A new speech encryption algorithm based on dual shuffling Hénon chaotic map

Received May 21, 2020 Revised Sep 23, 2020 Accepted Oct 4, 2020 Over the past few decades, many algorithms have been proposed to improve the performance of speech encryption over un-secure channel (i.e., Internet). In this paper, the security level was enhanced using a dynamic dual chaotic based on Hénon chaotic map. In the proposed algorithm, the speech elements are shuffled in a random fashion. Moreover, when both Hénon state variables are free to be used for shuffling the index is toggled randomly between them according to toggle bit. After index shuffling each speech element is modified with XOR operation between the original speech element value and the key that is selected randomly from the updated key table. The same chaotic map is used to initiate the empty or full table and provide new table entries from the values that are already shuffled. The experimental results show that the proposed crypto-system is simple, fast with extra random toggling behavior. The high order of substitution make it sensitive to initial condition, common cryptanalysis attacks such as linear and differential attacks are infeasible.


INTRODUCTION
Multimedia data is one of the most fundamental forms of human communications. Today, security and privacy are the two major requirements in the civilian and military applications to design and develop robustness crypto-systems for multimedia data (i.e., speech) [1,2]. Cryptography is a technique that holds themultimedia data communications secure and incomprehensible to un-authorized access over the un-secure channel (i.e., internet) and provide many security related services (i.e., non-repudiation, authentication, and integrity) [3][4][5]. Generally, cryptography is classified into four categories as shown in Figure 1.
Most of the conventional cryptographic algorithms are built to protect the content test messages which are not suitable for multimedia data (i.e., speech) during communication because it involves some inherent features such as encryption and decryption process of speech is different from that test messages, and data redundancy [6]. In recent years, extensive studies have been observed in the research community to apply a various algorithms based on chaos cryptographyto design a robustness crypto-system for multimedia data due to it is desirable features such as non-linear, deterministic, aperiodicity, sensitivity to initial conditions, and un-regular behaviours (i.e., random-like performance) [6][7][8][9][10][11][12][13][14], but unfortunately there are fundamental drawbacks in these chaotic crypto-systems in terms of cryptanalysis attacks (i.e., low level of security, and small key space) [15,16]. In general, chaotic crypto-systems can be classified into three categories based on their structure (i.e., analogue, or digital chaotic) each category represented by different equations (i.e., differential, and partial differential) [11, [17][18][19]. Figure   In this paper we have used chaos based cryptography (i.e., chaotic cryptography) to propose a new dynamic speech crypto-system using Hénon chaotic map to overcome the aforementioned drawbacks. The rest of this paper including the introduction is organized into seven sections as follows: Section 2 provides an overview of Hénon map. The next section i.e. section 3, describes the proposed algorithm. Section 4 presents and discusses the experimental results. Section 5 elaborates the security and performance analyses of the proposed speech crypto-system. A comparison with existing work (i.e., state-of-art) is given in section 6. The last section, i.e. section 7, concludes the paper.

HÉNON MAP
In the late 1946's the "Hénon map" was developed as a simplified for Lorenz map and named after its developer, M. Henon [18][19][20]. This chaotic map is a dynamical system (i.e., discrete-time) is presented by:

PROPOSED ALGORITHM
In the proposed crypt-system, Hénon map as an example, in (1) is selected to be used from the chaotic maps in the encryption process. In Figure 5 (in Appendix) the block diagram of the proposed encryption process is presented. The proposed speech crypt-system involves a series of sequential steps are presented in Algortihm 1.
Algorithm 1: Encryption 1. Initialization. In this step, an empty cipher vector C and a flag vector F which has same length l of the one dimensional plain speech frame , where j=132, represents the size of a 20-ms speech frame in { }each element is an 8-bit representation of the bit 0 (BIT-0: FF81) or the bit 1 (BIT-1: 007F) of the coder parameters which is codified on 8 bits. Finally, an empty key table is created with 0 initial pointer and toggle bit is also initiated to zero. 2. The input conditions are initiated as follow (X n+1 = 1 + Y n -αXn 2 , Y n+1 = βX n , with β = 0. 3 and α = 1.4), and the Hénon map is iterated 100 times to eliminate the transient effect. 3. In this step, the Hénon map is iterated once, and the result is converted into speech frame index l j is done based on (l j1 = x n+1 *10 14 mod l, l j2 =y n+1 *10 14 mod l). 4. Test the flag bit against both l j1 and l j2 , if both flag bit of the 8-bit index are true (1) (i.e., exists in step 3), so, go back to the previous step (i.e., step 3). If one of them is true, the other one will be used as index for shuffling. If both flags are false, in this case the toggle bit is used to select between the two indices and the toggle bit is inverted. Otherwise, the index with false flag either l j1 orl j2 will be utilized as new location for shuffling process. 5. Here, the key table is checked, if it is empty or all its contents are used (Key_P=0 or Key_P=table size), then, a single iteration of Hénon map is performed to add a new entry to key table based on XOR operation as follow: (l j1 = x n+1 *10 14 mod 132, l j2 =y n+1 *10 14 mod 132, Key_T (Key_p+1) = l j1 l j2 ). 6. As a next step, the current 8-bit speech element B j is encrypted using key bit value and XOR operation, then the result is stored in the cipher vector C(l jb ) according to the shuffled location. After that, the pointer of the key table is updated and the flag bit of the encrypted element is set to 1 based on ((C i (l jb ) = Key_T (Key_P)B j , Key_P=Key_P+1, F(l jb ) = 1). 7. Repeat step 3 to complete encryption for all speech elements.
On the other hand, the ciphered speech elements need to receive the proposed crypto-system parameters including the generated keys (i.e., secret) and follow Algorithm 1 (i.e., encryption steps) in reverse order for decryption process.

