指数λ_⊥必须小于零：In order to utilize chaotic synchronous decryption, the maximum lateral Lyapunov exponent λ _⊥ between network 14 and network 17 must be less than zero:

${λ λ}_{&perp; &perp;} = = \underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} \frac{11}{t t} ln ln ((\frac{| | X x ((t t - - τ τ)) - - Y Y ((t t)) | |}{| | X x ((00)) - - Y Y ((00)) | |})) < < 00$

该条件保证网络14和网络17处于混沌同步态：This condition guarantees that the network 14 and the network 17 are in a chaotic synchronization state:

$\underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} | | X x ((t t - - τ τ)) - - Y Y ((t t)) | | = = 00$

其中τ是混沌信号X(t)由A端网络14传送到B端网络17所需时间。选取适当的网络振子{f_i}及适当的耦合函数H_j(x_j)和h_j[D(C_A),x_j]并调整网络参数Where τ is the time required for the chaotic signal X(t) to be transmitted from the A-end network 14 to the B-end network 17 . Select the appropriate network oscillator {f _i } and the appropriate coupling functions H _j (x _j ) and h _j [D(C _A ),x _j ] and adjust the network parameters

Y={{a_i};{G_ij:i,j=1,2,...,n};{α_ij:i.j=1,2,...,n}}=ω_X Y={{a _i };{G _ij :i,j=1,2,...,n};{α _ij :ij=1,2,...,n}}=ω _X

可使最大横向Lyapunov指数λ_⊥小于小于零：λ_⊥《0It is possible to make the maximum lateral Lyapunov exponent λ _⊥ smaller than zero: λ _⊥ 《0

实际上两网络14和17间的混沌同步由共同驱动D(C_A)通过函数h_j[D(C_A),x_j]保证，这可从两网络的动力学方程看出。两网络动力学方程的初值X(0)和Y(0)是随机的。适当的网络构造可使In fact, the chaotic synchronization between the two networks 14 and 17 is guaranteed by the common drive D(C _A ) through the function h _j [D(C _A ), x _j ], which can be seen from the dynamic equations of the two networks. The initial values X(0) and Y(0) of the two network dynamic equations are random. Appropriate network construction can enable

λ_max》0,λ_⊥《0两条件同时成立，见图7。同样的计算可用于网络16和15。在实际使用时，这两组网络（14，17）和（16，15）可有相同的动力学结构，也可有不同的动力学结构。实际使用时，可将网络14和15用一个复杂混沌网络代替，而16和17用一个与之相同的复杂混沌网络代替。The two conditions of λ _max 》0,λ _⊥ 《0 are established at the same time, as shown in Figure 7. The same calculations can be used for networks 16 and 15. In actual use, the two groups of networks (14, 17) and (16, 15) can have the same dynamic structure or different dynamic structures. In actual use, the networks 14 and 15 can be replaced by a complex chaotic network, and the networks 16 and 17 can be replaced by the same complex chaotic network.

在信息发送端由网络14产生混沌密码有多种方式，若网络动力学变量x_ij用q位二进制数表示：x_ij=b^ij _qb^ij _q-1...b^ij ₁b^ij ₀,则N个网络动力学方程项在t时刻共可产生Nq个二进制数码，由选择器6从这Nq个二进制数码中按一定的方式（如随机选取等）选取p(1＜p≤Nq)个二进制数码经函数g₁构成混沌密码k₁ There are many ways to generate chaotic passwords by the network 14 at the information sending end. If the network dynamic variable x _ij is represented by a q-bit binary number: x _ij =b ^ij _q b ^ij _q-1 ...b ^ij ₁ b ^ij ₀ , Then the N network dynamics equation items can generate Nq binary numbers in total at time t, and the selector 6 selects p (1<p≤Nq) numbers from the Nq binary numbers in a certain way (such as random selection, etc.) The binary code forms the chaotic code k ₁ through the function g ₁

k₁(t)=g₁(X(t),p),1＜p≤Nqk ₁ (t)=g ₁ (X(t),p),1<p≤Nq

在信息接收端由选择器13采取与信息发送端同样的方式从混沌网络17选择数字混沌信号以产生与信息发送端同样的混沌密码：At the information receiving end, the selector 13 selects the digital chaotic signal from the chaotic network 17 in the same manner as the information sending end to generate the same chaotic code as the information sending end:

k′₁(t-τ)=g₁(Y(t-τ),p),1＜p≤Nqk′ ₁ (t-τ)=g ₁ (Y(t-τ),p),1<p≤Nq

由于网络14和网络17混沌同步，所以信息接收端与信息发送端的混沌密码处于混沌同步态。Since the network 14 and the network 17 are chaotically synchronized, the chaotic ciphers at the information receiving end and the information sending end are in a chaotic synchronous state.

$\underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} [[{k k}_{11}^{' '} ((t t - - τ τ)) - - {k k}_{11} ((t t))]] &RightArrow; &Right Arrow; 00$

因而合法信息接收终端可将密文解密变成明文，此处的t-τ是解密时刻。Therefore, the legal information receiving terminal can decrypt the ciphertext into plaintext, where t-τ is the decryption time.

在本发明技术中，混沌网络产生混沌密码的方式即函数g₁是保密的且可以是时间t的函数（既在通信过程中不同的时段可用不同的g₁函数）。可以看出，传送信息的安全性由混沌网络动力学方程dX/dt=F(X,a,G,α)和g₁函数决定，这相当于传统对称加密算法保密通信。在这种对称混沌保密通信中，通信双方所用的混沌网络动力学方程和g₁函数是事先约定的。In the technology of the present invention, the method of generating the chaotic password by the chaotic network, that is, the function g ₁ is confidential and can be a function of time t (that is, different g ₁ functions can be used at different periods in the communication process). It can be seen that the security of transmitted information is determined by the chaotic network dynamics equation dX/dt=F(X,a,G,α) and _g1 function, which is equivalent to the traditional symmetric encryption algorithm for secure communication. In this kind of symmetric chaotic secure communication, the chaotic network dynamic equation and _g1 function used by both communication parties are agreed in advance.

实际上，当复杂混沌网络（14和17）的尺寸足够大（几十个混沌节点即可）且其动力学方程不公开时，混沌加密解密函数g₁可公开，这是由于即使对相同的混沌密码产生函数g₁，不同的混沌网络也产生不同的混沌密码k₁，而窃密者很难从窃取的信息重建网络动力学方程，所以知道g₁函数也不能产生密码k₁和k′₁。这种非对称混沌保密通信为数字签名保密通信提供了方便。In fact, when the size of the complex chaotic network (14 and 17) is large enough (dozens of chaotic nodes are enough) and its dynamic equation is not public, the chaotic encryption and decryption function g ₁ can be made public, because even for the same Chaotic ciphers generate function g ₁ , and different chaotic networks also generate different chaotic ciphers k ₁ , and it is difficult for a stealer to reconstruct the network dynamic equation from the stolen information, so knowing g ₁ function can not generate ciphers k ₁ and k′ ₁ . This asymmetric chaotic secure communication provides convenience for digital signature secure communication.

另一方面，若混沌网络的参数空间On the other hand, if the parameter space of the chaotic network

ω_X={{a_i};{G_ij:i,j=1,2,...,n}:{α_ij:i.j=1,2,...,n}}ω _X ={{a _i };{G _ij :i,j=1,2,...,n}:{α _ij :ij=1,2,...,n}}

足够大（大尺寸混沌网络），我们也可公开网络的拓扑结构，而混沌网络的参数空间及加密和解密函数g₁不公开。Large enough (large-scale chaotic network), we can also disclose the topology of the network, while the parameter space of the chaotic network and the encryption and decryption function _g1 are not disclosed.

网络的驱动函数h[D(C),X]对密码k₁的影响也很大，知道网络结构和解密函数，但不知道D(C_A)也无法生成k₁。The driving function h[D(C),X] of the network also has a great influence on the password k ₁ , knowing the network structure and decryption function, but not knowing D(C _A ) can not generate k ₁ .

但最安全的混沌通信保密方案是混沌网络动力学方程、g₁和D(C_A)函数都不公开，其次安全但使用方便的混沌保密通信方案是非对称混沌保密通信方案既混沌网络动力学方程不公开而g₁函数公开，再其次保密方案是网络的拓扑结构公开，而混沌网络的参数空间、函数g₁及D(C_A)不公开。这三种混沌保密通信方案的安全性都优于传统算法密码方案。But the most secure chaotic communication security scheme is the chaotic network dynamics equation, g ₁ and D(C _A ) functions are not disclosed, and the next safest but easy-to-use chaotic security communication scheme is the asymmetric chaos security communication scheme that is both the chaotic network dynamics equation The g ₁ function is not public, and the second secrecy scheme is that the topology of the network is public, while the parameter space, function g ₁ and D(C _A ) of the chaotic network are not public. The security of these three chaotic secure communication schemes is better than that of traditional algorithm cipher schemes.

