Security and confidentiality of network communication using chaotic encryption technology

Abstract

The rapid development of network communication puts forward higher requirements for the security of communication, and chaotic encryption technology is a mature and effective method in the field of security and secrecy. In this study, the application of chaotic encryption technology in network communication security and confidentiality was studied. Firstly, the chaotic encryption technology was briefly introduced. Then a network communication system based on chaotic encryption technology was established, and the specific establishment process was analyzed. Finally, National Institute of Standards and Technology (NIST) randomness test, secret key sensitivity test and confidentiality analysis based on information throughput were carried out to analyze the security and confidentiality of the system. The results showed that the system passed NIST randomness test, effectively defended the external attacks, and kept a favourable stability of confidentiality under different throughput. The experimental results proves the good security of chaotic encryption algorithm in the field of network communication and provides some bases for its specific application.

Keywords

Chaotic encryption network communication security confidentiality National Institute of Standards and Technology test secret key sensitivity

1. Introduction

With the rapid development of network communication technology, the status of communication security is gradually rising. More and more enterprises and individuals have paid attention to the safety of personal information. On the one hand, it is necessary to ensure that relevant information is transmitted to the corresponding information receiver in time. On the other hand, it is necessary to ensure to avoid information loss, and the exposure of the privacy of businesses and individuals [1]. Therefore, the security and confidentiality of network communication becomes more and more important. Chaotic encryption technology has high sensitivity, orderliness and matching. It is an effective network communication security technology. It has broad prospects for development in communication security and has attracted extensive attention of researchers. Hu and Chan [3] designed a seven-dimensional hyperchaotic system with five positive Lyapunov exponents. The computational complexity was reduced by Walsh-Hadamard transform and discrete cosine transform, and the key space was increased. The experimental results showed that the encryption system had high security performance. Chai et al. [4] designed an image encryption algorithm which combined chaotic system with DNA matrix and found that the algorithm could effectively resist various attacks and protect image security. Gill et al. [5] combined chaotic encryption algorithm with secure hashing algorithm (SHA) to enhance the physical layer of the network and found that this method could protect the system from eavesdroppers and was a powerful and promising security strategy. Bi et al. [6] accelerated the allocation of chaotic subcarriers using chaotic mapping, achieved the maximum key space by dynamic chaotic permutation, and found that the encryption scheme had excellent security and robustness against exhaustive attacks. In this study, a network communication system was established based on chaotic encryption technology, the implementation of the algorithm was analyzed, and then the security and confidentiality of the system in network communication was verified through National Institute of Standards and Technology (NIST) randomness test, secret key sensitivity test and confidentiality analysis based on information throughput. This work is beneficial to the further application of chaotic encryption technology in the field of network communication and can make some contributions to the improvement of the security and confidentiality of network communication.

2. Application of chaotic encryption technology in communication security

There are many ways to guarantee data security, and data encryption is a relatively mature and reliable category. The complete data encryption system should include plaintext, ciphertext, encryption algorithm, and secret key [7]. The sender converts the unencrypted plaintext into the encrypted ciphertext using an encryption device or an encryption algorithm, and the accepting party restores the ciphertext to the plaintext using the decrypted secret key. The encryption algorithm is the principle of encryption, and the secret key is the control center. The plaintext is different from the ciphertext in the field sense. If the information is intercepted by a third party during the transmission process, then the ciphertext cannot be restored to the plaintext without obtaining the secret key, thereby ensuring the security of the information flow.

Chaos is a dynamic process, and the chaotic system derived from it has statistical characteristics, inherent randomness, ergodicity, sensitivity [8], which is not predictable in long-term and has good conditions for generating random numbers. The system is highly consistent to the cryptographic requirements. Therefore, it can play a good role in encryption technology.

The development of chaotic secret communication technology has generally gone through four periods [9]. The first generation was chaos masking and chaos key control techniques, and both poor in security and practicality. The second generation was chaotic modulation technology, and was improved compared with the previous generation. The chaotic encryption technology discussed in this study was the third generation, chaotic secret communication technology. It had a greater breakthrough in both theory and practice and had higher security and practicability, which basically met the needs of contemporary people. Nowadays, study of pulse synchronization based chaotic communication, the fourth generation of chaotic technology, is developing rapidly, and the technology will show its great capability in the future.

