CN115102685A - Physical layer information encryption method based on infinite dimension hyperchaos - Google Patents
Physical layer information encryption method based on infinite dimension hyperchaos Download PDFInfo
- Publication number
- CN115102685A CN115102685A CN202210708061.8A CN202210708061A CN115102685A CN 115102685 A CN115102685 A CN 115102685A CN 202210708061 A CN202210708061 A CN 202210708061A CN 115102685 A CN115102685 A CN 115102685A
- Authority
- CN
- China
- Prior art keywords
- sequence
- infinite
- infinite dimension
- length
- information
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
- H04L9/0643—Hash functions, e.g. MD5, SHA, HMAC or f9 MAC
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
Landscapes
- Engineering & Computer Science (AREA)
- Computer Security & Cryptography (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Power Engineering (AREA)
- Complex Calculations (AREA)
Abstract
The invention belongs to the technical field of information security, and particularly relates to a physical layer information encryption method based on infinite dimension hyperchaos. In order to improve the safety of data transmission in the current industrial Internet of things, when plaintext information is encrypted by using an infinite dimension hyperchaotic system, a key space can reach an infinite dimension of a theory; the invention uses the channel information between legal users as the input of the dynamic Hash key function based on the infinite dimension hyperchaos to obtain the dynamic key for encryption, thereby obtaining higher security; the invention utilizes the characteristics of the infinite dimension hyperchaotic system to generate a novel S-box, and has stronger anti-attack capability and better safety performance compared with the traditional S-box.
Description
Technical Field
The invention belongs to the technical field of information security, and particularly relates to a physical layer information encryption method based on infinite dimension hyperchaos.
Background
The 5G wireless communication era promotes the leap-type progress of various industries, and derives a plurality of new application scenes, such as industrial internet of things communication, millimeter wave communication, large-scale multiple-input multiple-output communication and the like. Information content security and privacy at wireless communication nodes is also becoming a concern. The main contribution of cryptographic algorithms is to provide a secure way to transmit or store sensitive information. At present, the traditional cryptographic technology is applied to the defense system of the industrial internet of things. Data transmission in the industrial internet of things has the characteristics of large data volume, high redundancy, strong correlation and the like, so that the reliability of some traditional cryptographic mechanisms (such as DES algorithm, ZUC algorithm, RSA algorithm and the like) can not meet the requirements any more.
The chaotic system is very suitable for digital encryption because of the characteristics of initial parameter sensitivity, randomness, ergodicity and the like. However, the conventional chaotic encryption algorithm still has many problems and disadvantages, for example, for an encryption method adopting a low-dimensional chaotic system, decoding can be performed by using a phase space reconstruction and a nonlinear prediction method. And for the chaotic system with few parameters or small parameter value range, the capability of resisting violent attack is poorer. The infinite dimension hyper-chaotic system has very complex dynamic behaviors, and has more excellent performance compared with a general chaotic system due to the infinite dimension characteristic of a theory in a parameter domain of a continuous delay interval. However, the encryption method based on the infinite-dimension hyper-chaotic system has disadvantages, such as low security of a key distribution system, and the like, and is vulnerable to selective plaintext attack or differential attack, so that data security is threatened.
Disclosure of Invention
Technical problem to be solved
The technical problem to be solved by the invention is as follows: how to provide a physical layer information encryption method based on infinite dimension hyperchaos.
(II) technical scheme
In order to solve the technical problem, the invention provides a physical layer information encryption method based on infinite dimension hyperchaos, which comprises the following steps:
step 1: by the phase of the channel of the current communication
Calculating temporary marks NN and AA with the amplitude A, and setting initial values of related parameters of the infinite dimension hyperchaotic system and Logistic mapping;
the step 1 comprises the following steps:
step 1.1: estimating the channel state between the current legal users to obtain the channel phase information
And the amplitude A, and calculating temporary marks NN and AA by formula (1);
AA＝3.8+0.2cos(A) (1)
assigning the value of NN to a parameter c in the infinite dimensional hyperchaotic system (2), and assigning the value of AA to a parameter mu in the Logistic mapping (3);
step 1.2: an infinite dimension hyper-chaotic system is adopted to generate a secret key, and the mathematical model of the secret key is expressed as follows:
wherein, a, b and c are control parameters of the infinite dimension hyperchaotic system, x, y and z are state variables of the infinite dimension hyperchaotic system, k is feedback gain, tau is delay time, the control parameters a, b, k and tau of the infinite dimension hyperchaotic attraction subsystem are given, and the parameter c is equal to NN;
generating a random number position index sequence by adopting Logistic mapping, wherein a mathematical model is represented as follows:
u n+1 ＝μu n (1-u n ) (3)
wherein u is a system state variable, subscript n represents the iteration number, mu is a control parameter, the control parameter mu of the Logistic mapping is given as AA, and an initial value u 0 Initial value x of state x of infinite dimension hyperchaotic system 0 The consistency is achieved;
step 2: generating 512-bit dynamic key DK by using dynamic Hash key function based on infinite dimension hyperchaos, wherein the dynamic Hash key function is input as lead code information S q Initial vector I 0 And step 1.2 to obtainThe output of the temporary marks NN and AA is a 512-bit key DK, wherein the preamble information S q Is a training sequence in the frame structure, the initial vector I 0 Is a binary sequence with length L agreed by the transmitting and receiving parties 1 +L 2 +L 3 ；
The step 2 comprises the following steps:
step 2.1: preamble information S q Partitioning, and mixing S q Grouping according to 128-bit binary sequences in each block, and dividing into a total
Group, where len is the total number of groups and length (. gth.) is the length of the sequence,
represents an up integer operation;
step 2.2: initial vector I 0 Are divided into lengths of L 1 、L 2 And L 3 The three binary sequences are transformed to sequentially carry out the initial value x of the hyper-chaotic system 0 ,y 0 ,z 0 Carrying out assignment by adopting the following formula (4);
x 0 ＝0.5+(I 0 (1:L 1 )) 2
y 0 ＝0.5+(I 0 (L 1 +1:L 1 +L 2 )) 2
z 0 ＝0.5+(I 0 (L 1 +L 2 +1:length(I 0 ))) 2 (4)
wherein, () 2 Representing a bitwise weighted conversion of a binary sequence to a decimal range [0,1 ]]Decimal fraction operation in between;
step 2.3: according to the parameters of the infinite dimension hyperchaotic system set in the step 1 and the initial conditions set in the step 2.2, the infinite dimension hyperchaotic system (2) evolves T 1 Time (T) 1 Sufficiently large) for the output of three sequences of system states x (T), y (T) and z (T) (T e [0, T) 1 ]) Diffusion treatment is carried out to obtain a range of [ -1,1]X ', Y ' and Z ',the state diffusion operation is shown below:
X′＝2*(x*10 8 -round(x*10 8 ))
Y′＝2*(y*10 8 -round(y*10 8 ))
Z′＝2*(z*10 8 -round(z*10 8 )) (5)
wherein round (.) represents a rounding operation;
step 2.4: giving initial value u of Logistic mapping 0 Equal to x obtained in step 2.2 0 Iterating the Logistic mapping (3) by L 1 +L 2 +L 3 Secondly, preprocessing the output sequence to obtain a position index sequence, wherein the preprocessing is as follows:
U k ＝mod(u k *10 8 ,1024) (6)
wherein, k 1 1 +L 2 +L 3 ，U k For the kth system output state u k The processed state quantity, mod (a, b) represents the remainder operation of dividing a by b;
step 2.5: selecting the positions of the state quantities X ', Y' and Z 'obtained in the step 2.3 by using the position index sequence obtained in the step 2.4, and then quantizing the values in the three sequences into binary sequences by taking symbols to obtain X' k, Y 'k and Z' k, wherein the process is shown as the following formula:
wherein sgn (.) represents the symbol-taking operation;
step 2.6, performing xor operation on the preamble information sequence in step 2.1 and the binary sequence obtained in step 2.5, as shown in the following formula:
W k ＝xor(W k ,S 1 (k))，k＝1,...,L 1 +L 2 +L 3 ， (8)