被传送数字信息M_A在A端由密码k₁经函数F₁运算加密转变成数字密文C_A The transmitted digital information M _A is converted into digital ciphertext C _A by the password k ₁ and encrypted by the function F ₁ on the A side

C_A=F′₁(M_A,k₁)C _A =F′ ₁ (M _A ,k ₁ )

由于k₁(t)是流密码，M_A被分段加密且每段的密码k₁(t)都不一样，因为k₁(t_i)≠k₁(t_j)。密文C_A经信道5传送至信息接收端B，在B端部分D(C_A)经回路12驱动B端混沌网络17以产生混沌同步密码k′₁(t)。数字密文C_A由混沌同步密码k′₁(t)经函数F₁ ^-1运算转变成数字明文Since k ₁ (t) is a stream cipher, _MA is encrypted by segments and the cipher k ₁ (t) of each segment is different, because k ₁ (t _i )≠k ₁ (t _j ). The ciphertext C _A is transmitted to the information receiving terminal B through the channel 5, and the part D(C _A ) at the B terminal drives the chaotic network 17 at the B terminal through the loop 12 to generate the chaotic synchronization code k′ ₁ (t). Digital ciphertext C _A is converted into digital plaintext by the operation of function F ₁ ^-1 from chaotic synchronous cipher k′ ₁ (t)

${M m}_{A A}^{' '} = = {F f}_{11}^{- - 11} (({C C}_{A A},, {k k}_{11}^{' '})) = = {M m}_{A A}$

但也可构建函数F₁使得But it is also possible to construct the function F ₁ such that

M′_A=F₁(C_A,k′₁)M′ _A =F ₁ (C _A ,k′ ₁ )

图1中回路7和12分别是混沌网络14和17的驱动信号D(C_A)回路，驱动信号D(C_A)要经数字处理系统（用于频谱设计、信号放大及信号稳定等）处理，以使A端和B端的驱动信号D(C_A)具有稳定且相同的强度，同时D(C_A)的频谱与网络14和17的频谱应交叠，从而保证A端网络14和B端17处于混沌同步态。Loops 7 and 12 in Fig. 1 are the drive signal D(C _A ) loops of chaotic networks 14 and 17 respectively, and the drive signal D(C _A ) should be processed by a digital processing system (for spectrum design, signal amplification and signal stabilization, etc.) , so that the driving signal D(C _A ) at the A terminal and the B terminal has a stable and the same strength, and at the same time the spectrum of D(C _A ) should overlap with the spectrum of the network 14 and 17, so as to ensure that the network 14 at the A terminal and the B terminal 17 is in a chaotic synchronous state.

若传送的数字信息M_A不同，则C_A也不同，因而每次传送信息M_A所产生的密码k₁（k′₁）也不同，所以混沌密码k₁和k′₁是一次性流密码，且密码长度与所传送信息M_A长度一样。If the transmitted digital information M _A is different, then C _A is also different, so the password k ₁ (k′ ₁ ) generated by each transmission of information _MA is also different, so the chaotic code k ₁ and k′ ₁ are one-time stream ciphers , and the length of the password is the same as the length of the transmitted information _MA .

在该混沌保密通信中可通过改变网络14和17的动力学参数设置用户密码D_A1和D_B1，如作下面的参数变换In this chaotic secure communication, user passwords D _A1 and D _B1 can be set by changing the dynamic parameters of networks 14 and 17, such as the following parameter transformation

${ω ω}_{X x} = = {{{a a}_{11},, {a a}_{22},, . . . . . .;; {{{G G}_{ij ij}}};; {{{α α}_{ij ij}}}}} &DoubleRightArrow; &DoubleRightArrow; {ω ω}_{X x} = = {{{{{a a}_{{i i}_{11}} + + {δ δ}_{{i i}_{11}}}};; {{{G G}_{ij ij}}};; {{{α α}_{ij ij}}}}}$

${ω ω}_{Y Y} = = {{{a a}_{11},, {a a}_{22},, . . . . . .;; {{{G G}_{ij ij}}};; {{{α α}_{ij ij}}}}} &DoubleRightArrow; &DoubleRightArrow; {ω ω}_{Y Y} = = {{{{{a a}_{{j j}_{11}} + + {&Element; &Element;}_{{i i}_{11}}}};; {{{G G}_{ij ij}}};; {{{α α}_{ij ij}}}}}$

A端用户可将 $δ = {δ_{i_{1}}, δ_{i_{2}}, . . .}$ A-side users can $δ = {δ_{i_{1}}, δ_{i_{2}}, . . .}$

作为A端设置用户密码D_A1的依据：A端不输入密码时，δ≠0As the basis for setting the user password D _A1 at terminal A: when terminal A does not enter a password, δ≠0

网络14和17不同步，B端无法利用混沌同步解密。A端输入密码时，δ=0Networks 14 and 17 are not synchronized, and B-side cannot use chaos to decrypt synchronously. When inputting the password on terminal A, δ=0

同样B端用户可将 $&Element; = {{&Element;}_{i_{1}}, {&Element;}_{i_{2}}, . . .}$ Similarly, B-end users can $&Element; = {{&Element;}_{i_{1}}, {&Element;}_{i_{2}}, . . .}$

作为设置用户密码D_B1的依据，B端不输入密码时，∈≠0As the basis for setting the user password D _B1 , when the B terminal does not input the password, ∈≠0

网络14和17不同步，B端无法利用混沌同步解密，B端输入密码时，∈=0Networks 14 and 17 are not synchronized, B-side cannot use chaos to decrypt synchronously, when B-side enters the password, ∈=0

可以看出，只有当A和B两端都输入密码时，密文C_A（C_B）才能被解密变成明文M_A（M_B）。It can be seen that the ciphertext C _A (C _B ) can be decrypted into plaintext M _A (M _B ) only when both ends of A and B enter passwords.

在此情形下，设计网络14和17时要保证下面两式成立。In this case, when designing networks 14 and 17, the following two equations should be guaranteed to hold.

$\underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} | | X x ((t t - - τ τ)) - - Y Y ((t t)) | | &NotEqual; &NotEqual; 00,,$ $\underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} | | {D D.}_{{A A}_{11}} [[X x ((t t - - τ τ))]] - - {D D.}_{{B B}_{11}} [[Y Y ((t t))]] | | = = 00$

这两个方程保证了混沌密码的同步：These two equations guarantee the synchronization of chaotic ciphers:

$\underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} | | {D D.}_{{A A}_{11}} [[{k k}_{11} ((t t - - τ τ))]] - - {D D.}_{{B B}_{11}} [[{k k}_{11}^{' '} ((t t))]] | | = = 00$

同样，B端可将数字信息M_B经函数F₂混沌加密变成数字密文C_B并将密文通过信道5传送至A端，A端经函数F₂ ^-1利用混沌同步将密文C_B转变成数字明文M_B。B→A的混沌保密通信过程与A→B的混沌保密通信过程完全一样。Similarly, terminal B can convert digital information M _B into digital ciphertext C _B through function F ₂ chaotic encryption, and transmit the ciphertext to terminal A through channel 5, and terminal A uses chaotic synchronization through function F ₂ ^-1 to convert ciphertext C _B is transformed into digital plaintext M _B . The chaotic secure communication process of B→A is exactly the same as that of A→B.

若A端要传送信息给其它合法信息接收者，如E端，则E端须有与A端网络14完全相同的网络（动力学结构完全相同），A→E（E→A）混沌保密通信过程与A→B（B→A）相同。与上面同样的原理和方法，可建立局域混沌保密通信网。If terminal A wants to transmit information to other legitimate information receivers, such as terminal E, then terminal E must have the same network (dynamic structure is exactly the same) as terminal A network 14, A→E (E→A) chaotic secure communication The process is the same as A→B (B→A). With the same principle and method as above, a local chaotic secure communication network can be established.

