A Novel Encryption Technique for LTE-PHY Layer with OFDM Modulation using Wavelet, Transform

A Novel Encryption Technique for LTE-PHY Layer with OFDM Modulation using Wavelet, Transform

Rakesh. S Prof. Prathima

PG Student Asst Professor

Department of ECE, M.Tech ( DCN ) Department of ECE, M.Tech ( DCN ) BTLITM, Bangalore, India BTLITM, Bangalore, India

AbstractOrthogonal Frequency Division Multiplexing (OFDM) and Multiple Input and Multiple Output (MIMO) are two main techniques employed in 4th Generation Long Term Evolution (LTE) with Conventional DFT for multicarrier data modulation and XOR encryption techniques performing bitwise XOR operation between one message bit and one key stream bit to generate one ciphertext bit. However, use of DFT is computationally complex and the use of XOR encryption results in large key size and hence higher frame size. Wavelet based OFDM provides good orthogonality and reduces the number of mathematical operations for multicarrier modulation, improving the Bit Error Rate (BER) and with the use of phase encryption on the modulated symbols the key length is reduced. The usage of wavelet based OFDM system does not require cyclic prefix which increases the spectral efficiency. Hence, we propose to use discrete wavelet transform(DWT) in place of Fast fourier transform(FFT) in the conventional OFDM system and with the inclusion of phase encryption, show that a wavelet based system with phase encryption provides a much better performance than a conventional OFDM system.

KeywordsOFDM; Wavelet; BER; Encyrption.

1. INTRODUCTION

   In the modern day wireless applications some of the major factors to consider are spectral efficiency and the efficient usage of available bandwidth. If we choose modulation using multiple carriers or multi carrier modulation, this divides the data into several streams which can be used to modulate the different carriers. Since the subcarriers in OFDM are always orthogonal to each other, bandwidth efficiency is obtained without the presence of any ICI (Inter Carrier Interference).

   A wavelet is a small waveform that has effectively limited duration having an average value of zero. Wavelet analysis consists of breaking up a signal into scaled and shifted versions of the original signal. . Wavelets are a class of functions used to localize a given function in both space and scaling. ISI (Inter Symbol Interference) and ICI (Inter Carrier Interference) are generally caused by loss of orthogonality between the carriers in a Discrete Fourier Transform (DFT) based OFDM. . ISI is between successive symbols of same sub-carrier and ICI is among different signals at different subcarriers. But, the use of cyclic prefix causes power loss and bandwidth inefficiency in DFT based OFDM.

   When we look at the implementation of an encryption system for the OFDM system, conventional encryption or the stream cipher encryption involves performing of XOR operation between one message bit and one key stream bit

   which generates a cipher text. The reason why XOR is chosen is due to its hardware efficiency. But when it comes to LTE which uses OFDM, phase encryption would be more suitable. It involves multiplying the real and imaginary components of time domain OFDM samples by two {1,1} binary key streams at the PHY layer to provide data confidentiality.

   In this paper we have compared the performance of wavelet based OFDM system with the performance of conventional OFDM system for different LTE modulation techniques with the application of XOR and PHASE encryption. For wavelet based system we have used daubechies2 and haar wavelets. Additive White Gaussian Noise (AWGN) channel is used for transmission.

2. CONVENTIONAL OFDM SYSTEM

   Orthogonal frequency division multiplexing (OFDM) is a multi-carrier modulation technique in which the original is split into many independent signals, each of which is modulated at a different frequency. The basic block diagram is shown in figure-1.As all the subcarriers are orthogonal to each other, they can be transmitted simultaneously over the same bandwidth without any interference. Thus, the available spectrum is utilized efficiently. The disadvantage of FDM i.e., the insertion of guard bands between the sub-carriers which results in wastage of the bandwidth is overcome here.

   Figure-1: Conventional OFDM system

   Practically, Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) are used for the implementation of the OFDM system because less number of computations required in FFT and IFFT. In order to protect the data from loss of symbols due to the synchronization problems a guard band or cyclic prefix is attached. Cyclic prefix is just the replica of a fraction of the signal. As long as the channel delay spread remains within the limit of the cyclic prefix there would not be any loss in orthogonality.

