A new dynamic speech encryption algorithm based on Lorenz chaotic map over internet protocol

Received Feb 3, 2020 Revised Mar 13, 2020 Accepted Mar 24, 2020 This paper introduces a dynamic speech encryption algorithm based on Lorenz chaotic map over internet protocol to enhance the services of the real-time applications such as increases the security level and reduces latency. The proposed algorithm was divided into two processes: dynamic key generation process using 128-bit hash value to dynamically alter the initial secret keys, and encryption and decryption process using Lorenz system. In the proposed algorithm, the performance evaluation is carried out through efficient simulations and implementations and statistical analysis. In addition, the average time delay in the proposed algorithm and some of the existing algorithms such as AES is compared. The obtained results concluded that, the proposed dynamic speech encryption algorithm is effectually secured against various cryptanalysis attacks and has useful cryptographic properties such as confusion and diffusion for better voice communication in the voice applications field in the Internet.


INTRODUCTION
Voice application over Internet protocol (i.e., VoIP) is a IP telephony technology that allows the voice data as human voice to transfers in real-time over Internet Protocol (i.e., IP) in a manner that emulates the traditional telephone service (i.e., PSTN) [1,2]. In general, the voice application over internet protocol only requires an program on the end-point computer (i.e., sender, or receiver) capable of encoding and decoding transmitting speech and Internet access [3,4].
Voice application over internet protocol technology provides more advantages when it is compared to the traditional telephone service. IP telephony technology is cheaper, can be integrated with other media services, portable, and allows for more efficient bandwidth utilization. Therefore, the service providers prefer the IP telephony technology as a method to reduce the cost over existing multimedia services. Moreover, the infrastructure of the IP telephony is considered as a solid economical ground in building the more recent revenue-generating services. Markedly, the deployment of IP telephony technology is becoming more popular and is considered as an integral part of a global competitive landscape [5,6]. Despite of all these positive features, the IP telephony technology is facing some difficulties and challenges such as security, packet loss, and latency. Consequently, more advanced techniques or strategies are warranted to competently manage these difficulties, which are expected to ensure the quality of the IP telephony technology services (i.e., QoS) [3,7]. For example, the threat of the intruders over IP networks is the greatest security challenge in IP telephony technology. The later will be a great concern since these offenders utilize various sniffing tools to compromise the conversation of the IP telephony. To managing the security challenges, cryptography serves as a valuable tool to maintain data secrecy [8,9]. The science of cryptology consists of two major parts: cryptography and cryptanalysis. The science of cryptology and its cryptographic primitives are categorized as illustrated in Figure 1. While cryptography is the art of maintaining data secrecy against unauthorized access (i.e., intruders), on the other sided, cryptanalysis is about analyzing and handling infringement of secure communication [10,11].

Figure 1. Taxonomy of cryptology
To maintain data secrecy against unauthorized access over IP networks the cryptography is widely used. However, most of the existing cryptographic algorithms are built to maintain text data secrecy. Therefore, these existing algorithms are not suitable for voice applications over internet protocol because it involves extensive computation and consumed a large amount of time (i.e., delay) [5,12]. The following four performance factors: encryption delay, the security level, message delay, and processing power are mainly used to measure the VoIP security. The security level (i.e., complexity) of the security algorithm seems to have an impact on these measurement factors [8,13,14]. Constructing new speech encryption algorithms based on chaos theory to increase the security level has drawn for many scientists and researchers attention [15][16][17][18][19][20][21], but unfortunately some of these constructed algorithms have a number of practical problems in terms of cryptanalysis attacks [22,23]. In this paper, a new dynamic speech encryption algorithm using Lorenz chaotic map over IP network is proposed. While generating a chaotic key stream, the system parameters and 128-bit hash value of the plain-speech are included in the proposed algorithm to obtain a highest security level.
The rest of this paper is organized into 5 sections including the introduction as follows: section 2 has described the proposed algorithm based on Lorenz system. Section 3 describes simulation result and security analysis, and explains the procedures used to test the proposed algorithm. In section 4, a comparison with existing work is given and finally conclusion is presented in sections 5.

PROPOSED ALGORITHM
In practical, Lorenz chaotic map has useful cryptographic properties such as confusion and diffusion, sensitivity to initial conditions and parameters, and un-predictability [20]. Therefore, Lorenz chaotic map is used in this paper to propose a new symmetric speech encryption algorithm. It consists of two major parts: keys generation using 128-bit hash value of plain speech frame and the logistic, and encrypting the speech frame using chaotic sequences which are generated by Lorenz system. The overall block diagram of the proposed algorithm architecture can be illustrated by Figure 2. Below, we will provide an introductory definition of the Lorenz system and analyze its main positive features regarding to cryptography. Then, the steps to implement such a process of the encryption parts will be discuss. The decryption steps for completeness will also be illustrated.

Lorenz chaotic system
Lorenz system is a dynamical system which was studied first by Edward Norton Lorenz around 1960 [24], This chaotic system is described by non-linear system of ordinary differential equations (i.e., ODEs) as given in (1).
The real numbers a, σ, b are called the control parameters, where x, y, z are variables called the state variables, and ẋ, ẏ, and ż are the time derivatives of x, y, and z. Usually, the Lorenz system (1) is commonly solved numerically using RK45 (Runge-Kutta methods) for given control parameters, and initial values of the state variables (i.e., x 0 , y 0 , z 0 ). In Figure 3 a chaotic attractor (i.e., Lorenz butterfly) of the dynamical Lorenz system (1) is presented. For different values of parameter σ the dynamical system (1) exhibits chaos. By having positive Lyapunov exponents (i.e., sensitivity to initial conditions), chaos can be recognized for many dynamical systems, and in particular (1). In Figure 4, the maximum Lyapunov exponent of (1) versus values of σ are plotted. In this paper, we have fixed a and b to be a = 10, b = 8/3, and allow value of σ to dynamically vary in the interval [28,90] to provide a large enough key-space to resist brute-force attacks. Moreover, this will guarantee that (1) has dense (chaotic) attractors, which is important in terms of cryptography; any change in initial conditions will cause trajectories to remain in the same attractor set, thus making it difficult to predict any outcome without knowing the exact initial conditions of the system as well as the iteration counts in the numerical solution.

Generation process for the initial values and parameters
In the generation process, we utilize the 128-bit hash value of the plain-speech frame generated by MD5 hash function to dynamically change the initial secret keysx 0 , y 0 , z 0 and σ 0 . In the following steps, the generation process is described in the details.

Step 3:
Set s = x n , y n , z n , 1 100 to construct the 128-bit string.
Step 7: Finally, the following formula is used to compute the new four chaotic keys ̅ , ̅, ̅ , and σ ̅:

Encryption process
In the encryption process, a several iterations over the plain speech frame that involves a set of operation such as substitutions, permutations, transformations, and transpositions are performed to complicate the process of decrypting cipher speech frame by cyber-intruders (i.e., unauthorized access) [25,26]. In Figure 5 the block diagram of the proposed decryption process is presented. The speech encryption algorithm proposed in this paper consists of the following sequential steps: Step 1: Arrange the 20-ms speech frame in = { 1 , 2 , … , } of length = 132, each element is the 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.

SIMULATION RESULT AND SECURITY ANALYSIS
This section discusses the proposed speech encryption algorithm, which simulated on a 1.6 GHz core (TM) i5, 1-TB hard disk capacities and 4-GB memory with MATLAB software. In this section, as an example, different speech samples of audio files are selected with different sampling rate (i.e., 5000 samples per second). The simulation result was validated by applying the statistical tests such as histogram analysis, correlation, randomness, and sensitivity to prove the performance metrics [22]. Below, standardized tests are given.

Histogram analysis test
To evaluate the quality of encrypted speech signals, this analysis is the most accurate test. Practically, the proposed algorithm is likely to encrypt the plain speech signals in a random manner (i.e., noisy signals). Histogram of the input speech signals are illustrated in Figure 6(a) and Figure 6(d).
The corresponding histogram of the encrypted speech signals using the secret keys: x 0 , y 0 , z 0 , σ 0 , and 128-bit hash value of the speech signals are illustrated in Figure 6(b) and Figure 6(e). The results in Figure 6 shows that the histograms of the encrypted speech signals are fairly uniform distributed and totally different from the plain speech signals. In addition, the result indicates that the proposed algorithm can be decrypted correctly with the correct keys as illustrated in Figure 6(c) and Figure 6

Correlation test
The chaotic system was found to produce a strong encryption method, which can be efficiently identified by correlation method [23]. The correlation method is computed as (2). where N is the number of speech samples. In proposed algorithm, the correlation coefficient cov(x, y) between the plain and the ciphered speech samples are tabulated in Table 1. The result in Table 1 shows that the proposed speech encryption algorithm is efficient enough, because the correlation test has been satisfied that would resist statistical attacks.