Network communication is to connect various isolated devices through the network, and realize the communication between people, people and machines, machines and machines through information exchange. Nowadays, chaotic encryption algorithms have become increasingly mature. At the same time, asynchronous response mode (ARM), digital signal processing (DSP), system on chip (SoC), field programmable gate array (FPGA), mobile phones and other universal and practical terminals that implement chaotic secret communication technology [10], which makes chaotic encryption technology widely used in network communication field. This study constructed a network communication system with chaotic encryption technology to briefly describe the algorithm of chaotic encryption system.

3. The chaotic encryption technology based network communication system

3.1 Design principle of chaotic encryption network communication system

A network system can usually increase its security by introducing passwords to the application layer or protocol stack layer (physical layer). In this study, the construction of information transmission channel which applied chaotic encryption algorithm in the physical layer was mainly described.

The chaotic encryption algorithm is based on the non-degenerate high-dimensional discrete hyperchaotic system. The stream cipher of the symmetric key is used as the architecture, and the scheme of encrypting and sending signals at chaotic signal low bit, closed-loop feedback and multi-round encryption is designed to obtain the high security against as many external attacks as possible, where the chaotic variate low order can effectively resist the divide-and-conquer attack, and the combination of closed-loop feedback and multi-round encryption method can effectively resist the differential attack.

As shown in Fig. 1, the design uses the combination of non-degenerate high-dimensional discrete hyperchaotic system, stream cipher, closed-loop feedback, and multi-round encryption, where $a$ and $a^{\prime}$ are the seed keys, $x$ and $x^{\prime}$ are the random sequences generated by system iteration, and $k$ and $k^{\prime}$ are the key streams.

Figure 1.

Design schematic diagram of chaotic encryption network communication system.

The specific operation mode is as follows. Firstly, the sender uses the non-degenerate high-dimensional discrete hyper-chaotic system to obtain a random sequence and takes modulus and integer to obtain the key stream $k$ . Then the sender performs multi-round encryption or operation with the input signal to obtain $p=m\otimes k$ , where $m$ stands for plaintext and is encrypted through parameter $c$ , and feeds it back to three-dimensional and non-degenerate discrete-time hyper-chaotic systems through multi-round encryption of the parameter $c$ . After receiving the signal, the receiver obtains $m^{\prime}=p\otimes k^{\prime}$ by multi-round decryption, where $m^{\prime}$ stands for the plaintext obtained after decryption. Key stream $k^{\prime}$ is obtained in a similar manner.

$m=m^{\prime}$ is obtained when the match and synchronization are successful.

3.2 Algorithm implementation of chaotic encrypted network communication system

It can be seen from the above that the key to chaotic encryption network communication system is how to construct a non-degenerate and high-dimensional discrete-time hyper-chaotic system. The method of construction is given below.

A nominal system that tends to be stable is designed. The general form of the iterative equation is as follows:

$\displaystyle x(k+1)=\left[D\right]_{n\times n}x(k),$ (1)

where $k=0,1,2,\ldots,x(k)=(x_{1}(k),x_{2}(k),\ldots x_{n}(k))^{T}$ , and the matrix $[D]_{n\times n}$ is block matrix. The form of $[D]_{n\times n}$ is as follows:

if $n$ is an even number,

$\displaystyle[D]_{n\times n}=\left(\begin{array}[]{ccccc}{[{D_{1}}]_{2\times 2% }}&0&\cdots&0&0\\ 0&{\left[{D_{2}}\right]_{2\times 2}}&\cdots&0&0\\ \vdots&\vdots&\ddots&\vdots&\vdots\\ 0&0&\cdots&{[{D_{n/2-1}}]_{2\times 2}}&0\\ 0&0&\cdots&0&{[{D{}_{n/2}}]_{2\times 2}}\\ \end{array}\right)$ (2)

if $n$ is an odd number,

$\displaystyle[D]_{n\times n}=\left(\begin{array}[]{ccccc}{\left[{D_{1}}\right]% _{2\times 2}}&0&\cdots&0&0\\ 0&{\left[{D_{2}}\right]_{2\times 2}}&\cdots&0&0\\ \vdots&\vdots&\ddots&\vdots&\vdots\\ 0&0&\cdots&{\left[{D_{\left\lfloor{n/2}\right\rfloor}}\right]_{2\times 2}}&0\\ 0&0&\cdots&0&\gamma\\ \end{array}\right)$ (3)