wherein xor (.) denotes a bitwise exclusive-or operation. By W k Updating the initial vector I in step 2.2 0 (ii) a To this end, S is completed q Processing of the first block;
step 2.7, looping through step 2.2 to step 2.6, when processing to the len-1 st block, i.e. processing information sequence S len-1 Stopping circulation; in the last cycle, when the system moves to step 2.4, since 512-bit key output needs to be constructed, L of step 2.4 and beyond is only used in the last operation 1 、L 2 And L 3 Value is updated to L' 1 、L′ 2 And L' 3 (L′ 1 +L′ 2 +L′ 3 512), L ' of the state quantities X ', Y ' and Z ' is selected ' 1 Bit, L' 2 L 'and L' 3 A new sequence formed by the bit states is quantized into a binary sequence and serially linked, so that a final 512-bit binary sequence is obtained and used as a dynamic key DK;
and step 3: setting an infinite dimension hyperchaotic system parameter by using the low 256 bits of the dynamic key DK obtained in the step 2, and performing label diffusion on plaintext information P after processing an output sequence of the infinite dimension hyperchaotic system parameter to obtain a ciphertext C';
the step 3 comprises the following steps:
step 3.1: converting plaintext information with any length into a one-dimensional binary plaintext data stream P;
step 3.2: and 3, assigning initial values of parameters and states of the infinite dimension hyper-chaotic system by taking the low 256 bits of the dynamic secret key DK obtained in the step 2, specifically, dividing the low 256 bits of the DK into two groups, wherein each group has 128 bits, and dividing one group into three groups, and the lengths of the three groups are L 4 、 L 5 And L 6 Then the six binary sequences are respectively applied to three control parameters a, b and c and three initial state values x of the infinite dimension hyper-chaotic system 0 、y 0 、z 0 Assigning;
step 3.3: evolves T the infinite dimension hyperchaotic system (2) 2 Time, using formula (5) to output states x (T) and y (T) of the hyper-chaotic system (T epsilon [0, T) 2 ]) Diffusion treatment is carried out to obtain a converted state quantity X' 1 And Y 1 'for state quantity X' 1 And Y 1 ' two groups of range are obtained by carrying out pretreatment as formula (9) < 0,255 >]Get the key sequence K between 1 And K 2 ；
K 1 ＝round(mod(X′ 1 (end-length(P)+1:end)*10 8 ,255))
K 2 ＝round(mod(Y 1 ′(end-length(P)+1:end)*10 8 ,255))， (9)
Where round (.) denotes a rounding operation, both key sequences are the same length as P;
step 3.4: calculating a mark value Mr and an initial ciphertext C '(1), defining a loop variable j to be 1: length (P) to represent processing a jth plaintext, and calculating the mark value Mr and the initial ciphertext C' (1) by adopting the following formula:
step 3.5, starting from the 2 nd bit plaintext, executing circular diffusion according to the following formula:
C′(i)＝bitxor(mod(P(i)+K 1 (i),256),mod(C′(i-1)+K 2 (i)+Mr*1000,256)) (11)
where i ═ 2, 3., length (p), bitxor (a, b) denotes bitxor operations in which a and b are converted into binary numbers, then bitxored, and then converted into decimal numbers, and the flag value Mr is updated once per one-bit plaintext processing as follows:
Mr＝Mr-P(i)， (12)
completing diffusion operation of all plaintext information through length (P) -1 circulation to obtain a one-dimensional ciphertext sequence C';
and 4, step 4: setting infinite dimension hyperchaotic system parameters by utilizing the high 256 bits of the dynamic key DK obtained in the step 2, and performing S-box confusion operation on the ciphertext C' after processing the output sequence of the infinite dimension hyperchaotic system parameters to obtain the encrypted ciphertext C;
the step 4 comprises the following steps:
step 4.1: dividing the high 256 bits of the dynamic key DK obtained in the step 2 into six groups of binary sequences, and dividing the six binary sequencesThe binary sequence respectively carries out three control parameters a, b and c and three state initial values x of the infinite dimension hyper-chaotic system 0 、y 0 、z 0 Assigning;
step 4.2: evolves the infinite dimension hyperchaotic system (2) by T 3 Time, using formula (5) to output states x (T), y (T) and z (T) (T E [0, T) to the hyper-chaotic system 3 ]) Diffusion treatment is carried out to obtain a state quantity X' 2 、Y′ 2 And Z' 2 . Defining M N K as the length of one-dimensional plaintext, and then taking the sequence with the length of M, N and K M N at the end of the evolution of the three states respectively to perform numerical transformation to obtain new sequences RX, RY and RZ, wherein the numerical transformation is shown as the following formula:
RX＝round(mod(X′ 2 (end-M+1:end)*10 8 ,M))
RY＝round(mod(Y′ 2 (end-N+1:end)*10 8 ,N))
RZ＝round(mod(Z′ 2 (end-(K*M*N)+1:end)*10 8 ,K*M*N)) (13)
then reforming the sequence RZ into an M N K matrix;
step 4.3: and (3) respectively arranging RX, RY and RZ obtained in the step 4.2 from large to small to obtain three groups of arranged sequences, and determining position index values of the arranged sequences to form three groups of S-boxes, namely SX, SY and SZ, as shown in the following formula:
SX＝sort(RX)
SY＝sort(RY)
SZ＝sort(RZ) (14)
wherein sort (·) represents arranging the sequence from large to small, and outputting the position index sequence of the arranged sequence, wherein SX and SY are two one-dimensional vectors with length of M and N, respectively, and their range is [1, M ] and [1, N ], because RZ is M × N × K matrix, the index value of the arrangement output is to sort K elements in M rows and N columns from large to small, so the position index matrix SZ is composed of M × N groups of elements with range of [1, K ];
step 4.4: and (3) reforming the one-dimensional ciphertext C' obtained in the step (3) into an M x N x K matrix, and performing confusion permutation operation by using the three groups of S-box obtained in the step (4.3) to obtain a confused ciphertext C, wherein the confusion permutation rule is to set a cyclic variable ii to be 1: M, jj to be 1: N, vv to be 1: K, and perform cyclic confusion permutation according to the following formula:
C(ii,jj,vv)＝C′(SX(ii),SY(jj),SZ(ii,jj,vv)) (15)
and performing M × N × K times of circular confusion permutation, and reforming the circular confusion permutation into a one-dimensional ciphertext matrix C, namely the encrypted ciphertext information.
(III) advantageous effects
In order to improve the security of data transmission in the current industrial Internet of things, the invention provides a physical layer information encryption method based on infinite-dimensional hyper-chaos, so that the security of data transmission is improved, and the capability of resisting malicious attack of an eavesdropper in a complex environment is enhanced. The invention aims to provide a physical layer information encryption method based on infinite dimension hyperchaos, and solves the problems of simple encryption process and low security of a key distribution system in the existing physical layer data transmission method of the industrial Internet of things.
Compared with the prior art, the invention has the following beneficial effects:
(1) when the infinite dimension hyperchaotic system is used for encrypting plaintext information, the key space can reach the infinite dimension of theory; (2) the invention uses the channel information between legal users as the input of the dynamic Hash key function based on the infinite dimension hyperchaos to obtain the dynamic key for encryption, thereby obtaining higher security; (3) the invention utilizes the characteristics of the infinite dimension hyperchaotic system to generate a novel S-box, and has stronger anti-attack capability and better safety performance compared with the traditional S-box.
Drawings
FIG. 1 is a general block diagram of the encryption method of the present invention;
FIG. 2 is a block diagram of infinite dimension hyperchaotic Hash-512 key generation of the encryption method of the present invention;
FIG. 3 is an attraction subgraph of an infinite dimensional hyperchaotic system of the encryption method of the present invention;
FIG. 4 is a diagram of infinite dimensional hyper-chaotic state sequence preprocessing of the encryption method of the present invention;
FIG. 5 is a "Lena" image before encryption for the encryption method of the present invention;
FIG. 6 is an encrypted "Lena" image of the encryption method of the present invention;
FIG. 7 is a pixel distribution histogram of an encrypted "Lena" image of the encryption method of the present invention;
FIG. 8 is a graph of correlation analysis of horizontally adjacent pixels before encryption by the encryption method of the present invention;
FIG. 9 is a diagram of correlation analysis of horizontally adjacent pixels after being encrypted by the encryption method of the present invention.
Detailed Description
In order to make the objects, contents, and advantages of the present invention more apparent, the following detailed description of the present invention will be made in conjunction with the accompanying drawings and examples.
