Speech Encryption Method Based on Two Dimensional Henon Mapping

2019 International Conference on Computer Science, Communications and Big Data (CSCBD 2019) ISBN: 978-1-60595-626-8

Speech Encryption Method Based on Two-Dimensional Henon Mapping

Qiu-yu ZHANG, Gai-li LI, Yin-jie HU and Deng-hai ZHANG

School of Computer and Communication, Lanzhou University of Technology, Gansu, Lanzhou, 730050, P.R. China

Keywords: Speech signal, Encryption/Decryption, Two-dimensional Henon map, Chaotic sequence, Logistic map.

Abstract. Chaos is a behavior controlled by nonlinear dynamic law and has high sensitivity to the initial key, In order to realize the secure storage of cloud speech files, and improve the encryption and decryption efficiency of speech files during the uploading and downloading process of encrypted, we present a speech encryption method based on two-dimensional Henon mapping in this paper. Our approach utilizes the chaotic sequence generated by the Henon map, and then XORs and modulo subtracts the sequence from the original speech-generated matrix, and finally obtains the encrypted speech. Experimental results show that the proposed method has good key sensitivity, correlation, and encryption efficiency and security.

Introduction

As a kind of multimedia, speech information is not only frequently used, but also often private, containing some important content or confidential information. These sensitive information needs special attention when it comes to storage and management. If you upload the cloud, you need to ensure security. From a cryptographic perspective, cloud storage is not a trusted third party. Therefore, sensitive speech data stored in the cloud, if not protected, may result in personal privacy as small as national security. Therefore, how to ensure speech-safe storage in a cloud environment is a major problem in using cloud storage technology to store speech data.

Currently, speech encryption methods are: DES [1], AES [2], RSA [3], SHA-3 (Hash algorithm) and AES-128 [4], One-dimensional Logistic[5] chaotic map encryption algorithm. Slimani et al. [6] proposed a speech signal encryption system based on row and column cyclic shift. The cryptosystem uses three keys. The original key is randomly generated using a pseudo noise sequence generator, and the other two keys are obtained by using the master key. The encryption system also uses discrete cosine transform (DCT) or discrete sine transform (DST) to eliminate signal intelligibility. Farsana et al. [7] proposed private key data encryption algorithm based on three-dimensional chaotic map. It is based on the confusion and spread of speech samples using secret keys generated by logical and two-dimensional Duffing mappings. Chaotic systems can generate pseudo-random numbers of highly complex dynamic characteristics. Sheela et al. [8] proposed a chaotic-based speech encryption algorithm, which uses improved Henon mapping and sinusoidal mapping.Al Saad et al. [9] proposed a new speech encryption system. It is based on the permutation and replacement of speech samples using secret keys in the time and transform domains. The system has multiple stages to increase security and present an encrypted signal with low residual intelligibility. Mostafa et al. [10] proposed a speech encryption algorithm based on substitution and permutation, which is encrypted by discrete transformation of speech signals. By analyzing the above literature, the chaotic mapping encryption algorithm has been used in speech because chaotic mapping is highly sensitive to the initial key.

In summary, because chaotic mapping has high sensitivity to the initial key, a speech encryption method based on two-dimensional Henon mapping is proposed. The experimental results show that the proposed method deals with the speech file data of three different types of man and woman in different formats such as WAV, FLAC and OGG in terms of speech encryption. According to the speech data of three different formats, the proposed method has very good key sensitivity, correlation, and encryption efficiency and security.

statement and preliminaries. The detailed proposed algorithm is described in Section 3. Section 4 gives the experimental results and performance analysis. Finally, we conclude our paper in Section 5.

Two-Dimensional Henon Map

Since speech data is relatively sensitive and widely used, it is more necessary to ensure security if it is uploaded to cloud. Therefore, this paper use two-dimensional Henon chaotic map encryption algorithm to construct encrypted speech. The encryption algorithm uses combination of XOR operation and modular subtraction. The principle of the algorithm is shown in Eq. (1).

2 1

1

1

k k k

k k

x ax y

y bx         

 (1)

Where, a and b have influence on Henon map, when 0.54<a<2, 0<|b|<1, the system is in a chaotic state, x and y are two variables to determine the iterative equation.

Construction of two-dimensional Henon map function, take the two-dimensional Henon map as follows:

2

k+1

1

0.3

x

 

ax



x

Where, x determines iteration process, when a increases from 0, Henon map goes to chaos via period-doubling bifurcation. when 0<a<0.35, Henon map has stable fixed points.

2 2

k k-1 i k

0.7 0.49 4

1 0.3

2

  

ax  x x a x a

a (3)

According to the Euclid formula and the two-dimensional Henon map function in the above mathematical knowledge, the following function will be constructed:

k

i k

k

0 0.5 1.5

c 1 0.5 0.5 ( 0,1 , 0,1 )

2 1.5 0.5

    _       _{  }  x

x i k

x

(4)

Where xk is in the range of [-0.5, 1.5], xk will be binarized to 0 and 1 according to the first two

functions of ci, the speech data is encrypted by the XOR.

When xk is in the range [-1.5, 0.5], the proposed algorithm converts xk to 2 according to third

function of ci, and then speech data is encrypted by subtractive computing. This completes

encryption of speech data.

Speech Encryption and Decryption

Speech Encryption Process

Cloud storage is not a trusted third party. Therefore, if sensitive speech data stored in cloud without protected, it may result to personal privacy or even cause great danger to national security. Therefore,speech data need to be encrypted before uploaded to cloud. With the reason that we use two-dimensional Henon chaotic map encrypted algorithm to encrypt the speech. The flow diagram of encryption algorithm is shown in Figure 1.