In Eqs (2) and (3), $|\gamma|<1$ , and to guarantee that the eigenvalue of $[D]_{n\times n}$ is in the unit circle , all the eigenvalues of $[D]_{n\times n}$ are in the unit circle, which makes Eq. (1) a system that tends to be stable.

Similarity transformation is performed on $[D]_{n\times n}$ , and we have:

$\displaystyle[A]_{n\times n}=[P]_{n\times n}[D]_{n\times n}[P]_{n\times n}^{-1}.$ (4)

The similarity transformation matrix is

$\displaystyle[P]_{n\times n}=\left(\begin{array}[]{ccccc}0&1&\cdots&1&1\\ 1&0&\cdots&1&1\\ \vdots&\vdots&\ddots&\vdots&\vdots\\ 1&1&\cdots&0&1\\ 1&1&\cdots&1&0\\ \end{array}\right)_{n\times n}.$ (5)

The nominal system after being transformed is

$\displaystyle x(k+1)=[P]_{n\times n}[D]_{n\times n}[P]_{n\times n}^{-1}x(k)=[A% ]_{n\times n}x(k)$ (6)

Let $[A]_{n\times n}$ as

$\displaystyle[A]_{n\times n}=\left(\begin{array}[]{ccccc}{a_{11}}&\cdots&{a_{1% m}}&\cdots&{a_{1n}}\\ \vdots&\ddots&\vdots&{\mathinner{\mskip 2.0mu \raise 1.0pt\hbox{.}\mskip 2.0mu% \raise 4.0pt\hbox{.}\mskip 2.0mu \raise 7.0pt\hbox{.}\mskip 1.0mu }}&\vdots\\ {a_{m1}}&\cdots&{a_{mm}}&\cdots&{a_{mn}}\\ \vdots&{\mathinner{\mskip 2.0mu \raise 1.0pt\hbox{.}\mskip 2.0mu \raise 4.0pt% \hbox{.}\mskip 2.0mu \raise 7.0pt\hbox{.}\mskip 1.0mu }}&\vdots&\ddots&\vdots% \\ {a_{n1}}&\cdots&{a_{nm}}&\cdots&{a_{nn}}\\ \end{array}\right)$ (7)

where $a_{ij}$ is constant. It is easy to find that Eqs (1) and (6) have the same eigenvalue and stability. Thus, Eq. (6) is also the nominal system that tends to be stable.

A uniformly bounded anti-controller $g(\sigma x(k),\varepsilon)$ [11] and control matrix $[B]_{n\times n}$ are configured to implement chaotic anti-control on Eq. (6). The expression for a bounded and globally controlled system is obtained:

$\displaystyle x(k+1)=[A]_{n\times n}x(k)+[B]_{n\times n}g(\sigma x(k),% \varepsilon).$ (8)

Pole configuration [12] is performed on Eq. (8) by using $[B]_{n\times n}$ , $\varepsilon$ , and $\sigma$ to make it a non-degenerate discrete-time hyper-chaotic system. Generally through ergodicity the form of $[B]_{n\times n}$ can be determined, and $\varepsilon$ is adjusted to have chaotic characteristics after each matrix is determined.

According to the information format that needs to be transmitted, the appropriate low order of chaotic variables is selected and the dimension of the hyper-chaotic system is determined. For example, the video is framed as images in the format of red, green, and blue (RGB). Each of R, G, and B individually occupies 8 bits, so the dimension is 3, and the iteration variate of the chaotic sequence is the low 8 bits. The three-dimensional and non-degenerate discrete-time hyper-chaotic system generates a chaotic sequence with random characteristics in every time of iteration to capture the pixels in each RGB format and encrypts them one by one to complete the security encryption of the information stream.