In order to solve the technical problem, the invention provides a physical layer information encryption method based on infinite dimension hyperchaos, which comprises the following steps:
step 1: channel phase through current communication
Calculating temporary marks NN and AA with the amplitude A, and setting initial values of related parameters of the infinite dimension hyperchaotic system and Logistic mapping;
the step 1 comprises the following steps:
step 1.1: estimating the channel state between the current legal users to obtain the channel phase information
And the amplitude A, and calculating the temporary marks NN and AA by the formula (1);
AA＝3.8+0.2cos(A) (1)
then assigning the value of NN to a parameter c in the infinite dimension hyper-chaotic system (2), and assigning the value of AA to a parameter mu in the Logistic mapping (3);
step 1.2: an infinite dimension hyper-chaotic system is adopted to generate a secret key, and the mathematical model of the secret key is expressed as follows:
wherein, a, b and c are control parameters of the infinite dimension hyperchaotic system, x, y and z are state variables of the infinite dimension hyperchaotic system, k is feedback gain, tau is more than 0, the control parameters a, b, k and tau of the infinite dimension hyperchaotic attraction subsystem are given, and the parameter c is NN;
generating a random number position index sequence by adopting Logistic mapping, wherein a mathematical model is represented as follows:
u n+1 ＝μu n (1-u n ) (3)
wherein u is a system state variable, subscript n represents the number of iterations, μ is a control parameter, the control parameter μ of the Logistic mapping is given as AA, and an initial value u 0 Initial value x of state x of infinite dimension hyperchaotic system 0 The consistency is achieved;
step 2: generating 512-bit dynamic key DK by using dynamic Hash key function based on infinite dimension hyperchaos, wherein the dynamic Hash key function is input as lead code information S q Initial vector I 0 And the temporary marks NN and AA obtained in the step 1.2 are output as 512-bit keys DK, wherein the lead code information S q Is a training sequence in the frame structure, the initial vector I 0 Is a binary sequence with length L agreed by the transmitting and receiving parties 1 +L 2 +L 3 ；
The step 2 comprises the following steps:
step 2.1: preamble information S q Partitioning, and adding S q Grouping according to 128-bit binary sequences in each block, and dividing into a total
Group, where len is the total number of groups and length (. gth.) is the length of the sequence,
represents an integer up operation;
step 2.2: an initial vector I 0 Are divided into lengths L 1 、L 2 And L 3 The three binary sequences are transformed to sequentially carry out the initial value x of the hyper-chaotic system 0 ,y 0 ,z 0 Carrying out assignment and adopting the following formula (4) for operation;
x 0 ＝0.5+(I 0 (1:L 1 )) 2
y 0 ＝0.5+(I 0 (L 1 +1:L 1 +L 2 )) 2
z 0 ＝0.5+(I 0 (L 1 +L 2 +1:length(I 0 ))) 2 (4)
wherein, the 2 Representing the bitwise weighted conversion of binary sequences to decimal ranges [0,1 ]]Decimal fraction operation in between;
step 2.3: according to the parameters of the infinite dimension hyperchaotic system set in the step 1 and the initial conditions set in the step 2.2, the infinite dimension hyperchaotic system (2) evolves T 1 Time (T) 1 Sufficiently large) for the output of three sequences of system states x (T), y (T) and z (T) (T e [0, T) 1 ]) Diffusion treatment is carried out to obtain a range of [ -1,1]X ', Y ', and Z ' between, the state diffusion operation is represented by the following equation:
X′＝2*(x*10 8 -round(x*10 8 ))
Y′＝2*(y*10 8 -round(y*10 8 ))
Z′＝2*(z*10 8 -round(z*10 8 )) (5)
wherein round (.) represents a rounding operation;
step 2.4: giving initial value u of Logistic mapping 0 Equal to x obtained in step 2.2 0 Iterating the Logistic mapping (3) by L 1 +L 2 +L 3 Secondly, preprocessing the output sequence to obtain a position index sequence, wherein the preprocessing is as follows:
U k ＝mod(u k *10 8 ,1024) (6)
wherein, k 1 1 +L 2 +L 3 ，U k Is the k-thSystem output state u k The processed state quantity, mod (a, b) represents the remainder operation of dividing a by b;
step 2.5: selecting the positions of the state quantities X ', Y ' and Z ' obtained in the step 2.3 by using the position index sequence obtained in the step 2.4, and then quantizing the values in the three sequences into a binary sequence by taking the symbols to obtain X ″ k 、Y″ k And Z ″) k The process is shown as follows:
wherein sgn (.) represents the symbol-taking operation;
step 2.6, performing xor operation on the preamble information sequence in step 2.1 and the binary sequence obtained in step 2.5, as shown in the following formula:
W k ＝xor(W k ,S 1 (k))，k＝1,...,L 1 +L 2 +L 3 ， (8)
wherein xor (.) denotes a bitwise exclusive-or operation. By W k Updating the initial vector I in step 2.2 0 (ii) a To this end, S is completed q Processing of the first block;
step 2.7, looping through step 2.2 to step 2.6, when processing to the len-1 st block, i.e. processing information sequence S len-1 Stopping circulation; in the last cycle, when the system moves to step 2.4, since 512-bit key output needs to be constructed, L of step 2.4 and beyond is only used in the last operation 1 、L 2 And L 3 Value is updated to L' 1 、L′ 2 And L' 3 (L′ 1 +L′ 2 +L′ 3 512), L ' of the state quantities X ', Y ' and Z ' is selected ' 1 Bit, L' 2 L 'and L' 3 A new sequence formed by the bit states is quantized into a binary sequence and serially linked, so that a final 512-bit binary sequence is obtained and used as a dynamic key DK;
and step 3: setting an infinite dimension hyperchaotic system parameter by using the low 256 bits of the dynamic key DK obtained in the step 2, and performing label diffusion on plaintext information P after processing an output sequence of the infinite dimension hyperchaotic system parameter to obtain a ciphertext C';
the step 3 comprises the following steps:
step 3.1: converting plaintext information with any length into a one-dimensional binary plaintext data stream P;
step 3.2: and (3) assigning initial values of parameters and states of the infinite dimension hyper-chaotic system by taking the low 256 bits of the dynamic key DK obtained in the step (2), specifically, dividing the low 256 bits of the DK into two groups, each group has 128 bits, dividing one group into three groups, and respectively setting the length of each group as L 4 、 L 5 And L 6 Then the six binary sequences are respectively applied to three control parameters a, b and c and three initial state values x of the infinite dimension hyper-chaotic system 0 、y 0 、z 0 Assigning;
step 3.3: evolves the infinite dimension hyperchaotic system (2) by T 2 Time, using formula (5) to output states x (T) and y (T) of the hyper-chaotic system (T epsilon [0, T) 2 ]) Diffusion treatment is carried out to obtain a converted state quantity X' 1 And Y' 1 To state quantity X' 1 And Y 1 ' two groups of pretreatment are carried out according to the formula (9) and are in the range of [0,255]Get the key sequence K between 1 And K 2 ；
K 1 ＝round(mod(X′ 1 (end-length(P)+1:end)*10 8 ,255))
K 2 ＝round(mod(Y 1 ′(end-length(P)+1:end)*10 8 ,255))， (9)
Wherein round (.) represents a rounding operation, and both key sequences are the same length as P;
step 3.4: calculating a mark value Mr and an initial ciphertext C '(1), defining a loop variable j to be 1: length (P) to represent processing a jth plaintext, and calculating the mark value Mr and the initial ciphertext C' (1) by adopting the following formula:
step 3.5, starting from the 2 nd bit plaintext, executing circular diffusion according to the following formula:
C′(i)＝bitxor(mod(P(i)+K 1 (i),256),mod(C′(i-1)+K 2 (i)+Mr*1000,256)) (11)
where i ═ 2, 3., length (p), bitxor (a, b) denotes that a and b are converted into binary numbers, then xor by bit, and then further converted into decimal number, and the flag value Mr is updated once per one-bit plaintext processing according to the following formula:
Mr＝Mr-P(i)， (12)
completing diffusion operation of all plaintext information through length (P) -1 circulation to obtain a one-dimensional ciphertext sequence C';
and 4, step 4: setting infinite dimension hyperchaotic system parameters by utilizing the high 256 bits of the dynamic key DK obtained in the step 2, and performing S-box confusion operation on the ciphertext C' after processing the output sequence of the infinite dimension hyperchaotic system parameters to obtain the encrypted ciphertext C;
the step 4 comprises the following steps:
step 4.1: dividing the high 256 bits of the dynamic key DK obtained in the step 2 into six groups of binary sequences, and respectively carrying out three control parameters a, b and c and three state initial values x on the infinite dimension hyper-chaotic system by using the six binary sequences 0 、y 0 、z 0 Assigning;
step 4.2: evolves the infinite dimension hyperchaotic system (2) by T 3 Time, using formula (5) to output states x (T), y (T) and z (T) (T E [0, T) to the hyper-chaotic system 3 ]) Diffusion treatment is carried out to obtain a state quantity X' 2 、Y′ 2 And Z' 2 . Defining M N K as the length of one-dimensional plaintext, and then taking the sequence with the length of M, N and K M N at the end of the evolution of the three states respectively to perform numerical transformation to obtain new sequences RX, RY and RZ, wherein the numerical transformation is shown as the following formula:
RX＝round(mod(X′ 2 (end-M+1:end)*10 8 ,M))
RY＝round(mod(Y′ 2 (end-N+1:end)*10 8 ,N))
RZ＝round(mod(Z′ 2 (end-(K*M*N)+1:end)*10 8 ,K*M*N)) (13)
then reforming the sequence RZ into an M N K matrix;
step 4.3: and (3) respectively arranging RX, RY and RZ obtained in the step 4.2 from large to small to obtain three groups of arranged sequences, and determining position index values of the arranged sequences to form three groups of S-boxes, namely SX, SY and SZ, as shown in the following formula:
SX＝sort(RX)
SY＝sort(RY)
SZ＝sort(RZ) (14)
wherein sort (·) represents arranging the sequence from large to small, and outputting the position index sequence of the arranged sequence, wherein SX and SY are two one-dimensional vectors with length of M and N, respectively, and their range is [1, M ] and [1, N ], because RZ is M × N × K matrix, the index value of the arrangement output is to sort K elements in M rows and N columns from large to small, so the position index matrix SZ is composed of M × N groups of elements with range of [1, K ];
step 4.4: and (3) reforming the one-dimensional ciphertext C' obtained in the step (3) into an M x N x K matrix, and performing confusion permutation operation by using the three groups of S-box obtained in the step (4.3) to obtain a confused ciphertext C, wherein the confusion permutation rule is to set a cyclic variable ii to be 1: M, jj to be 1: N, vv to be 1: K, and perform cyclic confusion permutation according to the following formula:
C(ii,jj,vv)＝C′(SX(ii),SY(jj),SZ(ii,jj,vv)) (15)
and performing M × N × K times of circular confusion permutation, and reforming the circular confusion permutation into a one-dimensional ciphertext matrix C, namely the encrypted ciphertext information.