上面图1所显示的全双工双向混沌保密通信系统可由图2所显示的半双工双向混沌保密通信系统代替。对双终端半双工双向混沌保密通信，加密函数F和解密函数F^-1满足The full-duplex two-way chaos secure communication system shown in FIG. 1 above can be replaced by the half-duplex two-way chaos secure communication system shown in FIG. 2 . For two-terminal half-duplex two-way chaotic secure communication, the encryption function F and decryption function F ^-1 satisfy

FF^-1=I或F²=F^-1F^-1=IFF ^-1 =I or F ² =F ^-1 F ^-1 =I

而对多终端(m个终端)半双工双向混沌保密通信，加密函数F和解密函数F^-1满足:But for multi-terminal (m terminals) half-duplex two-way chaotic secure communication, the encryption function F and decryption function F ^-1 satisfy:

F²=F^-1F^-1=IF ² =F ^-1 F ^-1 =I

图3是该发明技术的单向混沌保密通信系统，可用于密文的存储和读取，在此情形下，存储器是信道5的一部分。信息M_A由网络14产生的密码k经加密函数F加密变成数字密文C_A，C_A经信道存入存储器，从存储器经信道读取C_A然后由网络17产生的密码k′并经解密函数F^-1解密变成数字明文M_A，该过程可简单的表示为：Fig. 3 is the one-way chaotic secure communication system of this invention technology, which can be used for storage and reading of ciphertext, in this case, the memory is a part of channel 5. The information _MA is encrypted by the encryption function F by the password k generated by the network 14 to become digital ciphertext _CA , and _CA is stored in the memory through the channel, and _CA is read from the memory through the channel, and then the password k' generated by the network 17 is passed through Decryption function F ^-1 decrypts into digital plaintext M _A , the process can be simply expressed as:

M_A→F(M_A，k)=C_A→存储器→F^-1(M_A，k′)=M′_A=M_A M _A →F(M _A , k)=C _A →storage→F ^-1 (M _A ,k′)=M′ _A =M _A

也可将数字明文M_A直接经信道存入存储器，而在存储器的信息出口混沌加密，合法用户可用混沌解密将数字密文C_A解密变成数字明文M_A,该过程可简单的表示为：The digital plaintext M _A can also be directly stored in the memory through the channel, and the information output in the memory is chaotically encrypted, and legitimate users can decrypt the digital ciphertext C _A into digital plaintext M _A by chaotic decryption. The process can be simply expressed as:

M_A→存储器→F(M_A，k)=C_A→F^-1(M_A，k′)=M′_A=M_A M _A →memory →F(M _A ,k)=C _A →F ^-1 (M _A ,k′)=M′ _A =M _A

图3中用户可设置密码也可不设置密码，若设置密码则用户密码D_A和D_B的设置方法与图1系统是一样的。In Fig. 3, the user can set a password or not set a password. If a password is set, the setting method of the user password D _A and _DB is the same as that of the system in Fig. 1.

图3是单向混沌保密通信系统，可用于：身份识别（认证功能）；电子商务系统、电子现金系统、电子选举系统、电子招投标系统及电子彩票系统等。Figure 3 is a one-way chaotic secure communication system, which can be used for: identification (authentication function); e-commerce system, electronic cash system, electronic election system, electronic bidding system and electronic lottery system, etc.

图4是该发明技术的数字签名混沌保密系统。与图3相比，图4多了一层混沌网络18和19，网络18和19具有相同的拓扑结构和混沌动力学结构，这一层的混沌网络18和19与上一层的混沌网络14和17的拓扑结构和混沌动力学结构相同或不同。在A端被传送信息M_A由混沌网络18产生的数字混沌密码k_S经加密函数F_S运算转变成签名文件M_AS：Fig. 4 is the digital signature chaos security system of this invention technology. Compared with Fig. 3, Fig. 4 has one more layer of chaotic networks 18 and 19, the networks 18 and 19 have the same topology and chaotic dynamics structure, the chaotic networks 18 and 19 of this layer are the same as the chaotic network 14 of the previous layer The same or different topology and chaotic dynamics as 17. The information M _A transmitted on the A side is converted into a signature file M _AS by the digital chaotic password k _S generated by the chaotic network 18 through the encryption function F _S :

M_As=F′_s(M_A,k_s)M _As =F′ _s (M _A ,k _s )

M_AS由混沌网络14产生的数字混沌密码k经加密函数F运算转变成混沌加密的签名文件C_AS：M _AS is converted into a chaotic encrypted signature file C _AS by the digital chaotic password k generated by the chaotic network 14 through the operation of the encryption function F:

C_As=F(M_As,k)C _As =F(M _As ,k)

该混沌加密的数字签名文件C_AS经信道5传送至B终端。B终端利用网络17产生的混沌密码k’及混沌同步经解密函数F^-1运算解密接收到的C_AS变成M’_AS：The chaotically encrypted digital signature file _CAS is sent to the B terminal via channel 5. Terminal B utilizes the chaotic password k' generated by the network 17 and the chaotic synchronization, and decrypts the received C _AS through the decryption function F ^-1 to become M' _AS :

M′_As=F(C_As,k′)M′ _As =F(C _As ,k′)

该签名文件M′_AS经F_S ^-1运算并利用混沌同步和网络19产生的混沌密码k’_S转变成没签名的数字文件M′_A The signature file M′ _AS is converted into an unsigned digital file M′ A through F _S ^-1 calculation and using chaos synchronization and the chaotic password k' _S _generated by the network 19

M′_A=F_s(M′_As,k′_s)=M_A M′ _A =F _s (M′ _As ,k′ _s )=M _A

图4系统用于将混沌加密的文件从A终端传送到B终端，类似于图1和2，也可以利用全双工（见图8）或半双工（见图9）双向混沌保密通信系统将混沌加密的数字签名文件由B终端传送到A终端。B终端到A终端的数字签名混沌保密系统与A终端到B终端的数字签名混沌保密系统可相同也可不相同。通过增加通信终端，也可进行多终端数字签名混沌保密通信。通信网络中一对相互通信终端间的用于签名的混沌网络（如图4中的18和19）与另一对通信终端间的用于签名的混沌网络的拓扑结构和混沌动力学结构要相同。The system in Figure 4 is used to transmit chaotic encrypted files from Terminal A to Terminal B, similar to Figures 1 and 2, and can also use full-duplex (see Figure 8) or half-duplex (see Figure 9) two-way chaos security communication system Transmit the chaotic encrypted digital signature file from terminal B to terminal A. The digital signature chaotic security system from terminal B to terminal A may be the same as or different from the digital signature chaotic security system from terminal A to terminal B. By adding communication terminals, it is also possible to carry out multi-terminal digital signature chaotic secure communication. The chaotic network used for signature between a pair of mutual communication terminals in the communication network (such as 18 and 19 in Figure 4) and the chaotic network used for signature between another pair of communication terminals should have the same topology and chaotic dynamics structure .

实际上，与信道相连的一个通信终端只需一个复杂混沌网络即可，而通信网络中相互进行混沌保密通信的终端其复杂混沌网络的动力学结构应一样。同一终端不同的混沌加密密码k_i可由同一个混沌网络采用不同的产生方法，即不同的g_i函数产生，每一个g_i函数对应一个混沌密码选择器。这样图1、图4、图8和图9中A终端和B终端分别只需一个复杂网络即可，见图10。通信网络中相互进行混沌保密通信的终端除了其复杂混沌网络的动力学结构一样外，其对应的密码产生函数g和混沌网络驱动函数D(C)也应一样，且相应的加密和解密函数也应互为反函数关系。In fact, a communication terminal connected to the channel only needs a complex chaotic network, and the dynamic structure of the complex chaotic network should be the same for the terminals in the communication network that communicate with each other in chaotic security. Different chaotic encryption ciphers _ki for the same terminal can be generated by the same chaotic network using different methods, that is, different _gi functions, and each _gi function corresponds to a chaotic cipher selector. In this way, terminal A and terminal B in FIG. 1 , FIG. 4 , FIG. 8 and FIG. 9 only need one complex network, as shown in FIG. 10 . In addition to the same dynamic structure of the complex chaotic network, the terminals that perform chaotic secure communication in the communication network should also have the same password generation function g and chaotic network driving function D(C), and the corresponding encryption and decryption functions should also be the same. should be an inverse functional relationship.

图11是一个通信终端只有一个复杂混沌网络用于产生不同的混沌密码的多终端数字签名混沌保密通信系统(网络)。以该通信网络中的A与B间数字签名保密通信为例,A终端对传送信息M_A的数字签名密码k^s _Ai和对应的加密函数F^s _Ai与B终端的解密密码k^s _Bj和对应的加密函数[F^s _Bj]^-1对单向或全双工通信应满足关系：Fig. 11 is a multi-terminal digital signature chaotic secure communication system (network) in which a communication terminal has only one complex chaotic network for generating different chaotic ciphers. Taking the digital signature confidential communication between A and B in this communication network as an example, the digital signature password k ^s _Ai and the corresponding encryption function F ^s _Ai of the terminal _A to the transmission information MA are corresponding to the decryption password k ^s _Bj and the corresponding encryption function of the terminal B. The encryption function [F ^s _Bj ] ^-1 should satisfy the relationship for one-way or full-duplex communication:

${k k}_{Bj bj}^{S S} = = {k k}_{Ai Ai}^{S S},, {[[{F f}_{Bj bj}^{s the s}]]}^{- - 11} {F f}_{Ai Ai}^{s the s} = = I I$

或 $k_{Bj}^{S} = k_{Ai}^{S}, F_{Bj}^{s} F_{Ai}^{s} = I, {[F_{Bj}^{s}]}^{- 1} {[F_{Ai}^{s}]}^{- 1} = I$ or $k_{bj}^{S} = k_{Ai}^{S}, f_{bj}^{the s} f_{Ai}^{the s} = I, {[f_{bj}^{the s}]}^{- 1} {[f_{Ai}^{the s}]}^{- 1} = I$

而对半双工双向通信应满足关系：For half-duplex two-way communication, the relationship should be satisfied:

${k k}_{Bj bj}^{S S} = = {k k}_{Ai Ai}^{S S},, {F f}_{Bj bj}^{s the s} {F f}_{Ai Ai}^{s the s} = = I I,, {[[{F f}_{Bj bj}^{s the s}]]}^{- - 11} {[[{F f}_{Ai Ai}^{s the s}]]}^{- - 11} = = I I$

同样,A终端的的数字签名信息M_AS的加密密码k_Ai和对应的加密函数F_Ai与B终端的解密密码k_Bj和对应的解密函数[F_Bj]^-1对单向或全双工通信应满足关系：Similarly, the encryption password k _Ai and the corresponding encryption function F _Ai of the digital signature information M _AS of terminal A and the decryption password k _Bj of terminal B and the corresponding decryption function [F _Bj ] ^-1 pair one-way or full-duplex communication The relationship should be satisfied:

k_Bj=k_Ai,[F_Bj]^-1F_Ai=Ik _Bj =k _Ai ,[F _Bj ] ^-1 F _Ai =I

或k_Bj=k_Ai,F_BjF_Ai=I,[F_Bj]^-1[F_Ai]^-1=IOr k _Bj =k _Ai ,F _Bj F _Ai =I,[F _Bj ] ^-1 [F _Ai ] ^-1 =I

k_Bj=k_Ai,F_BjF_Ai=I,[F_Bj]^-1[F_Ai]^-1=Ik _Bj =k _Ai ,F _Bj F _Ai =I,[F _Bj ] ^-1 [F _Ai ] ^-1 =I

为设计简单，通信网络的任意两终端如A_i终端与A_j终端的所有签名加密解密函数和信息加密解密函数可取为一样：For simplicity of design, all signature encryption and decryption functions and information encryption and decryption functions of any two terminals in the communication network, such as A _i terminal and A _j terminal, can be taken as the same:

${F f}_{Bj bj}^{s the s} = = {F f}_{Ai Ai}^{s the s} = = {F f}^{S S},, i i,, j j = = 1,2 1,2,, . . . . . .,, l l$

F_Bj=F_Ai=F,i,j=1,2,...,lF _Bj =F _Ai =F,i,j=1,2,...,l

或 $F_{Bj}^{s} = F_{Ai}^{s} = F_{Bj} = F_{Ai} = F, i, j = 1,2, . . ., l$ or $f_{bj}^{the s} = f_{Ai}^{the s} = f_{bj} = f_{Ai} = f, i, j = 1,2, . . ., l$

从上面的介绍可以看出，该发明中与信道相连的某一混沌保密通信终端可有多层混沌网络（≥2层），如图4、8、9所示数字签名混沌保密通信系统中有两层混沌网络，某一混沌保密通信终端同一层也可有多个混沌网络（≥2个），如图1所示全双工双向混沌保密通信系统中有两个。由于这些混沌网络有连接，因而这些混沌子网络构成了一个模块混沌网络。该模块混沌网络可用一个混沌网络方程描写。所以尽管某一混沌保密通信终端可能有多个混沌子网络用于产生不同的密码函数g_i(i=1,2,3,…,)，实际上可看成是一个模块混沌网络，见图12。从这一模块混沌网络可构造多个混沌密码函数g_i,i=1,2,3,…。由于一个任意结构的复杂混沌网络，如正规结构网络，小世界网络，标度自由网络，随机结构网络等，也可构造多个混沌密码函数g_i,i=1,2,3,…，因此我们在讨论多个混沌密码函数g_i,i=1,2,3,…的产生时，不再区分一般复杂混沌网络和模块复杂混沌网络。图10、11混沌保密通信系统利用了该发明技术的这一思想。As can be seen from the above introduction, a certain chaotic secure communication terminal connected to the channel in this invention may have a multi-layer chaotic network (≥ 2 layers), as shown in Figures 4, 8, and 9, there are Two layers of chaotic networks, a chaotic secure communication terminal can also have multiple chaotic networks (≥2) on the same layer, as shown in Figure 1, there are two in the full-duplex two-way chaotic secure communication system. Since these chaotic networks are connected, these chaotic sub-networks constitute a modular chaotic network. The modular chaotic network can be described by a chaotic network equation. Therefore, although a chaotic secure communication terminal may have multiple chaotic sub-networks for generating different cryptographic functions g _i (i=1,2,3,...,), it can actually be regarded as a modular chaotic network, as shown in Fig. 12. Multiple chaotic cryptographic functions g _i , i=1, 2, 3, . . . can be constructed from this modular chaotic network. Since a complex chaotic network with any structure, such as a regular structure network, a small-world network, a scale-free network, a random structure network, etc., can also construct multiple chaotic cryptographic functions g _i , i=1,2,3,..., so When we discuss the generation of multiple chaotic cryptographic functions g _i , i=1,2,3,..., we no longer distinguish between general complex chaotic networks and modular complex chaotic networks. Fig. 10, 11 chaos secure communication system has utilized this idea of this invention technology.

该发明技术中图5和图6所示的混沌网络可以软件实现，也可硬件实现。在硬件实现时，既可用数字电路实现，也可用模拟电路实现。方案的选取依赖于应用环境。混沌网络的数字电路实现时将硬件描述语言（如Verilog HDL或VHDL等）写入可编程逻辑器件或设计专用集成电路形成数字混沌网络，并尽可能将硬件描述语言加密。The chaotic network shown in Fig. 5 and Fig. 6 in this inventive technology can be realized by software or by hardware. When implemented in hardware, it can be realized by both digital circuit and analog circuit. The selection of the scheme depends on the application environment. When the digital circuit of the chaotic network is realized, the hardware description language (such as Verilog HDL or VHDL, etc.) is written into the programmable logic device or an application-specific integrated circuit is designed to form a digital chaotic network, and the hardware description language is encrypted as much as possible.

数字混沌网络可由计算机软件实现，也可用高级语言在DSP等芯片上实现。The digital chaotic network can be realized by computer software, and it can also be realized on chips such as DSP by high-level language.

混沌网络14的n个节点的孤立混沌动力学要稳定（每个孤立振子方程的最大Lyapunov指数要大于0），且最好互不一样（节点混沌动力学方程不一样），至少要部分节点不一样，这样可产生复杂的时空混沌斑图，进而产生更多分布合理的的混沌密码k₁态。k₁密码的选取方式越多，信息M_A的破解难度就越大。所有k₁的选取方式构成一个分立空间：The isolated chaotic dynamics of the n nodes of the chaotic network 14 should be stable (the maximum Lyapunov exponent of each isolated oscillator equation should be greater than 0), and preferably different from each other (the chaotic dynamics equations of the nodes are different), at least some nodes must be different Similarly, this can produce complex spatio-temporal chaotic patterns, and then produce more k ₁ states of chaotic ciphers with reasonable distribution. The more ways to choose the k ₁ password, the more difficult it is to decipher the information _MA . All k ₁ choices form a discrete space:

K={g₁(X，p),p=1,2,...Nq;{g_1i,i=1,2,...}}K={g ₁ (X，p),p=1,2,...Nq;{g _1i ,i=1,2,...}}

由混沌网络14产生的混沌密码空间为：

The chaotic password space generated by the chaotic network 14 is:

当n个混沌阵子（节点）{f(x)}选定后，网络14的某一混沌态由该空间的一点决定，该点的选取要保证：1、网络14的最大Lyapunov指数要大于0以保证网络14有稳定的混沌网络动力学；2、网络14的最大横向Lyapunov指数要小于0以保证网络14与网络17有稳定的混沌斑图同步；3、矩阵α及函数h(x)的选取要合适以保证网络14与网络17在密文C_A驱动下混沌同步。When n chaotic elements (nodes) {f(x)} are selected, a certain chaotic state of the network 14 is determined by a point in this space, and the selection of this point must ensure that: 1. The maximum Lyapunov exponent of the network 14 must be greater than 0 To ensure that network 14 has stable chaotic network dynamics; 2, the maximum horizontal Lyapunov exponent of network 14 should be less than 0 to ensure that network 14 and network 17 have stable chaotic pattern synchronization; 3, matrix α and function h(x) The selection should be appropriate to ensure that the network 14 and the network 17 are chaotically synchronized under the drive _{of the} ciphertext CA.