4. Experiment of security and confidentiality research

Security is one of the important indicators for measuring cryptographic algorithms. This study described three methods, including NIST randomness test, secret key sensitivity test and confidentiality analysis based on information throughput, and specified the security and confidentiality of chaotic encryption technology in the field of network communication.

4.1 Introduction of the experiment

Chaotic ciphers are stream ciphers, so their security depends largely on the randomness of the key stream. The Special Publication 800-22 test kit from the National Institute of Standards and Technology (NIST), as the same as the NIST randomness test, contained 16 test methods that could be used to test the randomness of a binary sequence of arbitrary length of secure random or pseudo-random number generators [13]. If a system cannot pass NIST randomness test, then it indicates that the system is not safe. Therefore passing NIST randomness test is a guarantee of system security.

The key sensitivity of an encryption system is an important indicator of the quality of a system’s encryption. The method of controlling variable was used to test the maximum mismatch error $\max\{{|{\Delta a_{ij}}|=|{a_{ij}^{r}-a_{ij}^{s}}|}\}$ that could be tolerated by key parameter $a_{ij}^{s}$ of sender and key parameter $a_{ij}^{r}$ of receiver to consider the sensitivity of the secret key.

It was now defined that the the information throughput was the amount of data received by the system during normal operation for a specified period of time, described by Kb/s. The effects of chaotic system and traditional system on information confidentiality under different information throughput were compared to show the security performance of the test system.

4.2 Experimental methods and steps

The dimensions of the non-degenerate discrete-time chaotic systems used for different formats of network information are different. In this study, video information was taken as an example, the dimension was 3, and the iterative variate of the chaotic sequence was low 8 bits. The simulation experiment was carried out. When the dimension is three, a design scheme is given according to the above design ideas, as follows:

the encryption algorithm of design sender is

$\displaystyle\left\{\begin{array}[]{l}{x_{1}^{b}(k+1)=a_{11}x_{1}^{b}(k)+a_{12% }x_{2}^{b}(k)+a_{13}x_{3}^{b}(k)}\\ {x_{2}^{b}(k+1)=a_{21}p(k)+a_{22}x_{2}^{b}(k)+a_{23}x_{3}^{b}(k)}\\ {x_{3}^{b}(k+1)=a_{31}p(k)+a_{32}x_{2}^{b}(k)+a_{33}x_{3}^{b}(k)+\varepsilon% \times\sin(\sigma\times p(k))}\\ \end{array}\right.,$ (9)

the decryption algorithm of design receiver is

$\displaystyle\left\{\begin{array}[]{l}{x_{1}^{c}(k+1)=a_{11}x_{1}^{c}(k)+a_{12% }x_{2}^{c}(k)+a_{13}x_{3}^{c}(k)}\\ {x_{2}^{c}(k+1)=a_{21}p(k)+a_{22}x_{2}^{c}(k)+a_{23}x_{3}^{c}(k)}\\ {x_{3}^{c}(k+1)=a_{31}p(k)+a_{32}x_{2}^{c}(k)+a_{33}x_{3}^{c}(k)+\varepsilon% \times\sin(\sigma\times p(k))}\\ \end{array}\right.,$ (10)

where parameter $\varepsilon=3\times 10^{8}$ and $\sigma=2\times 10^{5}$ , the parameter of the secret key is

$\displaystyle\left(\begin{array}[]{ccc}{a_{11}}&{a_{12}}&{a_{13}}\\ {a_{21}}&{a_{22}}&{a_{23}}\\ {a_{31}}&{a_{32}}&{a_{33}}\\ \end{array}\right)=\left(\begin{array}[]{ccc}{0.205}&{-0.595}&{0.265}\\ {-0.265}&{-0.125}&{0.595}\\ {0.33}&{-0.33}&{0.47}\\ \end{array}\right),$ (11)

The Lee’s index [14] obtained after calculating was LE1 $=$ 14.3203, LE1 $=$ 14.3307 and LE1 $=$ 0.1822.

NIST randomness test. First, the simplest initial key and initial vector generated by C++ were all “0”, and the number of secret key words was 40,000 key stream sequences [15, 16]. The binary representation key stream file Chaos.txt could be obtained after running. In the Linux system, the location of the C compiler, GNU Compiler Collection (GCC), was modified, and the directory where the test package was was input, then the makefile was run to compile, and finally the file was imported to test all 16 items. In this study, the chaotic modulation algorithm [17] was also designed and performed NIST tests in a similar way for comparison.