Example 1
In this embodiment, referring to fig. 1 and fig. 2, a general design block diagram of the encryption method and a Hash-512 key generation block diagram based on the infinite dimensional hyper-chaos are respectively shown, and the method is specifically implemented according to the following steps:
the method is implemented according to the following steps:
step 1.1, estimating the channel state between the current legal users to obtain the channel phase information
And amplitude A, and calculating temporary marks NN and AA by (1),
AA＝3.8+0.2cos(A)， (1)
then assigning the value of NN to the parameter c of the infinite dimension hyper-chaotic system (2), and assigning the value of AA to the parameter mu of the Logistic mapping (3);
in the embodiment, the channel state between the current legal users is estimated by a channel estimation method to obtain the phase information of the current legal users
The amplitude information a is 0.7735, and the temporary markers NN 19.3090 and AA 3.9431 are calculated according to equation (1), and then are respectively assigned to the parameter c of the infinite dimensional hyper-chaotic system and the parameter μ of the Logistic map, i.e., c is 19.3090 and μ is 3.9431.
Step 1.2, generating a secret key by adopting an infinite dimension hyper-chaotic system, wherein a mathematical model of the secret key is expressed as follows:
wherein a, b and c are control parameters of the system, x, y and z are state variables of the system, k is feedback gain, tau is delay time, the control parameters a, b, k and tau of the infinite dimension hyperchaotic attraction subsystem are given, and the parameter c is NN;
in the embodiment, the infinite dimension hyper-chaotic system parameters a is set to 35, b is set to 3, c is set to 19.3090, k is set to 3.8, and τ is set to 0.3, and the chaotic system dynamics behaves as a composite multi-scroll attractor as shown in fig. 3.
Generating a random number position index sequence by adopting Logistic mapping, wherein a mathematical model is represented as follows:
u n+1 ＝u n μ(1-u n )， (3)
wherein u is a system state variable, subscript n represents the iteration number, mu is a control parameter, the control parameter mu of the Logistic mapping is given as AA, and an initial value u 0 Initial value x of state x of infinite dimension hyperchaotic system 0 The consistency is achieved;
in this embodiment, u is 3.9431, and the initial value u of the state 0 ＝0.5217。
Step 2.1, lead code information S q Partitioning, and mixing S q Grouping according to 128-bit binary sequences in each block, and dividing into a total
Group, where len is the total number of groups and length (. eta.) is the length of the sequence,
represents an integer up operation;
in an embodiment, S is set q The sequences are 2048-bit binary sequences, which are divided into len-16 groups, each group being a 128-bit binary sequence.
Step 2.2, initial vector I 0 Are divided into lengths L 1 、L 2 And L 3 The three binary sequences are transformed to sequentially carry out the initial stage of the hyper-chaotic systemValue x 0 ,y 0 ,z 0 The assignment is carried out by adopting the following formula,
x 0 ＝0.5+(I 0 (1:L 1 )) 2
y 0 ＝0.5+(I 0 (L 1 +1:L 1 +L 2 )) 2
z 0 ＝0.5+(I 0 (L 1 +L 2 +1:length(I 0 ))) 2 ， (4)
wherein, () 2 Representing the bitwise weighted conversion of binary sequences to decimal ranges [0,1 ]]Decimal operation in between;
in an embodiment, an initial vector I is set 0 Is a binary sequence with length of 128 bits, which is divided into L lengths 1 ＝42、L 2 42 and L 3 44, and then calculating an initial value of the infinite-dimensional hyper-chaotic system according to the formula (4) to obtain x 0 ＝0.5217、y 0 0.5861 and z 0 ＝0.5175。
Step 2.3, according to the parameters of the infinite dimension hyperchaotic system set in the step 1 and the initial conditions set in the step 2.2, the infinite dimension hyperchaotic system (2) evolves T 1 Time (T) 1 Sufficiently large) for the output of three sequences of system states x (T), y (T) and z (T) (T e [0, T) 1 ]) Diffusion treatment is carried out to obtain the product with the range of [ -1,1]X ', Y ', and Z ' between, the state diffusion operation is represented by the following equation:
X′＝2*(x*10 8 -round(x*10 8 ))
Y′＝2*(y*10 8 -round(y*10 8 ))
Z′＝2*(z*10 8 -round(z*10 8 ))， (5)
where round (.) represents a rounding operation;
in the embodiment, the infinite dimension hyperchaotic system (2) is evolved T by using the parameters set in the step 1 and the step 2.2 1 ＝1024/f s Time of which f s ＝4*10 7 For the system sampling frequency, then [0, T ] is paired using equation (5) 1 ]The system states x (t), y (t) and z (t) of time are diffusedThe processed state quantities X ', Y ' and Z ' are mapped in the phase space shown in FIG. 4. comparing FIG. 3, it is clear that the system output state is completely diffused to the range of [ -1,1 [ -1 [ ]]The phase space of (a).
Step 2.4, giving initial value u of Logistic mapping 0 Equal to x obtained in step 2.2 0 Iterating the Logistic mapping (3) by L 1 +L 2 +L 3 Secondly, preprocessing the output sequence to obtain a position index sequence, wherein the preprocessing is as follows:
U k ＝mod(u k *10 8 ,1024)， (6)
wherein, k is 1 1 +L 2 +L 3 ，U k For the kth system output state u k The processed state quantity, mod (a, b) represents the remainder operation of dividing a by b;
in an embodiment, a Logistic mapping parameter u is set 0 Iterating the Logistic map by L-0.5217 and μ -3.9431 1 +L 2 +L 3 Calculating the output state according to equation (6) to obtain a position index sequence U with a length of 128 bits 128 times k 。
Step 2.5, the position index sequence obtained in step 2.4 is used for selecting the positions of the state quantities X ', Y ' and Z ' obtained in step 2.3, and then the values in the three sequences are quantized into a binary sequence by taking the symbols to obtain X ″ k 、Y″ k And Z ″) k The process is shown as follows:
wherein sgn (.) represents a sign-taking operation;
in an embodiment, the three groups of state quantities X ', Y ' and Z ' obtained in step 2.3 are indexed according to the position index sequence U k Selecting the position according to formula (7) and converting the element into a binary number to obtain a length L 1 +L 2 +L 3 Binary sequence W k 。
Step 2.6, performing xor operation on the preamble information sequence in step 2.1 and the binary sequence obtained in step 2.5, as shown in the following formula:
W k ＝xor(W k ,S 1 (k))，k＝1,...,L 1 +L 2 +L 3 ， (8)
wherein xor (.) denotes a bitwise exclusive-or operation. This sequence is used to update the initial vector I in step 2.2 0 . To this end, S is completed q Processing of the first block;
in the examples, take S in step 2.1 q The first block of (2) is divided into three groups of sequences with the lengths of 42 bits, 42 bits and 44 bits, and the three groups of sequences are respectively subjected to exclusive OR operation with the binary sequence obtained in the step 2.5 bit by bit, as shown in the formula (8), so that a new 128-bit binary sequence is obtained as an exclusive OR operation result and is used for updating and replacing the vector I in the step 2.2 0 。
Step 2.7, looping through step 2.2 to step 2.6, when processing to the len-1 st block, i.e. processing information sequence S len-1 The cycle is stopped. In the last cycle, when the system moves to step 2.4, since 512-bit key output needs to be constructed, L of step 2.4 and beyond is only used in the last operation 1 、L 2 And L 3 Value is updated to L' 1 、L′ 2 And L' 3 (L′ 1 +L′ 2 +L′ 3 512) to obtain a final binary sequence of 512 bits as the dynamic key DK;
in an embodiment, the loop is performed in steps 2.2 to 2.6, each loop processing the preamble information S q Together, len-1 cycles. At the last cycle, L 'is updated as the system moves to step 2.4' 1 ＝170、L′ 2 170 and L' 3 172, a position index sequence U with a length of 512 bits is obtained k . And 2.5, executing the step to obtain a 512-bit binary sequence, namely the output dynamic key sequence DK.
