Pseudo Noise Sequence Generation using Elliptic Curve for CDMA and Security Application

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1 IJIRST International Journal for Innovative Research in Science & Technology Volume 1 Issue 11 April 2015 ISSN (online): Pseudo Noise Sequence Generation using Elliptic Curve for CDMA and Security Application Nivedita Singh BE Student Barkha Shrivastava BE Student Payal Dwivedi BE Student Manoj Kumar Assistant Professor Abstract Spread spectrum communication is a new theory and modulation technique and different from the conventional communication system. A good correlation property and large linear period of Pseudo-random sequence is the basis of spread spectrum communication systems intern CDMA (code division multiple access communication systems). In this paper PN (pseudo noise) sequence/ code which is referred as the high rate digital code is generated on MATLAB by use of cyclic elliptic curve. This paper presents an investigation on use of Genetic Algorithm (GA) for the purpose of encryption of audio and video input. A pseudo random sequences, is use in various applications like CDMA, image protection, speech security, watermark etc. The most commonly used sequences in direct sequence spread spectrum systems are maximal length codes, gold codes and barker codes. The sequence offers a variety of correlation properties like auto and cross correlation, sensitivity, key space etc. Based on a measure described in this, the correlation properties of sets of these sequences are compared to well-known sequence sets and after comparing it we can apply it in various applications. Keywords: Pseudo Noise sequence, Spread Spectrum, Code Division Multiple Access, Genetic Algorithm, Elliptic Curves I. INTRODUCTION Pseudo random binary sequences (PRBSs), also known as pseudo noise (F ), linear feedback shift register (LFSR) sequences or maximal length binary sequences (m sequences),are widely used in digital communications. In a truly random sequence the bit pattern never repeats. Pseudo-Noise (PN) sequences whose terms depend in a simple manner on their predecessors. Such sequences are easily generated by recursive procedures. PN sequences that are useful for speech encryption must have very good auto-correlation and cross-correlation properties as well as maintaining some randomness properties. The security offered by the system depends on the randomness of PN sequence. Pn-sequences generated by the use of elliptic curves have more randomness and thus, it behaves more like a noise, therefore difficult to detect. The objective of the paper is to generate PN sequence using elliptic curve and to test the properties of each generated PN sequence and compare the performance with the standard codes. This paper presents an investigation on use of GA for the purpose of encryption of audio and video input and followed by modulation based DSSS-CDMA technique. II. METHODOLOGY A pseudo random binary sequence is a semi-random sequence in the sense that it appears random within the sequence length, fulfilling the needs of randomness, but the entire sequence repeats indefinitely. To a casual observer the sequence appears totally random, however to a user who is aware of the way the sequence is generated all its properties are known. PN sequences have several interesting properties, which are exploited in a variety of applications. Because of their good autocorrelation two similar PN sequences can easily be phase synchronised, even when one of them is corrupted by noise. A PN sequence is an ideal test signal, as it simulates the random Characteristics of a digital signal and can be easily generated. An elliptic curve is a plane curve defined by an equation of the form y^2=x^3+ax+b All rights reserved by 222

2 Curves of this nature are called ELLIPTIC CURVES Consider the field F, defined by using polynomial representation with the irreducible polynomial f(x) = x 4 + x + 1. The element g = (0010) is a generator for the field. The powers of g are: g 0 = (0001) g 1 = (0010) g 2 = (0100) g 3 = (1000) g 4 = (0011) g 5 = (0110) g 6 = (1100) g 7 = (1011) g 8 = (0101) g 9 = (1010) g 10 = (0111) g 11 = (1110) g 12 = (1111) g 13 = (1101) g 14 = (1001) g 15 = (0001) Using generator notation allows multiplication without reference to the irreducible polynomial f(x)=x 4 +x+1. Consider the elliptic curve y 2 + xy = x 3 + g 4 x Here a = g 4 and b = g 0 =1. The point (g 5, g 3 ) satisfies this equation over F 2 m: y 2 +xy=x 3 +g 4 x 2 +1 (g 3 ) 2 +g 5 g 3 =(g 5 ) 3 +g 4 g g 6 +g 8 =g 15 +g (1100)+(0101)=(0001)+(1001)+(0001) (1001)=(1001) The fifteen points which satisfy this equation are: (1, g 13 ) (g 3, g 13 ) (g 5, g 11 ) (g 6, g 14 ) (g 9, g 13 ) (g 10, g 8 ) (g 12, g 12 ) (1, g 6 ) (g 3, g 8 ) (g 5, g 3 ) (g 6, g 8 ) (g 9, g 10 ) (g 10, g) (g 12, 0) (0, 1) Trace Function: The trace values of individual points lying on the field is calculated by xoring every point with trace function so obtained. Then the points form a unique pn-sequence by interleaving the x-coordinates & y-coordinates of each point as shown GENETIC ALGORITHM FOR ENCRYPTION Tx Antenna INPUT DATA (decimal to binary) XOR OPERA-TION PN- SEQUE NCE CROSS- OVER MUTA- TION MODU- LATION CARRIE R SIGNAL Fig. 1: Transmitter Section All rights reserved by 223