Original speech

Keys Chaotic sequence generator

XOR or modulo subtraction

The specific encryption processes are as follows:

Step 1: Matrix generation. Represent the original speech signal s(t) as matrix A.

Step 2: Key generation and speech encrypted. Set an initial value x0, x1 as the key. Where x0=1,

x1=1.2, a chaotic sequence C is generated according to the above Eq. (4). Finally, the matrix A

generated by the speech and the chaotic sequence C are subjected to XOR operation or modulo subtraction to obtain the encrypted speech s'(t).

Speech Decryption Process

Figure 2 shows the flow diagram of decryption algorithm.

Keys Chaotic sequence generator

XOR or modulo subtraction Encrypted

speech

Decrypted speech

Figure 2. The flow diagram of decryption algorithm.

The specific decryption process is as follows:

Step 1: According to the initial value x0, x1 in the encryption process and generate a chaotic

sequence according to Eq. (1).

Step 2: Chaotic sequence C is constructed to decrypt the speech to obtain the decryption speech s(t).

Experimental Results and Analysis

The speech data used in the experiment is speech chips of WAV, OGG, and FLAC recorded by Chinese men and women. The frequency of the speech clips is 16 kHz, the number of channels is mono, the sampling precision is 16 bit, and the length is 2s.

Experimental hardware platform: Intel (T) Core(TM) i5-2450M CPU, 2.50GHz, computer memory 8GB. Software environment: Windows 7, MATLAB R2016a.

Henon Chaotic Map

According to Eq. (1) the influence of parameters a and b on the mapping, this paper takes a=1.4, b=0.3 to generate chaotic state, and Figure 3 is the attractor of Henon map

Figure 3. The attractor of the Henon map.

Key Sensitivity

Figure 4. Encryption and decryption speech.

It can be seen from Figure 4(c) that the slight difference in the initial value in the chaotic sequence leads to the failure of speech decryption, which is determined by the high sensitivity of the chaotic sequence to the initial value, which is biased at the initial value. Two completely different chaotic sequences are produced. The chaotic sequence generated by the two-dimensional Henon map is more complicated, and the chaotic sequence is sensitive to the initial values x0, x1,

and the initial values x0, x1 have little change, and the generated chaotic sequence produces a great

change.

Encryption and Decryption Speed

Encryption and decryption are an important performance indicator of cryptography in addition to security. This paper uses two-dimensional Henon chaotic map encryption algorithm to encrypt speech. This experiment tests the time of speech encryption and decryption by three different speech formats, three speech formats. There are: WAV speech format, OGG speech format, FLAC speech format, and compare the man and woman of these three speech formats, the encryption and decryption time of different files are as follows:

Table 1. Encryption time(s) of three speed files.

Speech files WAV file OGG file FLAC file man 0.090636 0.091346 0.095452 woman 0.070861 0.077691 0.079372

Figure 5. Encryption time of three speed files.

As can be seen from Table 1 and Figure 5, for the encryption time analysis of the three speech files, the encryption time of the man of the OGG speech file is the shortest; for the woman speech analysis, the encryption time of the woman of the WAV speech file is the shortest, in order to improve the efficiency of encryption, we can choose WAV speech format.

Table 2. Decryption time(s) of three speed files.

Figure 6. Decryption time of three speed files.

It can be seen from Table 2 and Figure 6. For the analysis of man decryption time of three speech files, the decryption time of the man of OGG speech files is the shortest; for woman, the encryption time of woman of FLAC speech files is the shortest. Comprehensive encryption and decryption time. In order to improve the efficiency of decryption, we can select the WAV format woman speech for encryption and decryption.

Correlation Analysis

Correlation analysis measures the quality of the encryption algorithm. The correlation is the similarity between the original speech signal and the encrypted speech signal. The formula for calculating the parameter correlation is as follows

1 1 1

2 2

2 2

1 1 1 1

n n n

i i i i

i i i

n n n n

i i i i

i i i i

n x y x y r

n x x n y y

  

   

 



   

_{ }  _{ }

   



 









. (5)

If the correlation coefficient is 0, the original speech and the encrypted speech are completely different, so the correlation characteristics are reflected. The characteristics of speech encryption. Figure 7 is a correlation diagram of the original speech and the encrypted speech signal.

Figure 7. A correlation diagram.

The parameter correlation value of the encryption algorithm is 510-3, It can be seen from the figure that the starting position is 0, because the speech signal has non-stationaryness and then has a large amplitude value, indicating that it has great anti-noise performance, so the algorithm has good correlation and Anti-noise performance.

Anti-attack and Security

This paper uses a chaotic sequence based on a two-dimensional Henon map. From Section 2. It is known that by adjusting x0, x1 (as two keys), more complex chaotic sequences can be generated.

Conclusions

In this paper, we have proposed a speech encryption method based on two-dimensional Henon mapping. The proposed method uses the chaotic sequence generated by the Henon map, and then performs the XOR and modulo subtraction operations on the matrix generated by the original speech, and finally obtains the encrypted speech. The experimental results show that the proposed method can process the speech file data of three different formats of man and woman in WAV, FLAC and OGG in the aspect of speech encryption. By comparing the encryption and decryption time of the three speech formats, it is determined that the WAV speech files should be selected to improve efficiency of encryption and decryption, with good key sensitivity, correlation, and encryption efficiency and security.

Acknowledgment

This work is supported by the National Natural Science Foundation of China (No. 61862041, No. 61363078), the Research Project in Universities of Education Department of Gansu Province (2017B-16, 2018A-187). The authors would like to thank the anonymous reviewers for their helpful comments and suggestions.

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