step 3.1, converting the plaintext information with any length into a one-dimensional binary plaintext data stream P;
in the embodiment, 352 × 3 "Lena" image information is taken as information, and is converted into a binary one-dimensional plaintext data stream P with a length of 371712.
Step 3.2, assigning initial values of parameters and states of the infinite dimension hyper-chaotic system by taking the low 256 bits of the dynamic secret key DK obtained in the step 2, specifically, dividing the low 256 bits of the DK into two groups, each group has 128 bits, dividing one group into three groups, and the length of each group is L 4 、 L 5 And L 6 Then the six binary sequences are respectively applied to three control parameters a, b and c and three initial state values x of the infinite dimension hyper-chaotic system 0 、y 0 、z 0 Assigning;
in the embodiment, the low 256 bits of the dynamic key DK obtained in step 2 are taken and divided into two large groups of 128 bits, and each large group is divided into three small groups, and L is taken 4 ＝42、L 5 42 and L 6 44 is the sequence length of the three groups, and the six groups of binary sequences are assigned corresponding to the parameters and initial values of the infinite-dimensional hyper-chaotic system, which is specifically shown as the following formula:
wherein, the 2 Representing the bitwise weighted conversion of binary sequences to decimal ranges [0,1 ]]And performing decimal operation, and then adding two system parameters of k being 3.8 and tau being 0.26 to complete the setting of the infinite dimension hyperchaotic system parameters and the initial values.
Step 3.3, evolving the infinite dimension hyperchaotic system (2) to T 2 Time, using formula (5) to output states x (T) and y (T) of the hyper-chaotic system (T epsilon [0, T) 2 ]) Diffusion treatment is carried out to obtain a converted state quantity X' 1 And Y' 1 To state quantity X' 1 And Y' 1 Carrying out pretreatment as formula (9) to obtain two groups of ranges of [0,255 ]]Get the key sequence K between 1 And K 2 ，
K 1 ＝round(mod(X′ 1 (end-length(P)+1:end)*10 8 ,255))
K 2 ＝round(mod(Y 1 ′(end-length(P)+1:end)*10 8 ,255))， (10)
Where round (.) denotes a rounding operation, both key sequences are the same length as P;
in the embodiment, the infinite dimension hyper-chaotic system (2) T is evolved by using the system parameters and the initial values in the step 3.2 2 ＝512/f s Time of which f s ＝4*10 7 Outputting the state sequences x (T) and y (T) (T epsilon [0, T) to the system 2 ]) Is processed according to the formula (4) to obtain a state quantity X' 1 And Y 1 ' then, two sets of the state quantities are calculated from equation (10) to have a length of 371712 and a range of [0,255 ]]Key K of 1 And K 2 。
Step 3.4, calculating the mark value Mr and the initial ciphertext C '(1), defining a loop variable j as 1: length (p) to represent processing the jth plaintext, and calculating the mark value Mr and the initial ciphertext C' (1) by using the following formula:
in the embodiment, the flag value Mr of 47575010 and C' (1) of 128 are calculated by equation (11) based on the plaintext data stream P obtained in step 3.1.
Step 3.5, starting from the 2 nd bit plaintext, performing circular diffusion according to the following formula:
C′(i)＝bitxor(mod(P(i)+K 1 (i),256),mod(C′(i-1)+K 2 (i)+Mr*1000,256))， (12)
where i ═ 2, 3., length (p), bitxor (a, b) denotes bitxor operations in which a and b are converted into binary numbers, then bitxored, and then converted into decimal numbers, and the flag value Mr is updated once per one-bit plaintext processing as follows:
Mr＝Mr-P(i)， (13)
completing diffusion operation of all plaintext information through length (P) -1 circulation to obtain a one-dimensional ciphertext sequence C';
in the embodiment, the tag value C' (1) obtained in step 3.4 and the one-dimensional plaintext sequence P in step 3.1 are used to perform cyclic diffusion according to equations (12) and (13), and the tag value is updated once each time one-bit plaintext information is performed, so that the coupling degree between the current-bit ciphertext and all plaintext information is improved, and the current-bit ciphertext and all plaintext information have high correlation.
step 4.1, dividing the high 256 bits of the dynamic secret key DK obtained in the step 2 into six groups of binary sequences, and respectively carrying out three control parameters a, b and c and three state initial values x on the infinite dimension hyper-chaotic system by the six binary sequences 0 、y 0 、z 0 Assigning;
in the embodiment, 256 high bits of the dynamic key DK obtained in step 2 are taken and grouped, and the three control parameters and the three state initial values of the infinite dimension hyper-chaotic system are assigned by using the divided six groups of binary sequence application formulas (9), and the parameters k and τ are two system parameters of 3.8 and 0.26, so as to complete the setting of the parameters and the initial values of the infinite dimension hyper-chaotic system.
Step 4.2, evolving the infinite dimension hyperchaotic system (2) by T 3 Time, using the formula (5) to output the states x (T), y (T) and z (T) (T E [0, T) 3 ]) Diffusion treatment is carried out to obtain a state quantity X' 2 、Y′ 2 And Z' 2 . Defining M N K as the length of one-dimensional plaintext, and then taking the sequence with the length of M, N and K M N at the end of the evolution of the three states respectively to perform numerical transformation to obtain new sequences RX, RY and RZ, wherein the numerical transformation is shown as the following formula:
RX＝round(mod(X′ 2 (end-M+1:end)*10 8 ,M))
RY＝round(mod(Y′ 2 (end-N+1:end)*10 8 ,N))
RZ＝round(mod(Z′ 2 (end-(K*M*N)+1:end)*10 8 ,K*M*N))， (14)
then reforming the sequence RZ into an M N K matrix;
in the embodiment, the system parameters and the initial values obtained in the step 4.1 are utilized to evolve the infinite dimension hyper-chaotic system (2) T 3 ＝4*10 6 /f s Time, the sequence of states x (T), y (T), and z (T) (T e [0, T) 3 ]) Diffusion treatment is carried out to obtain a state quantity X' 2 、Y′ 2 And Z' 2 Since the "Lena" diagram used in the embodiment is 352 × 3, M, N, and K are taken as 352, and 3, and then the numerically-converted new sequences RX, RY, and RZ are calculated according to equation (14), and then RZ is reformed into a matrix of 352 × 3.
Step 4.3, obtaining three groups of arranged sequences by respectively arranging RX, RY and RZ obtained in step 4.2 from large to small, and determining position index values of the arranged sequences to form three groups of S-boxes, namely SX, SY and SZ, as shown in the following formula:
SX＝sort(RX)
SY＝sort(RY)
SZ＝sort(RZ)， (15)
wherein sort (·) represents a position index sequence in which sequences are arranged from large to small, and the position index sequence is output after the sequences are arranged, wherein SX and SY are one-dimensional vectors with lengths of M and N respectively and ranges of [1, M ] and [1, N ], and as RZ is an M x N x K matrix, the index values output by the arrangement are arranged by sequencing K elements in N columns of M rows from large to small, so that the position index matrix SZ is formed by M x N groups of elements with ranges of [1, K ];
in the embodiment, the new sequences RX, RY and RZ with the lengths of 352, 352 and 352 × 3 obtained in step 4.2 are arranged from large to small, and the position change index sequence of the arranged matrix is taken out as the S-box of the permutation operation, so as to obtain three groups of S-boxes, namely SX, SY and SZ, wherein SX and SY are both one-dimensional matrices with the length of 352 and the range of [1,352], SZ is formed by 352 × 352 groups of short sequences, and the short sequence elements are all [1,2,3] in different arrangements.