EXPERIMENTAL RESULTS
In this paper, some subjective tests were conducted including several speech samples (i.e., TIMIT database) with different sampling rate (i.e., 5000 samples/sec, and 8000 samples/sec) [21]. The obtained results are presented in this sectionto demonstrate the efficiency (i.e., security level) of the proposed speech encryption algorithm. The histograms of the input speech, ciphered speech, spectrogram (i.e., original speech, ciphered, and decrypted), and the decrypted speech are presented in Figure 6. Our simulation is conducted on LENOVO E320 with a 1.8 GHz core (TM) i5-8250U CPU, 1-TB hard disk, and 4-GB RAM with MATLAB (R2013a)software.

SECURITY ANALYSIS
In general, the security analyses must be satisfied when a new chaotic crypto-system is proposed. A perfect chaotic crypto-system should be robust against all kinds ofcryptanalysis attacks (i.e., brute-force, statistical, etc) [22,23]. Therefore, we have performed some security analyses to demonstrate the effectiveness of the proposed algorithm (i.e., security level). In this paper, as an example, in (2) is used to calculate the correlation coefficients.
The security tests values for different tests (i.e., correlation, ENT, DIEHARD, and NIST) are calculated and listed in Table 1. Additionally, the excellent quality of the encrypted speech must be sensitive in extreme way with respect to the secret keys [24,25] to ensure the security procedure against brute-force attacks. In the proposed algorithm, any small variation (i.e., bit flip) on the sensitivity factors (i.e., index location, keys, and other encryption parameters) that would generate a decryption speech signals which is completely different from the original signals as shown in Figure 7.

COMPARISON WITH EXISTING WORKS
In this section, a comparison is made between the average time needed in our proposed speech encryption algorithm with some of existing algorithms (i.e., advanced encryption standard) in both of encryption and decryption processes (i.e., delay budget). To be more accurate, the proposed algorithm and AES have been implemented and tested and evaluated in the same environment same platform and same conditions (i.e., parameters). The results of that test are presented in Table 2. The line charts showing the relationship between the proposed algorithm delay time and AES delay time in both cases (i.e., encryption, and decryption) are shown in Figures 8 and 9 respectively.
It is clear from Table 2 the average time needed (i.e., delay time) to encrypt and decrypt the speech packet using the proposed algorithm is much smaller than that in AES algorithm. The ratio is about 1:2 which make the proposed algorithm is considered to be big for this type of application such as Internet speech applications.

CONCLUSION
In this paper we have achieved our objectives of proposing a new dynamic dual chaotic based on Hénon chaotic map to enhance the multimedia data services (i.e., security level, reduces delay time). Our methodology was divided into three processes: initialization for flag, Hénon map, key table, key pointer, and toggle bit and encryption and decryption process. In the encryption process, the speech elements are shuffled in a random fashion. Moreover, when both Hénon state variables are free to be used for shuffling the index is toggled randomly between them according to toggle bit. After index shuffling each speech element is modified with XOR operation between the original speech elements value and the key that is selected in a random fashion from the updated key table. The same chaotic map is used to initiate the empty or full table and provide new table entries from the values that are already shuffled. The experimental results show that the cryptanalysis attacks such as linear and differential attacks are infeasible in the proposed crypto-system. In addition, the delay budget (i.e., delay time) of the proposed crypto-system is made compare to AES (i.e., existing algorithms) and the results endorse that the proposed crypto-system has the lowest average delay time, the ratio is about 1:2.