3. WAVELET BASED OFDM SYSTEM

   Figure-2: Wavelet Based OFDM system

   Wavelet transform helps in the joint analysis of the data signal in both the time and frequency domain jointly. It is a multi resolution analysis mechanism where-in the input data is decomposed into different frequency components. Wavelet Transform compared to Fourier Transform possesses better orthogonality and hence are capable of reducing the power of the ISI and ICI, which results from loss of orthogonality. A conventional OFDM system uses cyclic prefixes to deal with ISI and ICI which makes it bandwidth in-efficient but wavelets do not need such a cyclic prefix to guard against ISI or ICI. With the use of wavelet transforms the complexity reduces from O[N log2 N] for Fourier transform to O[N] for wavelet transform. Discrete wavelet transform (DWT) initially passes the signal through a series of filters that decompose the original signal into low pass band and high pass bands through the filters. During decomposition the high pass filter will remove the frequencies below half of the highest frequency and low pass filter will remove frequencies that are above half of the highest frequency. The decomposition halves the time resolution because half of the samples are used to characterize

   the signal similarly frequency resolution will be doubled and this decomposition process will be repeated again for obtaining the wavelet coefficients of required level.This process results in 2 types of co-efficients. First ones are called detailed co-efficients resulting from the high pass filters. The second ones are called coarse approximations resulting from low pass filters followed by the performing of

   decimation process. All these processes are performed until the required level is met.

   This entire process of decomposition through the filters can be expressed using the equations:

   [] = [] [2 ]

   [] = [] [2 ]

   x[n] is the original data signal, HPF[2k-n] is the impulse

   response of the high pass filter, LPF[2k-n] is the impulse response of the low pass filter, res[k] represents the resulting signals after filtering and decimation by a factor of 2.

   In inverse Discrete Wavelet Transform (IDWT) the reverse process of decimation occurs i.e., up-sampling followed by the passage of the signal through the filters and the resulting data will be the reconstructed data. It needs to be noted that both decimation and reconstruction processes will both have the same number of levels.

4. XOR AND PHASE ENCRYPTION

   XOR encryption involves performing of XOR operation between one bit of the message and one bit of the keystream thereby resulting in one bit of a ciphertext making this kind of an implementation very hardware efficient.

   Figure-3: XOR-Enc block.

   Here m, k & c represent the message stream, keystream and the ciphertext respectively. The ciphertext c is a result of the XOR operation between the message bits m and the keystream k.

   Phase-Enc on the other hand is performed on modulated symbols with each modulated symbol containing n = log2 M bits of message, where M is the constellation size. This means that phase enc depends upon the kind of modulation technique chosen.

   Figure-4: Phase-Encryption block.

   In the figure, Q(x) is a function that maps the message x to the modulated symbol. Q(x) is generally complex valued and it is dependent on the type of the employed modulation. If Q(m) is in general complex valued, we use two bits of key stream, one for the in-phase portion of the modulated symbol and one for the quadrature portion of the modulated symbol. If Q(m) is real valued, then only one branch is needed. In this case, the key streams required are reduced by half. For decryption first the imaginary and real components of the received ciphertext is multiplied by the keystreams a and b followed by the necessary demodulation and decoding techniques to recover the original transmitted message.

   methods. On the other hand, P-Enc takes place after the modulation; the required key stream size depends on the underlying modulation scheme as well as the constellation size.

5. MATHEMATICAL FORMULATIONS OF XOR-ENC AND P-ENC WITH DIFFERENT TYPES OF

   MODULATION

   1. PSK Modulation: Let fc be the carrier frequency, be the message symbol represented in phase, then the M-ary PSKmodulated passband signal s(t) has the form

      s(t) = cos( 2 + 2 ), 0

      where = 0, 1, . . . , (M 1).