And 4.4, reforming the one-dimensional ciphertext C' obtained in the step 3 into an M × N × K matrix, and performing confusion permutation operation by using the three groups of S-boxes obtained in the step 4.3 to obtain a confused ciphertext C, wherein the confusion permutation rule is to set a cyclic variable ii to be 1: M, jj to be 1: N, vv to be 1: K, and perform cyclic confusion permutation according to the following formula:
C(ii,jj,vv)＝C′(SX(ii),SY(jj),SZ(ii,jj,vv))， (16)
performing M × N × K times of circular confusion replacement, and reforming the circular confusion replacement into a one-dimensional ciphertext matrix C, namely the encrypted ciphertext information;
in the embodiment, the one-dimensional ciphertext C' obtained in step 3 is reformed into a 352 × 3 matrix, and then the three groups of S-boxes obtained in step 4.3 are used to perform obfuscating and replacing operations on the matrix, wherein each time the obfuscating and replacing operation is performed according to the calculation of the formula (16), 371712 times of cycles are performed, and finally, the obfuscating and replacing operation on the "Lena" graph is completed.
The invention relates to a physical layer information encryption method based on infinite dimension hyperchaos, which is used for performance test and analysis and specifically comprises the following parts:
firstly, analyzing encryption and decryption effects;
analyzing the S-box performance based on infinite dimension hyperchaotic;
thirdly, key space analysis;
NIST randomness test of the key stream DK;
analyzing the statistical attack resistance;
sixthly, information entropy analysis;
seventhly, analyzing differential attack;
to prove the universality of the invention, the test images are all selected from an international standard test image library.
Encryption and decryption effect analysis
Selecting a "Lena" graph (352 x 3) to perform encryption and decryption tests, as shown in fig. 5 and 6; FIG. 5 shows a "Lena" image before encryption, and FIG. 6 shows an encrypted image after encryption, so that it can be seen that the encrypted image information is similar to noise, and the original image information is well hidden; fig. 7 is a histogram of the encrypted image, which can be seen to be uniformly distributed, not showing any information of the original image. These are sufficient to demonstrate that the proposed image encryption algorithm is effective against statistical attacks.
S-box performance analysis based on infinite dimension hyperchaos
To simulate the proposed S-box generation mechanism, a processor with Intel core i5-7500 quad-core 3.4GHz and an 8GBRAM computer was used, MATLAB version R2016 b. And (3) evolving the infinite dimension hyperchaotic system for a period of time, and performing calculation analysis on the S-box with the length of 256 generated by the system, wherein the S-box comprises a plurality of characteristics such as bit independence, nonlinearity, strict avalanche property, linear and differential approximate probability and the like, and the comparison result is shown in table 1. As can be seen from the data in Table 1, the S-box generated based on the infinite-dimensional hyper-chaotic system has good performance.
TABLE 1S-box Performance based on infinite dimensional hyper-chaos
Key space analysis
If only 5 parameters (a, b, c, k, tau) and three initial values (x) of the infinite dimension hyper-chaotic system are used 0 ，y 0 ，z 0 ) When used as a key, the formed key space is 2 47×8 ＝2 376 (calculation accuracy 10) -15 ) (ii) a If the infinite dimension hyperchaotic system is in [ -tau, 0 [ -tau]The initial condition above also acts as a key, the key space will expand to an infinite dimension. Thus, the key space of the proposed image encryption algorithm is resistant to any brute force attacks.
NIST randomness test of keystream DK
The analysis is a statistical package provided by the national institute of standards and technology for determining non-randomness that may occur in the sequence. To ensure the randomness of the keystream used, the generated key DK was tested by NIST SP 800-22 using the proposed Hash-512 function. Test input 10 6 Bit key stream data, performing key stream14 basic tests have P values of 0,1]When the P value is higher than the threshold β of 0.01, this means that the sequence passes this test. Table 2 shows the results of the tests, and it can be seen that the keystream used has good randomness.
TABLE 2 Standard NIST SP 800-22 randomness test results
Statistical attack resistant analysis
Each set of picture data has R, G and B three channels, each of which is considered a grayscale image. In normal images, each pixel has a high degree of correlation with its neighboring pixels, the correlation coefficient C xy Close to 1 in each direction (horizontal, vertical and diagonal), and the correlation coefficient C of each direction of the image after being encrypted by a well-performing encryption algorithm xy Should be close to 0, this also indicates that the encryption algorithm conceals the plaintext information and has a high degree of homogenization. We randomly choose 1 ten thousand pairs of neighboring pixels in each direction to compute the pixel correlation coefficient in the encrypted picture and the correlation coefficient of the original picture. The neighboring pixel correlation calculation is expressed as:
wherein
N denotes the total number of adjacent pixel pairs in each direction, x i And y i Is the value of the adjacent pixel or pixels,
and
the mean value thereof is shown. Taking the "Lena" image before encryption to draw a horizontal direction correlation graph as shown in fig. 8, it can be seen that the values of the original image are substantially distributed on the diagonal lines of the graph, which shows that the correlation of the adjacent pixel values is close no matter in that direction. The horizontal direction correlation diagram of the encrypted image is shown in fig. 9, and the pixel values of the encrypted image are uniformly dispersed in the space, which shows that the adjacent pixels are almost irrelevant after encryption. The test results demonstrate that the encryption algorithm removes the correlation between the original image pixels, avoiding the possibility of attempting to crack the information from that perspective. Table 3 shows the calculation results of the correlation coefficients of the three directions and the three channels before and after encrypting 5 groups of pictures with different sizes in the standard test image library, and it can be seen that each correlation coefficient before encryption is close to 1, and the correlation coefficient after encryption is near 0, which indicates that the image pixels are almost irrelevant in each direction, thereby effectively concealing the original information of the image. Therefore, by analyzing the correlation of neighboring pixels, no useful information about the original picture can be obtained.
TABLE 3 Adjacent Pixel dependencies of test plots before and after encryption
Information entropy analysis
The randomness and unpredictability of the information can be represented by the entropy of the information. The larger the information entropy, the larger the randomness and the higher the security. The mathematical formula of the information entropy is as follows:
where p (L) is the probability of the occurrence of a pixel value of L, and L is the number of gray levels of the pixel. In general, when the number of gray levels of an image is 256, an ideal entropy value is 8 (uniform distribution). Table 4 gives the entropy of the information before and after encrypting the image information, close to the ideal value of 8. Therefore, the algorithm of the invention has good randomness and high safety.
TABLE 4 information entropy of test plots before and after encryption
Analysis against differential attacks
The pixel Number change rate (NPCR) and the normalized average changed intensity (UACI) can well measure the sensitivity of an image encryption algorithm to an original plaintext image and effectively analyze differential attacks. When only one pixel value of two original plaintext image information is different, if the pixel values of their encrypted image information at (i, j) points are respectively represented by C 1 (i, j) and C 2 (i, j), then NPCR and UACI can be calculated as follows:
for an image with a gray scale of 256(v ═ 8), the ideal expectation values for NPCR and UACI are 99.6094% and 33.4635%. For the test of the invention, 1 pixel point is randomly selected from the original plaintext image and the pixel value is changed, the plaintext image and the changed image are encrypted, and the NPCR and UACI values are calculated. The results obtained after averaging the NPCR and UACI values over 150 tests are shown in table 5. From the results in Table 5, it can be seen that both NPCR and UACI values are very close to the ideal. Therefore, the information encryption algorithm has strong differential attack resistance.