Key sensitivity test. Firstly, three indicators for evaluating sensitivity were established, which were the initial parameter value, the parameter value of the image contour which was still clear (the specific image was blurred), and the parameter value of the image with the snowflake point only, and they represent the complete decryption, the relatively complete decryption, and the incomplete decryption. By sequentially changing the values of the nine key parameters, the decryption of the video at the receiving end is sequentially conformed to the above criteria, and then the specific value was recorded.

Confidentiality analysis based on information throughput. The video was encrypted by using the traditional security system and the chaotic encryption system respectively. The throughput setting range was 0–140 Kb/s, and the stability of the received signal at the receiving end was considered as the confidentiality determination method.

4.3 Experimental results and analysis

4.4 Results of NIST randomness test

Results of the NIST randomness test are sorted and shown in Table 1.

Table 1
NIST randomness test results of the chaotic encryption system

Test items	$P$ -value
Frequency test	0.472732
Block frequency test ( $m=$ 128)	0.666651
Cumulative and sums test-forward	0.494869
Cumulative and sums test-reverse	0.698478
Runs test	0.302570
Longest run of ones test in the block	0.107361
Binary matrix rank test	0.579504
Fast Fourier Transform ( FFT) test	0.119332
Non overlapping template matching test ( $m=$ 9, $B=$ 000000001)	0.508713
Overlapping template matching test ( $m=$ 9)	0.739988
Universal general statistical test	0.338145
Approximate entropy test ( $m=$ 10)	0.112098
Random excursions test ( $x=+1$ )	0.135346
Random excursions variant test ( $x=-1$ )	0.429478
Linear complexity test ( $M=$ 500)	0.454872
Serial test ( $m=$ 16)	0.107280

The significance level in this study was $\alpha=$ 0.01. If all the $P$ -values of the sequences participating in the test satisfied 0.01 $\leqslant P\leqslant$ 1, the test would pass. The $P$ -values of the 16 test items in Table 1 were all larger than the significance level $\alpha=$ 0.01, indicating that the key stream sequence had very good random characteristics and was not easy to concentrate in a certain area. The further observation showed that the $P$ -values of 5 items, including block frequency test, cumulative and sums test, binary matrix rank test, non overlapping template matching test, and overlapping template matching test exceeded 0.5, indicating that the security performance of the encryption system in the five aspects is particularly prominent.

The results of NIST randomness test of the chaotic modulation system are in Table 2.

Table 2

Results of NIST randomness test of the chaotic modulation system

Test items	$P$ -value
Frequency test	0.272732
Block frequency test ( $m=$ 128)	0.066651
Cumulative and sums test-forward	0.245911
Cumulative and sums test-reverse	0.495521
Runs test	0.104270
Longest run of ones test in the block	0.008266
Binary matrix rank test	0.266595
Fast Fourier Transform ( FFT) test	0.000217
Non overlapping template matching test ( $m=$ 9, $B=$ 000000001)	0.363955
Overlapping template matching test ( $m=$ 9)	0.253378
Universal general statistical test	0.171440
Approximate entropy test ( $m=$ 10)	0.000693
Random excursions test ( $x=+$ 1)	0.000475
Random excursions variant test ( $x=-$ 1)	0.250504
Linear complexity test ( $M=$ 500)	0.335481
Serial test ( $m=$ 16)	0.063080

It was easy to find that 4 of the 16 test items (the longest run of ones test in the block, Fast Fourier Transform test, approximate entropy test, random excursions test) had $P$ -values that were less than the significance level $\alpha=$ 0.01, which meant that they failed the test, i.e., the cryptographic sequence generated by the chaotic modulation system was not sufficiently randomized in these aspects, and there might be security risks. In addition, none of the tested $P$ -values were more than 0.5, indicating that the system was relatively vulnerable to external attacks, its randomness was not very high, and the corresponding password security was relatively low. The comparison of the NIST randomness test results between the two systems showed that the chaotic encryption system designed in this study could pass the NIST randomness test, and the data encryption means, operation time and space and complexity of data form made it have the functions and means to defend external attacks. Thus the designed system had excellent confidentiality and significantly higher security than the chaotic modulation system.