      Now, let QPSK () be a function that maps i th symbol to one of the M phases, again and denote key streams used for encrypting ith symbol in XOR-Enc and P-Enc, respectively, and g( mi, ) be the phase shift of ith symbol using P-Enc with key stream then we can model the ith modulated ciphertext symbol and with XOR-Enc and P-

      Enc, respectively, by

      () = cos (2 + ( + ) 2) -(1)

      () = cos (2 +

      ( ) 2 + (

      )) -(2)

      ,

      Figure-5: System Level XOR and Phase Encryption

      In figure-5 blocks A and A represent the positions of XOR Encryption and Decryption respectively in a communication system. Blocks B and B represent Phase Encryption and decryption respectively.

      XOR-Enc and P-Enc in a communication system are illustrated in Figs below,

      Figure-6: XOR encryption in a communication system

      Figure-7: Phase-encryption in a communication system

      In these two figures, m is the message, again Q(x) is a function that maps the message x to the modulated symbol. c and c are the resulting modulated cipher text symbols for XOR-Enc and P-Enc, respectively. we see the order of encryption and modulation is reversed between XOR-Enc and P-Enc. XOR-Enc takes place prior to the modulation. Consequently, XOR-Enc is independent of the modulation

      Comparing (1) and (2), we observe in XOR-Enc, similar to

      ASK modulation, ciphertext + takes on the same space as message . Therefore, the phase offset between the modulated message and ciphertext symbols is 2lM , where l

      = 1, . . . , M 1. Recall that P-Enc is performed by multiplying each of real and quadrature components of the modulated symbol by a {1,1} valued key stream, then the modulated ciphertext symbol using P-Enc only takes on four phase values which lies in four different quadrants and it is determined by the four key streams. Without loss of generality, we denote the phase that lies in the first quadrant as p0 , then the other three phase values are p0 , + p0 and 2 p0 .

      Remark: If the M-ary PSK signal constellation is not symmetrical along the x-axis and y-axis, as it is the case when M is odd, then there exists an attack. When M is odd, the signal constellation is symmetrical only along the x-axis. Therefore, only two out of all four phases of the modulated ciphertext symbol lie in the valid signal constellation, the adversary can identify and remove those that are not belong to the signal constellation. Therefore, the searching space is reduced by half. This attack only exists when M is odd. In practice, n = 2M, or M = 2 . In this case, M is always even and all four phases of the modulated ciphertext lie in the

      valid signal constellation. Therefore, this attack is not applicable in practice. In general, n is an integer greater than or equal to 2. Thus, in terms of required key stream size, if message m contains k symbols, then the total required key stream size is nk for XOR-Enc. This number becomes 2k for

      P-Enc. Equivalently, the encryption efficiency for XOR-Enc Comparing (3) and (4), we see for XOR-Enc, the

      and P-Enc are 1 and , respectively. The required key

      2

      streams for P-Enc would always be smaller than or equal to

      that of XOR-Enc. In general, the key stream size is reduced by a factor of 2 using P-Enc compared to XOR-Enc in a PSK-

      modulated communication system.

      Remark: If Binary PSK (BPSK) modulation is used, then n = 1 and the modulated symbol only contains only the inphase signal (real valued). This is identical to binary ASK. Thus, we only perform encryption on the real part of the modulated symbol. Consequently, the number of key streams required for XOR-Enc and P-Enc are still identical. In conclusion, P-Enc would always require smaller or equal amount of key streams for PSK-modulated systems. If the adversary performs random guessing on the received ciphertext symbols, excluding the BPSK case, then his successful probability for recovering message m with XOR- Enc , and P-Enc , are, respectively

      1

      modulated ciphertext symbol space is identical to the modulated message symbol space. Therefore, the modulated ciphertext symbol could be lie on any one of the valid signal constellations. However, encryption using P-Enc is achieved by only changing the phase of the modulated message symbol, the amplitude remains unchanged. For P-Enc in QAM modulation, modulated ciphertext symbol also takes on four phase values and these four phase values are identical to PSK modulation. Using the same notation as PSK modulation, these four phase values are p0 , p0 , + p0 and 2 p0.