Randomness tests
To measure the strength of the encrypted speech frames against cryptanalysis attacks, we have performed a different suite of statistical tests in this section known as DIEHARD (i.e., 18-tests) and NIST (i.e., 15-tests) test suite [23,27]. For given sequence, these suites are designed mainly to measure the quality of the randomness. As can be seen from Table 2 and Table 3, the p-value of each test ranges from 0.01 to 0.99 (i.e., success range), which means the encrypted sequence is random at the 99% of confidence level.

Information entropy
Information entropy is used usually as a measure of disorder, or randomness in encrypted speech signal [28]. The entropy function ( )of a source s can be computed as (3).
where P(Si) represents Si probability. The entropy value for the encrypted speech signals should ideally be 8.
In other words, if the entropy value of the encrypted speech signals is less than 8, then the predictability threats to the encrypted speech signals are exists. In this paper, ENT test suite is used to calculate the information entropy value. Practically, ENT is a suite composed of the following three tests: entropy, serial correlation, and chi-square coefficient as shown in Table 4. From these results, the obtained values are evaluated to be almost as the theoretical value, which means that the proposed speech encryption algorithm is efficient enough (i.e., secure) upon the cryptanalysis attacks (i.e., entropy).

Key sensitivity test
To ensure the security against brute-force attacks, the excellent encrypted speech quality must be sensitive in extreme way with respect to the secret keys [24,29]. In the proposed algorithm, any slightly change (i.e., bit flip) on the following sensitivity factors: hash values, keys, and other encryption keys such as parameters that would generate a completely different decryption results as shown in Figure 7.

COMPARISON WITH EXISTING WORKS
There are several types of delay in the current IP telephony networks such as processing (i.e., coder, decoder, digital signal processing), serialization, queuing, propagation, and network delay as shown in Figure 8. Some of them are fixed while others are variable as illustrated in Table 5. IP telephony applications are delay sensitive. Therefore, the ITU-T has recommended that the maximum threshold of the delay time (i.e., ∑delay sources) is 150 ms [2,5,6]. The adaptive multi-rate wideband (AMR-WB G.722.2) speech codec is used in this paper to collect N speech samples as one frame because it supports the GSM features such as discontinuous transmission, comfort noise generation, and voice activity detection [30].  A practical comparison on the average time delay between advanced encryption standard algorithm and proposed algorithm in the same environment and conditions is made in this section. In end-to-end delay, the implementation result shows that the average time delay to encrypt the speech data using the proposed algorithm is 2.287701494 ms and the average time delay to encrypt the speech data using AES is 2.7832762824 ms as illustrated in Table 6 and Table 7 respectively. In other words, a column chart showing the AES algorithm is slower than the proposed speech encryption algorithm is presented in Figure 9. Table 6. End-to-end delay time for fast Ethernet using the proposed speech encryption algorithm Int J Elec & Comp Eng ISSN: 2088-8708  Table 7. End-to-end delay time for fast ethernet using AES algorithm Figure 9. Average delay time

CONCLUSION
In this paper we have achieved our objective of designing a dynamic speech encryption algorithm based on Lorenz chaotic map over internet protocol to enhance the real-time services. The proposed algorithm was divided into two processes: key generation process using 128-bit hash value, and encryption and decryption process using Lorenz system. To evaluate the security level of the proposed algorithm, efficient simulations and implementations and analysis have been conducted. The security level is increased by using a multi key with every new speech packet and increasing a key length which protects the proposed algorithm against various cryptanalysis attacks. In addition, a comparison between the average time delay in the proposed algorithm and some of the existing encryption algorithms is made. The results endorse that the proposed algorithm achieved a higher security level with a lowest average delay time and it is an excellent choice for voice communication in practical applications in the Internet.