图1中，A终端混沌密码选择器6在t₁时刻从数字混沌网络14产生的二进制数码（如1011001010…）中按一定方式选取m个二进制数码并载入寄存器形成混沌密码k₁(t₁)：In Fig. 1, the A-terminal chaotic code selector 6 selects m binary codes in a certain way from the binary codes (such as 1011001010...) generated by the digital chaotic network 14 at time _t1 and loads them into the register to form a chaotic code k ₁ (t ₁ ):

k₁(t₁)=g₁(X(t₁),p)k ₁ (t ₁ )=g ₁ (X(t ₁ ),p)

该密码与载入另一寄存器的二进制数码信息M_A经加密函数F运算变成数字密文C_A(t₁)，密文C_A经信道5传送给合法信息接受终端B。The password and the binary digital information M _A loaded into another register are converted into digital ciphertext C _A (t ₁ ) by the encryption function F, and the ciphertext C _A is transmitted to the legal information receiving terminal B through the channel 5.

A终端混沌密码选择器6在t₂时刻从数字混沌网络14产生的二进制数码中按同样的方式选取二进制数码并载入寄存器形成混沌密码k₁(t₂)The A-terminal chaos code selector 6 selects the binary code from the binary code generated by the digital chaos network 14 in the same way at time _t2 and loads it into the register to form the chaotic code k ₁ (t ₂ )

k₁(t₂)=g₁(X(t₂),p)k ₁ (t ₂ )=g ₁ (X(t ₂ ),p)

一般情况下k_l(t₁)≠k₁(t₂)In general k _l (t ₁ )≠k ₁ (t ₂ )

该密码与载入另一寄存器的二进制数码信息M_A经加密函数F运算变成数字密文C_A(t₂)，密文C_A经信道5传送给合法信息接受终端B，反复该加密过程，信息M_A转变成数字密文C_A。The password and the binary digital information M _A loaded into another register are converted into digital ciphertext C _A (t ₂ ) through the encryption function F, and the ciphertext C _A is transmitted to the legal information receiving terminal B through the channel 5, and the encryption process is repeated , the information M _A is transformed into digital ciphertext C _A .

可以看出，k₁(t_i)≠k₁(t_j)，该混沌密码是流密码。对不同的被加密信息M_A，网络14的混沌态不一样，因而该混沌密码k₁是一次性密码，与传统的算法密码相比，保密性更强。在加密时不同信息段的加密密码k₁(t)也可用不同的方式选取，即g₁函数在不同信息段不一样。It can be seen that k ₁ (t _i )≠k ₁ (t _j ), the chaotic cipher is a stream cipher. For different encrypted information M _A , the chaotic state of the network 14 is different, so the chaotic password k ₁ is a one-time password, which is more secure than the traditional algorithmic password. The encryption ciphers k ₁ (t) of different information segments can also be selected in different ways during encryption, that is, the g ₁ function is different in different information segments.

可以看出，信息的混沌加密与通常的加密是一样的，也是信息的分段加密，与通常加密不一样的是，在混沌加密中每段加密密码是不一样的k₁(t_i)≠k₁(t_j)。It can be seen that the chaotic encryption of information is the same as the usual encryption, and it is also a segmented encryption of information. What is different from the usual encryption is that in chaotic encryption, each encrypted password is different k ₁ (t _i )≠ k ₁ (t _j ).

这种灵活的混沌密码k₁的生成方式增加了窃密者破解密文C_A的难度。The generation method of this flexible chaotic cipher k ₁ increases the difficulty for the stealer to decipher the ciphertext C _A.

本发明中，另一种构造简单密码选择函数g₁的方式是构造网络动力学变量X(t)的函数组P={P_j(X),j=1,2,…},然后从函数组的二进制数码中按一定的方式选取二进制码构造密码k₁=g₁(P(X),p)。以多项式函数为例构造P：In the present invention, another way to construct the simple password selection function _g1 is to construct the function group P={P _j (X), j=1,2,...} of the network dynamics variable X(t), and then from the function Select the binary code in a certain way from the group of binary codes to construct the password k ₁ =g ₁ (P(X),p). Take the polynomial function as an example to construct P:

{P_a({x_i}),P_b({x_i}),P_c({x_i}),...}{P _a ({ _xi }),P _b ({ _xi }),P _c ({xi _} ),...}

${P P}_{α α} (({{{x x}_{i i}}})) = = {Σ Σ}_{i i = = 11}^{N N} {a a}_{i i} {x x}_{i i} + + {Σ Σ}_{i i,, j j = = 11}^{N N} {α α}_{ij ij} {x x}_{i i} {x x}_{j j} + + \underset{{n no}_{11} {n no}_{22} {n no}_{33 . . . . . .}}{Σ Σ} {Σ Σ}_{ijk ijk . . . . . .}^{N N} {α α}_{ijk ijk . . . . . .} (({n no}_{11},, {n no}_{22},, . . . . . .)) {x x}_{i i}^{{n no}_{11}} {x x}_{j j}^{{n no}_{22}} {x x}_{k k}^{{n no}_{33}} . . . . . . + + \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot$

{n₁,n₂,n₃,...}∈integers{n ₁ ,n ₂ ,n ₃ ,...}∈integers

{a_i,b_i,a_ij,b_ij,d_ijk...,…}∈R¹ {a _i ,b _i ,a _ij ,b _ij ,d _ijk ...,…}∈R ¹

其中（不公开）of which (unpublished)

{{a_i,b_i,a_ij,b_ij,d_ijk...,…},{n₁,n₂,n₃,...}}{{a _i ,b _i ,a _ij ,b _ij ,d _ijk ...,...},{n ₁ ,n ₂ ,n ₃ ,...}}

构成一参数空间。form a parameter space.

从数字多项式组P（不公开）{P_a({x_i}),P_b({x_i}),P_c({x_i}),...}From the set of digital polynomials P (not public) {P _a ({ _xi }),P _b ({xi _} ),P _c ({ _xi }),...}

所产生的二进制数码中按任意方式（如随机方式，一定规则方式等）选取数码经函数g₁构造混沌密码k₁=g₁(P,p)。函数组P要便于计算，其占用芯片资源要少，混沌密码k₁的产生速率要高。The generated binary numbers are selected in any way (such as random way, certain rule way, etc.) to construct the chaotic cipher k ₁ =g ₁ (P,p) through the function g ₁ . The function group P should be easy to calculate, it should occupy less chip resources, and the generation rate of the chaotic code k ₁ should be high.

上面关于复杂混沌网络14及二进制混沌密码k₁的数字电路实现也可由计算机和DSP等数字系统利用软件实现。显然The digital circuit implementation of the above complex chaotic network 14 and binary chaotic code k ₁ can also be realized by digital systems such as computers and DSPs using software. obviously

k₁(t₁)=g₁(P(t_l),p)k ₁ (t ₁ )=g ₁ (P(t _l ),p)

包含k₁(t₂)=g_l(X(t₂),p)Contains k ₁ (t ₂ )=g _l (X(t ₂ ),p)

本发明中所用的数字信息和混沌数字密码不限于二进制数码，也可是其它数字信息和混沌数字密码。二进制数字密文信息C_A可以远距离传输，解决了以往混沌加密信息（主要是模拟混沌加密等，信道中传输的是模拟加密信息）不能远距离传输的难题，这一世该发明技术的重要一点。The digital information and chaotic digital ciphers used in the present invention are not limited to binary numbers, and may be other digital information and chaotic digital ciphers. Binary digital ciphertext information C _A can be transmitted over long distances, which solves the problem that chaotic encrypted information (mainly analog chaotic encryption, etc., and the transmission of analog encrypted information in the channel) cannot be transmitted over long distances in the past. This is an important point of this invention technology .