TABLE 5 test results (%) of NPCR and UACI
The invention relates to a physical layer information encryption method based on infinite dimension hyperchaotic, which utilizes an infinite dimension hyperchaotic system to encrypt information, and a key space can reach the theoretical infinity; the encryption scheme uses the unique channel information between legal channels as the input of the Hash-512 function, so that a dynamic key stream is obtained, and the information security is effectively improved; a new S-box is constructed by utilizing the infinite dimension hyperchaotic system and is used for data confusion operation, and the S-box has better confusion performance and improves the encryption safety performance; the infinite-dimension hyperchaotic system is utilized to combine the label diffusion and the novel S-box confusion operation, and the method has stronger anti-attack capability and better safety performance.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (10)
1. A physical layer information encryption method based on infinite dimension hyperchaos is characterized by comprising the following steps:
step 1: channel phase through current communication
Calculating temporary marks NN and AA with the amplitude A, and setting initial values of related parameters of the infinite dimension hyperchaotic system and Logistic mapping;
the step 1 comprises the following steps:
step 1.1:estimating the channel state between the current legal users to obtain the channel phase information
And the amplitude A, and calculating the temporary marks NN and AA by the formula (1);
AA＝3.8+0.2cos(A) (1)
then assigning the value of NN to a parameter c in the infinite dimension hyper-chaotic system (2), and assigning the value of AA to a parameter mu in the Logistic mapping (3);
step 1.2: an infinite dimension hyperchaotic system is adopted to generate a secret key, and the mathematical model of the secret key is expressed as follows:
wherein, a, b and c are control parameters of the infinite dimension hyperchaotic system, x, y and z are state variables of the infinite dimension hyperchaotic system, k is feedback gain, tau is delay time, the control parameters a, b, k and tau of the infinite dimension hyperchaotic attraction subsystem are given, and the parameter c is equal to NN;
generating a random number position index sequence by using Logistic mapping, wherein a mathematical model is represented as follows:
u n+1 ＝μu n (1-u n ) (3)
wherein u is a system state variable, subscript n represents the iteration number, mu is a control parameter, the control parameter mu of the Logistic mapping is given as AA, and an initial value u 0 Initial value x of state x of infinite dimension hyperchaotic system 0 The consistency is achieved;
step 2: generating 512-bit dynamic key DK by using dynamic Hash key function based on infinite dimension hyperchaos, wherein the dynamic Hash key function is input as lead code information S q Initial vector I 0 And the temporary marks NN and AA obtained in step 1.2, the output is a 512-bit key DKIn (3), preamble information S q Is a training sequence in the frame structure, the initial vector I 0 Is a binary sequence with length L agreed by the transmitting and receiving parties 1 +L 2 +L 3 ；
The step 2 comprises the following steps:
step 2.1: preamble information S q Partitioning, and mixing S q Grouping according to 128-bit binary sequences in each block, and dividing into a total
Group, where len is the total number of groups and length (. gth.) is the length of the sequence,
represents an integer up operation;
step 2.2: initial vector I 0 Are divided into lengths L 1 、L 2 And L 3 The three binary sequences are transformed to sequentially carry out the initial value x of the hyper-chaotic system 0 ,y 0 ,z 0 Carrying out assignment by adopting the following formula (4);
x 0 ＝0.5+(I 0 (1:L 1 )) 2
y 0 ＝0.5+(I 0 (L 1 +1:L 1 +L 2 )) 2
z 0 ＝0.5+(I 0 (L 1 +L 2 +1:length(I 0 ))) 2 (4)
wherein, () 2 Representing the bitwise weighted conversion of binary sequences to decimal ranges [0,1 ]]Decimal fraction operation in between;
step 2.3: according to the parameters of the infinite dimension hyperchaotic system set in the step 1 and the initial conditions set in the step 2.2, the infinite dimension hyperchaotic system (2) evolves T 1 Time (T) 1 Sufficiently large) for the output of three sequences of system states x (T), y (T) and z (T) (T e [0, T) 1 ]) Diffusion treatment is carried out to obtain a range of [ -1,1]The state quantities X ', Y ', and Z ' therebetween, the state diffusion operation is represented by the following formula:
X′＝2*(x*10 8 -round(x*10 8 ))
Y′＝2*(y*10 8 -round(y*10 8 ))
Z′＝2*(z*10 8 -round(z*10 8 )) (5)
wherein round (.) represents a rounding operation;
step 2.4: giving initial value u of Logistic mapping 0 Equal to x obtained in step 2.2 0 Iterating the Logistic mapping (3) by L 1 +L 2 +L 3 Secondly, preprocessing the output sequence to obtain a position index sequence, wherein the preprocessing is as follows:
U k ＝mod(u k *10 8 ,1024) (6)
wherein, k 1 1 +L 2 +L 3 ，U k For the kth system output state u k The processed state quantity, mod (a, b) represents the remainder operation of dividing a by b;
step 2.5: selecting the positions of the state quantities X ', Y ' and Z ' obtained in the step 2.3 by using the position index sequence obtained in the step 2.4, and then quantizing the values in the three sequences into a binary sequence by taking the symbols to obtain X ″ k 、Y″ k And Z ″) k The process is shown as the following formula:
wherein sgn (.) represents a sign operation;
step 2.6, performing xor operation on the preamble information sequence in step 2.1 and the binary sequence obtained in step 2.5, as shown in the following formula:
W k ＝xor(W k ,S 1 (k))，k＝1,...,L 1 +L 2 +L 3 ， (8)
wherein xor (.) represents a bitwise exclusive-or operation; by W k Update initial vector I in step 2.2 0 (ii) a To this end, S is completed q Processing of the first block;
step 2.7, go to step according to step 2.2Step 2.6 Loop, when processing to the len-1 st Block, i.e. processing the information sequence S len-1 Stopping circulation; in the last cycle, when the system moves to step 2.4, since 512-bit key output needs to be constructed, L of step 2.4 and beyond is only used in the last operation 1 、L 2 And L 3 Value is updated to L' 1 、L′ 2 And L' 3 (L′ 1 +L′ 2 +L′ 3 512), L ' of the state quantities X ', Y ' and Z ' is selected ' 1 Bit and L' 2 L 'and L' 3 A new sequence formed by the bit states is quantized into a binary sequence and is serially linked, so that a final 512-bit binary sequence is obtained and is used as a dynamic key DK;
and step 3: setting an infinite dimension hyperchaotic system parameter by using the low 256 bits of the dynamic key DK obtained in the step 2, and performing label diffusion on plaintext information P after processing an output sequence of the infinite dimension hyperchaotic system parameter to obtain a ciphertext C';
the step 3 comprises the following steps:
step 3.1: converting plaintext information with any length into a one-dimensional binary plaintext data stream P;
step 3.2: and (3) assigning initial values of parameters and states of the infinite dimension hyper-chaotic system by taking the low 256 bits of the dynamic key DK obtained in the step (2), specifically, dividing the low 256 bits of the DK into two groups, each group has 128 bits, dividing one group into three groups, and respectively setting the length of each group as L 4 、L 5 And L 6 Then the six binary sequences are respectively applied to three control parameters a, b and c and three initial state values x of the infinite dimension hyper-chaotic system 0 、y 0 、z 0 Assigning;
step 3.3: evolves the infinite dimension hyperchaotic system (2) by T 2 Time, using formula (5) to output states x (T) and y (T) of the hyper-chaotic system (T epsilon [0, T) 2 ]) Diffusion treatment is carried out to obtain a converted state quantity X' 1 And Y' 1 To state quantity X' 1 And Y' 1 Carrying out pretreatment as formula (9) to obtain two groups of ranges of [0,255 ]]Get the key sequence K between 1 And K 2 ；
K 1 ＝round(mod(X′ 1 (end-length(P)+1:end)*10 8 ,255))
K 2 ＝round(mod(Y′ 1 (end-length(P)+1:end)*10 8 ,255))， (9)
Where round (.) denotes a rounding operation, both key sequences are the same length as P;
step 3.4: calculating a mark value Mr and an initial ciphertext C '(1), defining a loop variable j to be 1: length (P) to represent processing a jth plaintext, and calculating the mark value Mr and the initial ciphertext C' (1) by adopting the following formula:
step 3.5, starting from the 2 nd bit plaintext, performing circular diffusion according to the following formula:
C′(i)＝bitxor(mod(P(i)+K 1 (i),256),mod(C′(i-1)+K 2 (i)+Mr*1000,256)) (11)
where i ═ 2, 3., length (p), bitxor (a, b) denotes bitxor operations in which a and b are converted into binary numbers, then bitxored, and then converted into decimal numbers, and the flag value Mr is updated once per one-bit plaintext processing as follows:
Mr＝Mr-P(i)， (12)
completing diffusion operation of all plaintext information through length (P) -1 circulation to obtain a one-dimensional ciphertext sequence C';
and 4, step 4: setting infinite dimension hyperchaotic system parameters by utilizing the high 256 bits of the dynamic key DK obtained in the step 2, and performing S-box confusion operation on the ciphertext C' after processing the output sequence of the infinite dimension hyperchaotic system parameters to obtain the encrypted ciphertext C;