4.4.1 Results of secrete key sensitivity test

The relevant values of the nine key parameters are shown in Table 3.

Table 3
Maximum mismatch error of key parameter

Key parameter	Initial parameter value	Snowflake spots of images	Clearness of image contour	Order of magnitude $\|{\Delta a_{ij}}\|$
$a_{11}$	0.205	0.205001	0.2050001	$10^{-6}$
$a_{12}$	$-$ 0.595	$-$ 0.595001	$-$ 0.5950001	$10^{-6}$
$a_{13}$	0.265	0.265001	0.2650001	$10^{-6}$
$a_{21}$	$-$ 0.265	$-$ 1.265	$-$ 0.465	$10^{0}$
$a_{22}$	$-$ 0.125	$-$ 0.125001	$-$ 0.1250001	$10^{-6}$
$a_{23}$	0.595	0.595001	0.5950001	$10^{-6}$
$a_{31}$	0.33	1.33	0.53	$10^{0}$
$a_{32}$	$-$ 0.33	$-$ 0.33001	$-$ 0.330001	$10^{-5}$
$a_{33}$	0.47	0.470001	0.4700001	$10^{-6}$

Figure 2.

Comparison of the confidentiality of two different systems under different throughput.

It was easy to find out after the test the amount of variation of parameter values except the parameter $a_{21}$ and $a_{31}$ was less than 10 ${}^{-5}$ when the decryption was relatively complete, and their amount of variation was less than 10 ${}^{-4}$ when the decryption was not complete, indicating that the sensitivity of those parameters was 10 ${}^{-5}$ , which was relatively high and was not easy to be compromised by similar numerical simulation in the face of exhaustive attacks. Thus, it was relatively secure.

4.4.2 Results of confidentiality analysis based on information throughput

The comparison of the confidentiality of the traditional system and chaotic encryption system under different throughput is shown in Fig. 2.

According to Fig. 2, when the throughput was lower than 20 Kb/s, the confidentiality of the traditional system to the network communication was always about 20% lower than that of the chaotic encryption system. Considering the highest degree of confidentiality, it could be seen that when the throughput was 105 Kb/s, the traditional system had the highest degree of confidentiality for network communication, which was 78%. When the throughput was 95 Kb/s, the chaotic encryption system had the highest degree of confidentiality for network communication, which was 96%, and the difference between the two was 18%. Considering the minimum degree of confidentiality, when the throughput was 85 Kb/s, the traditional system had the lowest degree of confidentiality for network communication, which was 5%. When the throughput was 82 Kb/s, the chaotic encryption system had the lowest degree of confidentiality for network communication, which was 25%, and the difference between them was 20%. Considering the average degree of confidentiality, the traditional system was 44.43%, and the chaotic encryption system was 63.14%. In general, throughput had a greater impact on the confidentiality of traditional systems, while chaotic security systems had relatively good stability and higher confidentiality compared to the traditional system, further verifying the high advantage of chaotic encryption systems in network communication.

5. Conclusion

In this study, the security and confidentiality of network communication using chaotic encryption technology were researched. A network communication system using chaotic encryption technology was constructed, NIST randomness test, key sensitivity test and confidentiality analysis based on information throughput were applied to verify the security and practicability of chaotic encryption technology, and its feasibility and reliability in network communication were proved. This work provides some theoretical bases for the further application of chaotic encryption technology in the field of network communication and can make some contributions to the development of network communication security and confidentiality.

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Security and confidentiality of network communication using chaotic encryption technology

Abstract

Keywords

1. Introduction

2. Application of chaotic encryption technology in communication security

3. The chaotic encryption technology based network communication system

3.1 Design principle of chaotic encryption network communication system

4.1 Introduction of the experiment

4.2 Experimental methods and steps

4.4 Results of NIST randomness test

Table 1 NIST randomness test results of the chaotic encryption system

Table 3 Maximum mismatch error of key parameter

5. Conclusion

References

Table 1
NIST randomness test results of the chaotic encryption system

Table 3
Maximum mismatch error of key parameter