      Remark: Note that for M-ary QAM, signal constellation is always symmetrical along the x-axis and y- axis. The modulated ciphertext symbols of all four phases are also a valid modulated message symbol. Therefore, the attack described previously for PSK modulation is not applicable here. In terms of required key stream size, if the message m contains k symbols, then for XOR-Enc, the total key stream size is nk. This number becomes 2k for P-Enc. Equivalently,

      the encryption efficiency for XOR-Enc and P-Enc are 1 and

      , =

      2

      2

      , respectively. In general, the key stream size is reduced by a

      1

      =

      factor of 2 using P-Enc compared to XOR-Enc in a QAM-

      ,

      22

      modu

      communication system. . If the adversary

      If BPSK modulation is used, , has the same form as ASK modulation, namely

      1

      , = 2

      lated

      performs random guessing on the received ciphertext symbols, then his successful probability for recovering message m with XOR-Enc , and P-Enc

      , are identical to the PSK case, namely

      1

   2. QAM Modulation: Let fc be the carrier frequency,

   be the symbol amplitude and be the phase, then the M- ary QAM

   modulated passband signal s(t) has the form

   s(t) = Al cos( 2 + l), 0

   , =

   , =

   2

   1

   22

   where l = 1, 2, . . ,M.

   Unlike ASK and PSK modulations where the modulation is performed either on the amplitude or the phase, QAM modulates message using both the amplitude and phase. Note that the values of amplitude Al and phase l depend on the type of the employed QAM.

   Now, let QQAM() be a function that maps ith symbol to one of the M symbols using QAM modulation which contains a amplitude of |QQAM()| and a phase of

   QQAM(), let and represent key streams used for encrypting ith symbol in XOR-Enc and P-Enc, respectively,

   and g( , ) be the phase shift of ith symbol using P-Enc

6. PROPOSED DWT BASED OFDM SYSTEM WITH PHASE ENCRYPTION

   As shown in the figure in our proposed model we replace the blocks of DFT and IDFT in a conventional OFDM system with DWT and IDWT blocks. Also the conventional encryption technique or XOR encryption is replaced by Phase encryption. Thus, the original data will be modulated and then phase encryption is applied on it. Then the data after being converted to parallel form is subjected to inverse discrete wavelet transform followed by cyclic prefixing before being sent over the channel. At the receiver

   with key strea

   m , then we can model the ith modulated

   end, the parallel data after passing through a frequency

   domain equalizer and after removal of the guard band is

   ciphertext symbol and with XOR-Enc and P-Enc, respectively, by

   () = |( + )|cos (2 + ( + )) -(3)

   () = |()|cos (2 + () + ( , )) -(4)

   subjected to discrete wavelet transform. This data will then be converted to serial form and demodulated to obtain the original data.

   Figure-8: DWT based OFDM system with Phase-encryption.

7. BER PERFORMANCE EVALUATION

   In matlab for the different modulation techniques, we obtain the performance characteristics of both DFT based OFDM system and DWT based OFDM system. For the purpose of simulation, signal to noise ratio (SNR) of different values are introduced through AWGN channel. The modulation techniques chosen are PSK and QAM. From the SNR plots, we can see that the BER performance of the DWT based OFDM system with phase encryption is much better than the performance of the DFT based OFDM system with XOR encryption for constellation sizes of M = 2, 4 and 16.

   Figure-9: SER versus SNR for M = 2

   Figure-10: SER versus SNR for M = 4

   Figure-11: SER versus SNR for M = 16

8. CONCLUSION

   In this paper we first compared the XOR and Phase Encryption techniques. Using mathematical formulations we compared the security and encryption efficiency of these two encryption methods. Through this we showed that phase encryption requires a much smaller keystream size than that needed by XOR encryption. We then compared the performances of the wavelet based OFDM system with phase encryption with the performances of DFT based OFDM system with XOR encryption for both PSK and QAM modulation techniques for different constellation sizes. Observing the performance curves we can say that the BER performance of the wavelet based OFDM system is clearly better than the DFT based OFDM system.

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