the step 4 comprises the following steps:
step 4.1: dividing the high 256 bits of the dynamic key DK obtained in the step 2 into six groups of binary sequences, and respectively aligning the six binary sequences to the infinite dimension hyper-chaotic systemThree control parameters a, b and c and three initial state values x 0 、y 0 、z 0 Assigning;
step 4.2: evolves the infinite dimension hyperchaotic system (2) by T 3 Time, using formula (5) to output states x (T), y (T) and z (T) (T E [0, T) to the hyper-chaotic system 3 ]) Diffusion treatment is carried out to obtain a state quantity X' 2 、Y′ 2 And Z' 2 (ii) a Defining M N K as the length of one-dimensional plaintext, and then taking the sequence with the length of M, N and K M N at the end of the evolution of the three states respectively to perform numerical transformation to obtain new sequences RX, RY and RZ, wherein the numerical transformation is shown as the following formula:
RX＝round(mod(X′ 2 (end-M+1:end)*10 8 ,M))
RY＝round(mod(Y′ 2 (end-N+1:end)*10 8 ,N))
RZ＝round(mod(Z′ 2 (end-(K*M*N)+1:end)*10 8 ,K*M*N)) (13)
then reforming the sequence RZ into an M N K matrix;
step 4.3: and (3) respectively arranging RX, RY and RZ obtained in the step 4.2 from large to small to obtain three groups of arranged sequences, and determining position index values of the arranged sequences to form three groups of S-boxes, namely SX, SY and SZ, as shown in the following formula:
SX＝sort(RX)
SY＝sort(RY)
SZ＝sort(RZ) (14)
wherein sort (·) represents arranging the sequence from large to small, and outputting the position index sequence of the arranged sequence, wherein SX and SY are two one-dimensional vectors with length of M and N, respectively, and their range is [1, M ] and [1, N ], because RZ is M × N × K matrix, the index value of the arrangement output is to sort K elements in M rows and N columns from large to small, so the position index matrix SZ is composed of M × N groups of elements with range of [1, K ];
step 4.4: and (3) reforming the one-dimensional ciphertext C' obtained in the step (3) into an M x N x K matrix, and performing confusion permutation operation by using the three groups of S-box obtained in the step (4.3) to obtain a confused ciphertext C, wherein the confusion permutation rule is to set a cyclic variable ii to be 1: M, jj to be 1: N, vv to be 1: K, and perform cyclic confusion permutation according to the following formula:
C(ii,jj,vv)＝C′(SX(ii),SY(jj),SZ(ii,jj,vv)) (15)
and performing M × N × K times of circular confusion permutation, and reforming the circular confusion permutation into a one-dimensional ciphertext matrix C, namely the encrypted ciphertext information.
2. The method for encrypting physical layer information based on the infinite dimension hyperchaotic as defined in claim 1, wherein in the step 1.2, a, b and c are control parameters of the system, x, y and z are state variables of the system, k is feedback gain, τ >0 is delay time, the control parameters a, b, k and τ of the infinite dimension hyperchaotic attraction subsystem are given, and the parameter c is equal to NN.
3. The physical layer information encryption method based on infinite dimensional hyperchaos as claimed in claim 1, wherein in step 1.2, u is a system state variable, subscript n represents the number of iterations, μ is a control parameter, the control parameter μ ═ AA of a given Logistic map, and an initial value u is an initial value 0 Initial value x of state x of infinite dimension hyperchaotic system 0 And (5) the consistency is achieved.
4. The method for encrypting the physical layer information based on the infinite dimensional hyperchaos as claimed in claim 1, wherein in the step 2.1, len is the total group number, length (.) is the length of the fetch sequence,
indicating an integer up operation.
5. The method for encrypting the information of the physical layer based on the infinite dimensional hyperchaotic as claimed in claim 1, wherein in the step 2.2, (.) 2 Representing the bitwise weighted conversion of binary sequences to decimal ranges [0,1 ]]Decimal fraction operation in between.
6. The method for encrypting the information of the physical layer based on the infinite dimensional hyperchaos as claimed in claim 1, wherein in the step 2.3, round (.) represents a rounding operation.
7. The method for encrypting the physical layer information based on the infinite dimensional hyperchaotic as recited in claim 1, wherein in the step 2.4, k is 1 1 +L 2 +L 3 ，U k For the kth system output state u k The processed state quantity, mod (a, b), represents the division of a by b remainder operation.
8. The method for encrypting the physical layer information based on the infinite dimensional hyper-chaos as claimed in claim 1, wherein in the step 2.5, sgn (.) represents a sign operation.
9. The method for encrypting the physical layer information based on the infinite dimensional hyper-chaos as claimed in claim 1, wherein in the step 2.6, xor (.) represents a bitwise xor operation.
10. The method for encrypting the physical layer information based on the infinite dimensional hyperchaotic as recited in claim 1, wherein in the step 3.5, i ═ 2, 3.., length (p).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210708061.8A CN115102685A (en) | 2022-06-21 | 2022-06-21 | Physical layer information encryption method based on infinite dimension hyperchaos |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210708061.8A CN115102685A (en) | 2022-06-21 | 2022-06-21 | Physical layer information encryption method based on infinite dimension hyperchaos |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115102685A true CN115102685A (en) | 2022-09-23 |
Family
ID=83293171
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210708061.8A Pending CN115102685A (en) | 2022-06-21 | 2022-06-21 | Physical layer information encryption method based on infinite dimension hyperchaos |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115102685A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117544309A (en) * | 2024-01-10 | 2024-02-09 | 厦门身份宝网络科技有限公司 | Mixed computing storage and transmission method and system for plaintext and ciphertext |
-
2022
- 2022-06-21 CN CN202210708061.8A patent/CN115102685A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117544309A (en) * | 2024-01-10 | 2024-02-09 | 厦门身份宝网络科技有限公司 | Mixed computing storage and transmission method and system for plaintext and ciphertext |
| CN117544309B (en) * | 2024-01-10 | 2024-03-22 | 厦门身份宝网络科技有限公司 | Mixed computing storage and transmission method and system for plaintext and ciphertext |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Hua et al. | Visually secure image encryption using adaptive-thresholding sparsification and parallel compressive sensing | |
| Alawida et al. | An image encryption scheme based on hybridizing digital chaos and finite state machine | |
| Ahmad et al. | A secure image encryption scheme based on chaotic maps and affine transformation | |
| Fouda et al. | A fast chaotic block cipher for image encryption | |
| Chen et al. | Image security system using recursive cellular automata substitution | |
| Trujillo-Toledo et al. | Real-time RGB image encryption for IoT applications using enhanced sequences from chaotic maps | |
| Zhang et al. | A new image encryption algorithm based on non-adjacent coupled map lattices | |
| Liang et al. | A new one-dimensional chaotic map for image encryption scheme based on random DNA coding | |
| Norouzi et al. | A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion process | |
| Ping et al. | Image encryption based on non-affine and balanced cellular automata | |
| Liu et al. | Color image encryption using spatial bit-level permutation and high-dimension chaotic system | |
| Wang et al. | On the security of 3D Cat map based symmetric image encryption scheme | |
| Li et al. | A novel plaintext-related chaotic image encryption scheme with no additional plaintext information | |
| Naim et al. | A novel satellite image encryption algorithm based on hyperchaotic systems and Josephus problem | |
| CN104270247B (en) | Suitable for the efficient general Hash functions authentication method of quantum cryptography system | |
| Zhao et al. | On the security analysis of an image scrambling encryption of pixel bit and its improved scheme based on self-correlation encryption | |
| Wang et al. | Security analysis on a color image encryption based on DNA encoding and chaos map | |
| CN111597574B (en) | Parallel image encryption system and method based on spatial diffusion structure | |
| Gnanajeyaraman et al. | Audio encryption using higher dimensional chaotic map | |
| Brahim et al. | A new image encryption scheme based on a hyperchaotic system & multi specific S-boxes | |
| CN113691362A (en) | Bit plane image compression encryption algorithm based on hyperchaotic system and DNA coding | |
| CN112769545B (en) | Image encryption method based on adjacent pixel Joseph transformation and Mealy state machine | |
| CN115102685A (en) | Physical layer information encryption method based on infinite dimension hyperchaos | |
| Shakir et al. | A new four-dimensional hyper-chaotic system for image encryption | |
| Slimane et al. | A novel image encryption scheme using chaos, hyper-chaos systems and the secure Hash algorithm SHA-1 |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |