HARDWARE AND SOFTWARE REALIZATION OF THE TRANSMISSION OF AUDIO INFORMATION ENCRYPTED BY CHAOTIC SEQUENCES

. An audio information transmitting system, encrypted by chaotic sequences, which are generated on the base of discrete one-dimensional mappings is described in the article. The operation of the system is considered on the example of the information transmission between two computers.


Introduction
Along with the rapid development of telecommunication systems, internet technologies, in particular, IP-telephony the problem of the protection of audio information, which is transmitted by digital communication channels through Internet / Ethernet network, was raised. The modern telecommunication systems require a high confidentiality level of communications. The protection of the information, which is transmitted in telecommunication systems, can be realized by means of closing them by chaotic sequences. This approach resulted in the development of fundamentally new methods of encoding, encryption and transmission of information, in particular, cryptographic methods based on the theory of dynamical systems with their inherent chaotic properties. Nowadays, the cryptographic methods of information protection remain the most stable and secure methods of data transmission [3,6].
One of the main problems of the design of secure communication systems is the synchronization between the receiving and transmitting components of the communication systems. The majority of the methods of secure data transmission with the synchronization by chaos are based on the total chaotic synchronization, which requires a high degree of identity of the generators of transmitting and receiving components of the information transmitting system. The improvement of the techniques of the secure data transmission, based on the systems with the chaotic synchronization is an important task for the research in the field of information and telecommunication systems based on chaos [3,6].
The aim of our work is software and hardware realization of the audio information transmitting system with the encryption by pseudorandom sequences, which are generated on the basis of one-dimensional discrete chaotic mappings with the synchronization of transmitting and receiving components of the system.

Encryption algorithm
There are the following methods of the audio information protection: digital scrambling, streaming encryption and standard encryption. The most effective way for the protection of audio information from possible threats (the unauthorized access, the loss of the integrity and authenticity of information) is the cryptographic transformation. The aforementioned methods of information protection possess the following disadvantages: the digital scrambling results in the additional delays during the transmission of audio information that is caused by the scrambling algorithm itself; the standard cryptographic encryption, according to the known algorithms, provides satisfactory protection of audio information, but it is costly in terms of speed and complexity of computing [11]. The most preferred, in terms of speed and complexity of computing, is the bitwise addition on module 2 (XOR operation) of the digitized parts of the input sequence of audio information with an infinite or periodic key, which may be formed, for example, by a generator of pseudorandom sequences (PRS) [4,11].
As the encryption sequence the pseudochaotic sequences can be used. Their generation algorithms can be realized on the basis of the dynamic chaos, which is sensitive to the initial conditions. The one-dimensional discreet mapping, called the logistic equation, is used for the generation of chaotic digital sequences [1,4,10]: where λ is the parameter, x 0 is the initial condition for the generation process. The generation of a chaotic sequence, governed by the logistic equation (1), occurs if the value The block diagrams of the proposed systems of the information transmission as well as the diagrams of the encoder and decoder are shown in Figures 1 and 2, respectively. The input audio information (analogue signal) from a source of information is fed to the input of the analog-digital converter (ADC), which is a computer sound card, and is turned into a bit representation. The following one-dimensional discrete chaotic mapping (logistic mapping) is used in order to generate the pseudorandom sequences: ( The generated sequence of numbers is converted into the binary bit representation according to the following equation [9]: where L is the digit capacity of the binary representation. The digitized audio information m i is added to the elements of the generated chaotic sequence, according to module 2 (using the XOR operation): The decryption is performed by the adding, according to module 2, of the received encrypted information to the chaotic sequence, which is generated by the receiver using the same logistic equation and initial conditions [2,5].
The reliability of the system is determined by the keyspace for the generation of the sequences that is the value of the parameter of the logistic mapping λ and the initial value of x 0 . The amount of the keyspace can be calculated as follows: where n is the accuracy of the given parameters (the number decimal digits). In our case, the accuracy of the parameters is given by the program and is equal to 10. Thus, the keyspace is equal to (10 10 ) 2 = 10 20 that is a satisfactory result for a two-parametric system. The possibility of the faultless reproduction of information is realized by the application of one of the synchronization methods (complete, generalized, phase, etc.) in similar systems. In works [7,8] the synchronization is carried out by means of the constant sync pulses by their shape and duration. A sync pulse is transmitted over a time interval, which consists of the duration of the informational signal and the synchronization sequence Т i and T s , respectively. The time diagram of the transmission of the sync pulse and the informational signal is shown in Figure 3. In our system the synchronization is proposed to be realized by the transmission of the current value of x n , which is generated by the logistic mapping, over some time intervals.
The transmission period of the value x n depends on the performance of a computer and on the distance between the system subscribers. The setting of the period is carried out at the program level. The maximum value of the transmission period of x n was equal to 21 μs in the case of Intel P-IV 2.4 GHz computers. The synchronization was stable at the transmission period less than 21 μs that resulted in the almost faultless reproduction of the information.

Implementation of the system
Modern computers usually allow to input/output audio signals by means of a standard sound card. The digitization, conversion and reproduction of audio signals are carried out by a computer and are controlled by the application of programming interface (API) of an operating system (Windows or other alternative operating systems). Modern programming environments C++ Builder, Delphi, Visual C + + and others can use the API interface and, thus, can be applied to create the programs of the input, conversion and reproduction of audio files.
The modern software, in particular, programming language Delphi 7.0, was used for the design of the system. The system operates in real-time in the full duplex mode at any hardware implementation of the Internet access. The system subscribers only need to enter the IP address.
The developed program allows: 1) to receive and reproduce the signal from a microphone connected to the built-in PC sound card, with the digital capacity of 8/16 bits and the sampling rate of 44100 Hz; 2) to encrypt/decrypt in real-time audio information (addition on module 2) by means of the periodic sequences obtained from the generator of pseudorandom sequences; 3) to set the parameters of the audio information processing (the digital capacity of 8/16 bits and the sampling rate of 44100 Hz); 4) to set the initial conditions for the generation of pseudorandom sequences.
The results of the program operation are shown in Figure 4. The value of the parameter of the encryption key λ is equal to 3.94 for the sender and recipient (Figure 4 a,b). The initial value x 0 is entered only at the beginning of the exchange of information. Afterward, the current value of х n is shown in the program window. The left top window in Figure 4 a) shows the audio information, which comes from the microphone of the user A, the left bottom window in Figure 4 a)the encrypted information, the right top windowthe received encrypted information by user B, the bottom right windowthe decoded information by user B. The user B can transmit audio information to the user A in the same manner (Figure 4 b).

Conclusions
We proposed the system for the transmission of audio information with its encryption by chaotic sequences, generated by the logistic equation. The value of the parameter λ of the logistic equation is given within the range from 3.65 to 3.95.
The synchronization of the audio information transmission is carried out by means of the transmission of the current value of x n , generated by the logistic mapping, through the communication channel over some time intervals. The transmission period of the value x n depends on the performance of a computer and on the distance between the system subscribers. The trouble free reproduction of the audio information by the recipient was achieved by setting the optimal transmission period of the current value of x n .
The reliability of the system is determined by the keyspace for the generation of the sequences that is the value of the parameter of the logistic mapping λ and the initial value of x 0 . In our case, the accuracy of the parameters is given by the program and is equal to 10 that results in the satisfactory keyspace (10 10 ) 2 = 10 20 for a two-parametric system.