3 GENETIC ALGORITHM Rx Antenna FOR DECRYPTION DEMODU- LATION DMUTA - TION REVERS E CROSS- OVER XOR OPER A- TION OUTPUT DATA (binary to Decimal) CARRIER SIGNAL PN- SEQUEN CE Fig. 2: Receiver Section The GA is a stochastic global search method that mimics the metaphor of natural biological evolution. A genetic algorithm (or short GA) is a search technique used in computing to find true or approximate solutions to optimization and search problems. Genetic algorithms are categorized as global search heuristics. Genetic algorithms are a particular class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and recombination. Genetic algorithms (GAs) can be applied to any process control application for optimization of different parameters. Genetic algorithms (GAs) use various operators viz. the crossover, mutation for the proper selection of optimized value. Selection of proper crossover and mutation technique depends upon the encoding method and as per the requirement of the problem. A. Crossover: It is the process in which genes are selected from the parent chromosomes and new offspring is created. Crossover can be performed with binary encoding, permutation encoding, value encoding and tree encoding. B. Binary Encoding Crossover: In binary encoding, the chromosomes may crossover at single point, two points, uniformly or arithmetically. In single point crossover, a single crossover point is chosen and the data before this point are exactly copied from first parent and the data after this point are exactly copied from the second parent to create new off springs. Two parents in this method give two new off springs. Before Crossover after Crossover Fig. 3: Binary encoding crossover C. Mutation: Premature convergence is a critical problem in most optimization techniques, consisting of populations, which occurs when highly fit parent chromosomes in the population breed many similar off springs in early evolution time. Crossover operation of genetic algorithms (GAs) cannot generate quite different off springs from their parents because the acquired information is used to crossover the chromosomes. An alternate operator, mutation, can search new areas in contrast to the crossover. Crossover is referred as exploitation operator whereas the mutation is exploration one. Like crossover, mutation can also be performed for all types of encoding techniques. D. Binary Encoding Mutation: In binary encoding mutation, the bits selected for creating new offsprings are inverted. In binary encoding mutation, if the bit 1 is converted into bit 0, it decreases the numerical value of the chromosome, and is known as down mutation. Similarly, if the bit 0 is converted into bit 1, the numerical value of the chromosome increases and is referred as up mutation. All rights reserved by 224

4 Before Mutation after Mutation Fig. 4: Binary encoding mutation III. RESULT AND DISCUSSION Fig. 5: The 32 bit p-n sequence generated using the elliptic curve1 is In this audio signal, there are total samples. Some of the encrypted sample values are:- 30 th sample: st sample: nd sample: Fig. 6: Encrypted Samples of Audio Signal All rights reserved by 225

5 IV. O/P WAVEFORMS OF AUDIO INPUT APPLICATION Fig. 7: O/P Waveforms of Audio Input Application In application part, the audio signal is encrypted using the pseudo random sequence generated by elliptic curve method. The pseudo random sequence so generated is of thirty two bits, out of which only sixteen bits have been considered. For encryption of audio signal, firstly it has been converted to digital samples. Then genetic algorithm has been applied to these digital samples and the pseudo random sequence for obtaining the encrypted sample values. The genetic algorithm has two main operators that is crossover and mutation. Firstly, the sample values are XOR-ed with the generated pn-sequence. Then crossover operation is performed considering the two consecutive sample values at a time and are finally mutated. In this way all the digital samples are encrypted. Now the encrypted samples are modulated using pn-sequence based on the principle of DSSS. These modulated samples are thus received at the receiver end; where the demodulation and decryption operation is performed. The above operation is the simplest type of CODE DIVISION MULTIPLE ACCESS. The pseudo random sequence which is used; is generated using elliptic curve because it will provide maximum randomness to the sequence and also because of its computational complexity. For its generation; an elliptic curve has been selected and the galois field is chosen. The galois coefficients are calculated such that they satisfy the galois field. Then the trace function is calculated. The roots of the elliptic curve are computed which will be in the form of galois coefficients ;they are xored with trace function and finally trace value is calculated to obtain single bit x, y coordinates. These x, y coordinates are then interleaved to form the pseudo random sequence. This computational complexity will provide sufficient randomness to the sequence thus making it look like a noise; thereby providing high security against unauthorised access. V. CONCLUSIONS AND FUTURE SCOPE In this paper we have provided simple and comprehensive technique for generation of Pn sequences which can be used for purposes like echo hiding, spread spectrum modulation and watermarking. A. Echo Hiding: It is a method of audio watermarking. It is based on the fact that one cannot perceive short echoes of the order of a millisecond. Echo hiding embeds data into a cover audio signal. To encode ones and zeros, two types of echoes with different delays are used. Thus, an arbitrary sequence of ones and zeros can be embedded. B. Spread Spectrum Modulation: It is a digital radio frequency modulation technique. This modulation method is immune to interference and interception. Here, a given binary signal sequence is multiplied with other PN sequences to spread the signal over a much larger frequency band. The resulting signal is much below the noise floor. At the receiver, correlation receiver/matched filter is used to recover the original binary signal sequence. The precise detection requires the original PN sequence also. By using difference PN sequences for spreading difference binary signal sequence, it is possible to send multiple signal sequence simultaneously, over a given frequency band. All rights reserved by 226