该数字混沌保密技术的安全性依赖于：The security of this digital chaos security technology depends on:

（1），网络的几何结构， (1), the geometry of the network,

（2），网络节点的选取，f_ω={f_i(x_i):i=1,2,...,n};(2), selection of network nodes, f _ω ={f _i (x _i ):i=1,2,...,n};

(3)，网络的动力学参数，ω_X={{a_i};{G_ij};{α_ij}};(3), the dynamic parameters of the network, ω _X ={{a _i };{G _ij };{α _ij }};

（4），k₁的选取方式，K={g₁(X,p),p=1,2,...Nq;{g_1i,i=1,2,...}}(4), the selection method of k ₁ , K={g ₁ (X,p),p=1,2,...Nq;{g _1i ,i=1,2,...}}

（5），混沌网络驱动函数的构造，H,h[D(C_A),X](5), the construction of chaotic network driving function, H,h[D(C _A ),X]

假如网络的几何结构和网络节点的选取已知，即If the geometric structure of the network and the selection of network nodes are known, that is

和f_ω={f_i(x_i):i=1,2,...,n}and f _ω ={f _i (x _i ):i=1,2,...,n}

已知，我们估算要获得一组特定的动力学参数ω_x={{a_i};{G_ij};{α_ij}}和确定的数字混沌密码k₁，在密码空间至少要计算多少个点。网络动力学参数空间是连续的，我们要针对网络动力学参数空间中的混沌和混沌同步区域的每一点计算网络动力学方程，当然这种计算量是巨大的。为了便于估算，选取相邻的参数点使得混沌同步误差与混沌波幅数量级一样，假定参数空间中的混沌和混沌同步区域是边长为1的正多面体（实际区域远大于此），则要计算It is _known _that _we _estimate how _many at least point. The network dynamics parameter space is continuous, and we need to calculate the network dynamics equation for every point in the chaos and chaotic synchronous regions in the network dynamics parameter space, of course, the amount of calculation is huge. In order to facilitate the estimation, adjacent parameter points are selected so that the chaos synchronization error has the same order of magnitude as the chaos amplitude. Assuming that the chaos and the chaos synchronization area in the parameter space are regular polyhedrons with side length 1 (the actual area is much larger than this), it is necessary to calculate

N_ω=10^2Q N _ω =10 ^2Q

个点的网络动力学方程，Q是网络动力学参数的数目。假如Q=40，每秒计算10⁸个点，则至少需10⁶⁵年.point network dynamics equation, Q is the number of network dynamics parameters. If Q=40, and calculate 10 ⁸ points per second, it will take at least 10 ⁶⁵ years.

假定网络动力学变量由q位二进制数表示，混沌密码直接取自网络动力学变量，则共有Assuming that the network dynamic variables are represented by q-bit binary numbers, and the chaotic code is directly taken from the network dynamic variables, there are a total of

${N N}_{K K} = = qN QUR \frac{{((qN QUR - - 11))}^{qN QUR} - - 11}{qN QUR - - 22} \approx \approx {((qN QUR))}^{qN QUR}$

个混沌密码k₁的选择方案。因此窃密者为了获得混沌密码k₁，要从(qN)^qN个k₁中寻找一个特定的k₁。若N=20,q=32,则(qN)^qN=(640)⁶⁴⁰≈2⁵⁹⁶⁶≈10¹⁷⁹⁶。假如每秒可寻找10¹³个密钥k₁，经典算法则需约10¹⁷⁷⁵年。特别是由于网络动力学对其参数的敏感性，(qN)^qN个密钥k₁中还不一定含有混沌加密所用的特定密钥k₁。如果进一步考虑网络混沌振子的选取和网络的空间结构，可以看出，窃密者基本上不可能破解混沌加密信息。A selection scheme for a chaotic cipher k ₁ . Therefore, in order to obtain the chaotic password k ₁ , the stealer needs to find a specific k ₁ from (qN) ^qN k ₁ . If N=20, q=32, then (qN) ^qN =(640) ⁶⁴⁰ ≈2 ⁵⁹⁶⁶ ≈10 ¹⁷⁹⁶ . If 10 ¹³ keys k ₁ can be found per second, the classical algorithm will take about 10 ¹⁷⁷⁵ years. Especially due to the sensitivity of network dynamics to its parameters, the (qN) ^qN keys k ₁ may not necessarily contain the specific key k ₁ used in chaotic encryption. If we further consider the selection of network chaotic oscillators and the spatial structure of the network, it can be seen that it is basically impossible for a stealer to crack chaotic encrypted information.

实施例：现在通过一个例子来说明数字信息的混沌加密和解密。A端与信道5相连的用于产生混沌密码k₁的网络14由两个节点构成，分别由下面两个孤立节点动力学方程描写，Embodiment: An example is now used to illustrate the chaotic encryption and decryption of digital information. The network 14 used to generate the chaotic code k ₁ connected to the channel 5 at the A end is composed of two nodes, which are described by the following two isolated node dynamic equations respectively,

节点1的动力学变量由3-维矢量x₁=(x₁₁,x₁₂,x₁₃)^T描写，节点1的孤立动力学方程为：The dynamic variables of node 1 are described by a 3-dimensional vector x ₁ =(x ₁₁ ,x ₁₂ ,x ₁₃ ) ^T , and the isolated dynamic equation of node 1 is:

$\frac{{dx dx}_{1111}}{dt dt} = = - - {a a}_{11} {x x}_{1111} - - {a a}_{22} {x x}_{1212}$

$\frac{{dx dx}_{1212}}{dt dt} = = {a a}_{33} {x x}_{1111} + + {a a}_{44} {x x}_{1111} {x x}_{1313}$

$\frac{{dx dx}_{1313}}{dt dt} = = - - {a a}_{55} {x x}_{1313} - - {a a}_{66} {x x}_{1111} {x x}_{1212} - - {a a}_{77}$

节点2的动力学变量由3-维矢量x₂=(x₂₁,x₂₂,x₂₃)^T描写，节点2的孤立动力学方程为：The dynamic variables of node 2 are described by a 3-dimensional vector x ₂ =(x ₂₁ ,x ₂₂ ,x ₂₃ ) ^T , and the isolated dynamic equation of node 2 is:

$\frac{{dx dx}_{21 twenty one}}{dt dt} = = - - {a a}_{88} {x x}_{21 twenty one} - - {a a}_{99} {x x}_{22 twenty two}$

$\frac{{dx dx}_{22 twenty two}}{dt dt} = = {a a}_{1010} {x x}_{21 twenty one} + + {a a}_{1111} {x x}_{21 twenty one} {x x}_{23 twenty three} + + {a a}_{1212} {x x}_{22 twenty two}$

$\frac{{dx dx}_{23 twenty three}}{dt dt} = = - - {a a}_{1313} {x x}_{23 twenty three} - - {a a}_{1414} {(({x x}_{21 twenty one}))}^{22} - - {a a}_{1515}$

两个方程都是类Lorenz方程，通过耦合项Both equations are Lorenz-like equations, through the coupling term

G₁(x₁₁-x₂₁)G ₁ (x ₁₁ -x ₂₁ )

耦合起来形成网络，该网络由6个动力学变量X=(x₁,x₂)=(x₁ ¹,x₁ ²,x₁ ³,x₂ ¹,x₂ ²,x₂ ³)^T描写，满足网络动力学方程：Coupled to form a network, the network is described by six dynamic variables X=(x ₁ ,x ₂ )=(x ₁ ¹ ,x ₁ ² ,x ₁ ³ ,x ₂ ¹ ,x ₂ ² ,x ₂ ³ ) ^T , satisfying the network dynamics equation:

$\frac{{dx dx}_{1212}}{dt dt} = = {a a}_{33} {x x}_{1111} + + {a a}_{44} {x x}_{1111} {x x}_{1313} + + α α [[D D. (({C C}_{A A}))]] + + {x x}_{21 twenty one} - - {x x}_{1111}]]$

$\frac{{dx dx}_{1313}}{dt dt} = = - - {a a}_{55} {x x}_{1313} - - {a a}_{66} {x x}_{1111} {x x}_{1313} - - {a a}_{77}$

$\frac{{dx dx}_{22 twenty two}}{dt dt} = = {a a}_{1010} {x x}_{21 twenty one} + + {a a}_{1111} {x x}_{21 twenty one} {x x}_{23 twenty three} + + {a a}_{1212} {x x}_{22 twenty two} + + {G G}_{11} (({x x}_{1111} - - {x x}_{21 twenty one}))$

耦合矩阵为：The coupling matrix is:

$G G = = (\begin{matrix} 00 & 00 \\ {G G}_{21 twenty one} & {G G}_{22 twenty two} \end{matrix}) = = {G G}_{21 twenty one} (\begin{matrix} 00 & 00 \\ 11 & - - 11 \end{matrix})$

耦合函数为The coupling function is

H₁(x₁)=E₁x₁,H₂(x₂)=E₂x₂ H ₁ (x ₁ )=E ₁ x ₁ ,H ₂ (x ₂ )=E ₂ x ₂

${E E.}_{11} = = {E E.}_{22} = = E E. = = (\begin{matrix} 11 & 00 & 00 \\ 00 & 00 & 00 \\ 00 & 00 & 00 \end{matrix})$

网络的驱动函数h和相应的耦合矩阵为：The driving function h of the network and the corresponding coupling matrix are:

$α α = = (\begin{matrix} {α α}_{1111} & {α α}_{1212} \\ 00 & 00 \end{matrix}) = = {α α}_{1212} (\begin{matrix} - - 11 & 11 \\ 00 & 00 \end{matrix})$

h₁[D(C_A),x₁]=Ex₁+C_A h ₁ [D(C _A ),x ₁ ]=Ex ₁ +C _A

h₂[D(C_A),x₂]=Ex₂+2C_A h ₂ [D(C _A ),x ₂ ]=Ex ₂ +2C _A

17个网络动力学参数可取为：The 17 network dynamic parameters can be taken as:

ω=({a_i};{G_ij};{α_ij})=(a₁,a₂,...,a₁₅;G₁;α)ω=({a _i };{G _ij };{α _ij })=(a ₁ ,a ₂ ,...,a ₁₅ ;G ₁ ;α)

=(1,1,2.5,1.2,0.28,1.2,0.5,1,1,2.5,1.2,1,0.28,1.2,0.5;1.6;2.5)=(1,1,2.5,1.2,0.28,1.2,0.5,1,1,2.5,1.2,1,0.28,1.2,0.5;1.6;2.5)

网络方程中，项In the network equation, the term

α[D(C_A)+x₂₁-x₁₁]α[D(C _A )+x ₂₁ -x ₁₁ ]

是数字密文混沌信号C_A的函数S对网络14网络动力学方程的驱动项。B端产生混沌密码k₁，的网络17的动力学方程及网络参数与A端完全相同。在选定的网络参数下，网络的最大Lyapunov指数及两网络间的横向Lyapunov指数分别为λ_max＞0，λ_⊥＜0。若x_i和y_i的二进制数表示为is the driving term of the function S of the digital ciphertext chaotic signal _CA to the network dynamics equation of the network 14 . The dynamic equation and network parameters of the network 17 generated by terminal B to generate chaotic code k ₁ are exactly the same as those of terminal A. Under the selected network parameters, the maximum Lyapunov exponent of the network and the horizontal Lyapunov exponent between the two networks are λ _max >0 and λ _⊥ <0 respectively. If the binary numbers of x _i and y _i are expressed as

x₁₁=b_nb_n-1...b₁b₀,x₁₂=c_nc_n-1...c₁c₀,x₂₁=d_nd_n-1...d₁d₀ x ₁₁ =b _n b _n-1 ...b ₁ b ₀ ,x ₁₂ =c _n c _n-1 ...c ₁ c ₀ ,x ₂₁ =d _n d _n-1 ...d ₁ d ₀

x₂₂=e_ne_n-1...e₁e₀,y₁₁=B_nB_n-1...B₁B₀,y₁₂=C_nC_n-1...C₁C₀ x ₂₂ =e _n e _n-1 ...e ₁ e ₀ ,y ₁₁ =B _n B _n-1 ...B ₁ B ₀ ,y ₁₂ =C _n C _n-1 ...C ₁ C ₀

y₂₁=D_nD_n-1...D₁D₀,y₂₂=E_nE_n-1...E₁E₀ y ₂₁ = D _n D _n-1 ... D ₁ D ₀ , y ₂₂ = E _n E _n-1 ... E ₁ E ₀

则A端数字加密密码k₁取为：Then the A terminal digital encryption password k ₁ is taken as:

k₁=g₁(x₁₁,x₁₂,x₂₁,x₂₂)=c_j1e_jkc_jmb_j1d_j2...e_j2b_jld_j1c_j2d_jpe_j1 k ₁ =g ₁ (x ₁₁ ,x ₁₂ ,x ₂₁ ,x ₂₂ )=c _j1 e _jk c _jm b _j1 d _j2 ...e _j2 b _jl d _j1 c _j2 d _jp e _j1

加密函数F取为数字混沌密码k₁与传送数字信息M_A的异或运算：The encryption function F is taken as the XOR operation of the digital chaotic cipher k ₁ and the transmitted digital information _MA :

C_A=F(M_A,k₁)=M_A⊕k₁ C _A =F(M _A ,k ₁ )=M _A ⊕k ₁

B端数字解密密码k₁，取为：B-side digital decryption password k ₁ is taken as:

k′₁=g₁(y₁₁,y₁₂,y₂₁,y₂₂)=C_j1E_jkC_jmB_j1D_j2B_j2...E_j2B_jlD_j1C_j2D_jpE_j1 k′ ₁ =g ₁ (y ₁₁ ,y ₁₂ ,y ₂₁ ,y ₂₂ )=C _j1 E _jk C _jm B _j1 D _j2 B _j2 ...E _j2 B _jl D _j1 C _j2 D _jp E _j1

解密函数F^-1取为数字混沌密码k₁，与传送数字密文信息C_A的异或运算，因混沌同步，所以k₁⊕k′₁=0,密文经混沌同步解密变成明文：The decryption function F ^-1 is taken as the digital chaotic password k ₁ , and the XOR operation with the transmitted digital ciphertext information C _A is synchronous due to chaos, so k ₁ ⊕k′ ₁ =0, and the ciphertext is decrypted into plaintext by chaotic synchronous decryption:

${M m}_{A A}^{' '} {= = F f}^{- - 11} (({C C}_{A A},, {k k}_{11}^{' '})) = = {C C}_{A A} &CirclePlus; &CirclePlus; {k k}_{11}^{' '} = = {M m}_{A A}$

我们也可以对信息M用不同的密码k_i和不同加密函数F_i连续加密，则密文为We can also continuously encrypt the information M with different passwords _ki and different encryption functions F _i , then the ciphertext is

C=b_jF_j(b_j-1...b₃F₃(b₂F₂(b₁F₁(M,k₁),k₂),k₃)...k_j)C=b _j F _j (b _j-1 ...b ₃ F ₃ (b ₂ F ₂ (b ₁ F ₁ (M,k ₁ ),k ₂ ),k ₃ )...k _j )

接收方用相反的次序和相反的方式解密Receiver decrypts in reverse order and in reverse

${M m}^{' '} = = {F f}_{11}^{- - 11} (({b b}_{11}^{- - 11} {F f}_{22}^{- - 11} (({b b}_{22}^{- - 11} {F f}_{33}^{- - 11} (({b b}_{33}^{- - 11} . . . . . . {b b}_{j j - - 11}^{- - 11} {F f}_{j j}^{- - 11} (({b b}_{j j}^{- - 11} C C,, {k k}_{j j}^{' '})) . . . . . .,, {k k}_{33}^{' '})),, {k k}_{22}^{' '})),, {k k}_{11}^{' '})) = = M m$

如连续三次对信息M加密，则密文为If the information M is encrypted three times in a row, the ciphertext is

C=b₃F₃(b₂F₂(b₁F₁(M,k₁),k₂),k₃)C=b ₃ F ₃ (b ₂ F ₂ (b ₁ F ₁ (M,k ₁ ),k ₂ ),k ₃ )

解密过程为The decryption process is

${M m}^{' '} = = {F f}_{11}^{- - 11} (({b b}_{11}^{- - 11} {F f}_{22}^{- - 11} (({b b}_{22}^{- - 11} {F f}_{33}^{- - 11} (({b b}_{33}^{- - 11} C C,, {k k}_{33}^{' '})),, {k k}_{22}^{' '})),, {k k}_{11}^{' '})) = = M m$

本混沌加密技术也可与传统非对称和对称加密技术联合使用。This chaotic encryption technology can also be used in conjunction with traditional asymmetric and symmetric encryption technologies.

在数字混沌保密通信中要用计算机程序（低级或高级语言）将上述与所述信道相连的复杂混沌网络方程数字化，或将由上述复杂混沌网络动力学方程所描述的模拟电路产生的混沌信号用模-数转换器转变成数字混沌信号，In digital chaos secure communication, computer program (low-level or high-level language) should be used to digitize the above-mentioned complex chaotic network equation connected to the channel, or the chaotic signal generated by the analog circuit described by the above-mentioned complex chaotic network dynamics equation -digital converter to convert digital chaotic signal,

上面对该发明技术的介绍仅是部分描述并不是该发明技术的全部，对任意复杂结构的混沌网络采用分布式数码耦合及分布式数码计算以产生混沌数码并按一定方式从计算混沌网络所得数码中选取混沌数码，由此数码按一定方式生成密码并按一定方式加密信息和混沌同步解密信息，且通信系统的信息发送端和信息接收端都采用密文的编码函数作为混沌网络的驱动都属于该发明技术范畴。该发明的技术和方法范围由下面的权利申请所描述而不是由前面的介绍描述，所有与权利申请内容等价的变化都被认为包含在下面权利要求之中。The above introduction to the invention technology is only a partial description and not the whole of the invention technology. For the chaotic network with any complex structure, distributed digital coupling and distributed digital calculation are used to generate chaotic numbers and are obtained from the calculation of chaotic networks in a certain way. The chaotic code is selected from the digital, and the code is generated according to a certain method, and the information is encrypted and the chaos is decrypted synchronously according to a certain method, and the information sending end and the information receiving end of the communication system both use the encoding function of the ciphertext as the driver of the chaotic network. It belongs to the technical category of the invention. The technical and method scope of the invention is described by the following claims rather than the foregoing introduction, and all changes equivalent to the content of the claims are considered to be included in the following claims.

Claims

1. the generation method of digital chaos password in the chaos security communication system, it is characterized in that the chaos security communication system comprises:

1), the communication channel between the information sending end A and the information receiving end B,

2) A digital chaotic network connected to the channel for generating chaotic digital numbers. From the digital numbers generated by the digital chaotic network, select a certain length of chaotic numbers and convert them into chaotic codes k ₁ through the password generation function g ₁ of chaotic encoding. (t), k ₁ (t)=g ₁ (X,p), where X is the digital code generated by the digital chaotic network, and p is the digital length selected from the digital chaotic network at time t; The information M transmitted in the cipher k ₁ is encrypted by the encryption function F to become the ciphertext C for transmission in the channel: C(t)=F[M(t), k ₁ (t)];

The information sender and the receiver each have chaotic networks for chaotic encryption and chaotic decryption, and the encryption or decryption passwords of one party are generated by different chaotic networks; the encryption function F _i (i=1,2) satisfies F _i F _i ^-1 = I; the digital information M is encrypted by the chaotic cipher through the F function operation and the ciphertext C passes through the channel; the channel contains digital multiplexers, modulators, demodulators, digital splitters and other digital signal processors; after being transmitted to the receiving end Through the inverse function F _i ^-1 operation, use the chaotic synchronous decryption to obtain the transmitted information M; perform information processing on the long-distance communication and received information;

The information receiving end B receives the ciphertext C from the channel, and then decrypts the ciphertext C by the chaotic code k′ ₁ through the chaotic decryption function F ⁻¹ : M′(t)=F ⁻¹ [C(t), k′ ₁ (t)]=M(t)

The chaotic password _k'1 is generated by the chaotic password generating system of the information receiving end, and the password generating system is composed of a digital chaotic network and a password generating function _g1 that generate digital numbers and are connected to the channel, _g1 will be in the same way as the receiving end The number selected from the digital chaotic network becomes the chaotic password k′ ₁ (t-τ)=g ₁ [Y(t-τ),p]

Among them, Y is the digital code generated by the chaotic network at the information receiving end, p is the digital length selected from the complex chaotic network at time t; and the chaotic code k′ ₁ at the information receiving end is chaotically synchronized with the chaotic code k ₁ at the information sending end:

\underset{t t &RightArrow; &Right Arrow; \infty \infty}{lim lim} [[{k k}_{11}^{' '} ((t t - - τ τ)) - - {k k}_{11} ((t t))]] &RightArrow; &Right Arrow; 00

The digital chaotic network in which the information sending end A is connected to the channel and the digital chaotic network in which the information receiving end B is connected to the channel has the following characteristics:

1) With the same topology and dynamic structure, driven by a common signal and the two are in a chaotic synchronous state, under the condition that the chaotic dynamics of the two network patterns are synchronized, the digital chaotic network includes a complex chaotic network, and a complex chaotic network is an arbitrary topology Structural structures, including regular networks, random networks, small-world networks, scale-free networks, and modular networks;

2) The complex chaotic network dynamics equation used by information sending terminal A to generate chaotic digital numbers is described by differential dynamics equations, iterative dynamics equations, or both differential dynamics equations and iterative dynamics equations;

The two complex chaotic networks for sending and receiving are calculated in exactly the same way to obtain chaotic synchronous digital numbers; the chaotic code is generated or decrypted from the digital chaotic network through the chaotic code generation and the chaotic encryption or decryption module of plain text:

(1) The length of the password k ₁ is one to many digits, and all the original digital B generated by the digital network have a total of Nq, where N is the number of items of the complex chaotic network equation, and q is the number of digits of the equation variable digitization; if only using The original number, then the longest password k ₁ is k ₁ =Nq; in general, a certain number of p numbers are selected randomly or regularly from the chaotic numbers generated by the chaotic network to construct the password k ₁ =g ₁ [X,p] , p≤q;

(2) Perform a series of function b _i operations on all the original numbers generated by the complex network to generate a series of new digital functions,

b ₁ (X,p ₁ ),b ₂ (X,p ₂ ),…,b _m (X,p _m ), where b _i is a polynomial function, and then select a number randomly from this series of number functions Construct password by function g ₁ : k ₁ =g ₁ [b ₁ (X,p ₁ ),b ₂ (X,p ₂ ),…b _m (X,p _m ),p], where g ₁ is random, or a regular encoding function,

(3) The password k ₁ is also generated by a certain function F(B) of the digital B generated by the complex chaotic network: k ₁ =g ₁ [F(B)],

(4) The generated chaotic code should conform to a certain code distribution, such as noise distribution, etc., and the power spectrum of the code should cover the power spectrum of the information,

(5) At the information receiving end, the generation method of the decryption code k′ ₁ is the same as the generation method of the encryption code k ₁ at the information sending end;

(6) Selecting numbers from a digital complex network or its function group means that the number selector continuously selects numbers to generate a password.

2. according to the generation method of digital chaos password in the chaos security communication system described in claim 1, it is characterized in that from the chaos number produced by the complex chaos network of the information sending end, choose different modes to choose the number in the same or different ways, press Generate chaotic codes k ₁ , k ₂ ,..., _ki ,... in the same or different ways, select codes from the chaotic codes generated by the complex chaotic network at the information receiving end according to the same rules as the information sending end, and generate decrypted chaotic codes... k′ _i ,...k′ ₂ ,k′ ₁ , where k′ _i −k _i =0.

3. the generation method of digital chaos password in the chaos secure communication system according to claim 1, it is characterized in that choosing the selector of digital structure password, the generator of password, the encryptor of information and the drive function of network from complex chaos network All devices are implemented by digital integrated circuits, including hardware description languages on logic chips or ASICs, or computer programs on signal processors.

4. the generation method of digital chaos password in the chaos secure communication system according to claim 1 is characterized in that in the chaos encryption module that chaos password is generated and plaintext, comprises:

The first register is used to accept and store the generated chaotic password k ₁ for encrypting the information M,

The second register is used to accept and store the information M to be encrypted,

The third register is used to accept and store chaotic encrypted information C,

A register is also used to store all or part of the numbers of the calculated chaotic network,

At least one selector is used to select numbers from the complex chaotic network for constructing passwords,

at least one encryption function generator, i.e. information encryption function operator,

At least one password generating function operator for generating chaotic password k ₁ is used to convert the numbers selected from the complex chaotic network into chaotic password k ₁ .

5. the generation method of digital chaos password in the chaos secure communication system according to claim 1, it is characterized in that in the generation of information receiving terminal chaos decryption password and the deciphering module of ciphertext C, comprise:

The first register is used to accept and store the generated chaotic password for decrypting ciphertext C,

The second register is used to accept and store the ciphertext C to be decrypted,

The third register is used to accept and store chaos decryption information M,

At least one selector is used to select codes from the complex chaotic network for decrypting the code,

At least one decryption function generator, that is, a ciphertext decryption function operator,

At least one password generating function operator for generating chaotic password k′ ₁ is used to change the number selected from the complex chaotic network into chaotic password k′ ₁ .

6. According to any one of claims 1-5, the generation method of the digital chaos code in the chaotic secure communication system is characterized in that the information sender and the information receiver respectively include m digital functions b ₁ (X, p ₁ ), b ₂ (X,p ₂ ),…b _m (X,p _m ) generating modules and corresponding function registers.

7. According to the generation method of the digital chaos password in the described chaos secure communication system according to one of claims 1-5, it is characterized in that the information sender and the information receiver respectively comprise the driving function generator and the corresponding driving function of complex chaotic network register.

8. According to the generation method of the digital chaos password in the described chaos secure communication system according to one of claims 1-5, it is characterized in that the mode of selecting numbers from the digital chaos network to generate the chaos password can be from the digital chaos network in a random manner. It can also be selected in the form of rules, scale freedom, small-world network, etc. The chaotic password generation function g ₁ can be a function such as random coding and regular coding of network code selection, or it can be a function of network code selection such as polynomial, etc. Function operation, and then encoding.

9. according to the generation method of digital chaos password in the described chaos secure communication system of one of claim 1-5, it is characterized in that from digital chaos network, select digital to produce the mode _g1 of chaos password to be produced by digital chaos network All digital functions.