6 C. Watermarking: Watermarking is also a sub-discipline of information hiding. Watermarking secures the content. Thus, any attempt to modify the content can be easily detected.it is the process of embedding secret and robust identifiers inside audio-visual content.to overcome the limitations in watermarking due to methods like LSB substitution and to make the system more robust against attacks, the watermark can be spread across the cover object by using more number of bits than the minimum required.this scheme of hiding the data uses the concepts of code division multiple access(cdma).this technique ensures the survival of watermark under various attacks due to redundancy. Each of the data bits is represented by using a large number of bits out of which a significant portion may be lost without totally losing the watermark information. D. Watermarking Using PN Sequences: Psuedonoise sequences are used for watermarking because of their very good correlation properties, noise like characteristics and resistance to interference.each data bit of the watermark is represented by a large number of bits, out of which a significant portion may be lost without losing the watermark thoroughly.this method ensures the survival of watermark because of redundancy.a general method that is followed for watermarking using PN sequences is embedding a PN sequences into the data where every PN sequence represents one bit of watermarking information. For the watermark extraction the sequence of marked bits are correlated with known PN sequence. A pseudorandom noise (PN) sequence is a sequence of binary numbers, which appears to be random, but is in fact perfectly deterministic. The sequence appears to be random in the sense that the binary values and groups or runs of the same binary value occur in the sequence in the same proportion. Pseudo Noise Sequence (PN Sequence) is also known as maximum length sequence. It has properties of a random binary sequence.pn sequence is a periodic binary sequence. It is generated by an n-bit linear feedback shift register. Its bit duration is fraction of information bit duration. PN sequence is used as spreading sequence in spread spectrum transmitter. Different PN sequences can be generated by feeding in different n-bit initial sequence. The CDMA technique is a spread spectrum technique, that spreads the transmitted or the narrowband message over a wide frequency band, which is much wider than the actual minimum bandwidth required and this large bandwidth signal is called as the spreading signal. One method of widening the bandwidth is by use of modulation. Pseudorandom sequences or the PN sequences are used as the spreading sequences. REFERENCES [1] Ahmad A, Al-Busaidi S S et al. (2013). Study on cyclic cross-correlation behavior of maximal length pseudo-random binary sequences, Indian Journal of Industrial and Applied Mathematics (Taylor & Francis), vol 4(1) [2] Ahmad A (2012). Better PN generators for CDMA application, a Verilog-HDL implementation approach, International Journal of Information Engineering (IJIE), vol 2(1), [3] Golomb S W (1982). Shift Register Sequences, Aegean Park Press, Revised Edition. [4] S. V. Sathyanarayana(2012). Symmetric Key Image Encryption Scheme with Key Sequences Derived from Random Sequence Elliptic Curve of Cyclic, International Journal of Network Security, Vol.12, No.3, PP.137(150) [5] Pal, M. Chattopadhyay(2010). A novel orthogonal mini mum cross-correlation spreading code in CDMA system Emerging Trends in Robotics and Communication Technologies (INTERACT), 2010 International Conference on Digital Object, 2010, pp [6] Abhijit Mitra (2008). On the Properties of Pseudo Noise Sequences with a Simple Proposal of Randomness Test, International Journal of Electrical and Computer Engineering 3:3. All rights reserved by 227