Lucas Algorithm for Medical Images Encryption and Transmission using Orthogonal Frequency Division Multiplexing for Medical Health Information Systems and its VLSI Realization

—Security of medical images is critical for transmission of medical images and relevant patient information through public health information systems networks. Image encryption is an important tool for protecting medical images by converting them into unrecognisable formats for the transmission and reception of medical images. This paper proposes an algorithm for medical image encryption using Lucas Algorithm, and a discrete wavelet transform based transmission and reception technique, which is known as orthogonal frequency division multiplexing (OFDM). This paper presents an implementation of Lucas Algorithm for image encryption and combines it with Discrete wavelet transform orthogonal frequency division multiplexing using Field Programmable Gate Array.


Introduction
Security of medical images is critical for transmission of medical images and relevant patient information through public health information systems networks. OFDM uses the orthogonality principle. In orthogonal frequency division multiplexing (OFDM), adjacent subcarriers are orthogonal to each other and there are no guard-bands for signal recovery [1]. Fast Fourier Transform is useful as an OFDM transmitter. FFT-based orthogonal frequency division (OFDM) is complex to transmit high speed data. Wireless communications networks are based on technology of Fourier transform. Fourier decomposition decomposes information into elementary frequencies, but these are sines and cosines. The wavelet basis functions are much more compact than sine functions and cosine functions. The wavelet transform refers to different resolutions, in time and space. Wavelet base functions offer a multifaceted solution to wireless communication systems [2]. High-speed data networks are going to boost future communication tools [3][4][5][6][7]. Wavelet transform based system can give powerful control over neighbour subcarriers. Remote and private wireless networks can now be more easily accessed [8]. The security of digital medical images is extremely vital as images are distributed through the public network [9][10].
This paper proposes Lucas image encryption algorithm and wavelet transform based Orthogonal Frequency Division Multiplexing (WOFDM) for transmission and reception for protected medical image communication.

The Proposed Encryption and Decryption Using Lucas Transform Algorithm
The Lucas Transform is used to scramble the input image marix X to generate the image Y.In Lucas Transform , basically, the Lucas sequence is a recursive sequence and defined by.
By applying the equation (1) and (2), we have construct the series and Lucas series containing numbers. and Lucas transform can be easily represented as a 2-by-2 matrix by any four consecutive terms of the numbers, this matrix can be used to scramble an image by using a mask. A generalized and Lucas mask can be described in general way.
Where x,y, xnew ,ynew ∈ 0,1,2,3,4,… fi,Li are the ith term of the and Lucas series. [ ] is the pixel coordinate in origin image and xnew, ynew is the new coordinate for the pixel in the scrambled image. This scanner will scramble an image and generate a new photo.
Encryption method using Lucas and transform at the transmitter is shown in figure1 and described as: 1. The input image will be read as a matrix X. It is necessary to process the image or matrix to squared matrix to get the highest possible quality output. 2. Randomly rotates the individual elements of matrix X by using Lucas and transform on input matrix to get matrix Y.
The encrypted image Y is applied to wavelet transform based Orthogonal Frequency Division Multiplexing (WOFDM) for transmission and received image is decrypted using decryption algorithm.
Decryption method using and Lucas transform at the receiver is shown in figure2 and described as: The original image X can be generated by the inverse of the Lucas transform described in the equation [3].

Implementation of Discrete Wavelet Transform (DWT) OFDM System
The DWT OFDM system was modelled using VHDL and implemented using FPGA is shown in Figure3. The two-level inverse wavelet packet data transform structure and wavelet packet data transform structure are shown in fig.4a and fig.4b. Discrete wavelet transform can be used as a reversible and lossless transform. Below are the equations for forward and inverse wavelets transform filters.

Conclusion
In this paper, Lucas algorithm based medical image encryption and discrete wavelet transform based OFDM transmitter and receiver is proposed and implemented using FPGA. The effectiveness of the VLSI architecture designed for the proposed algorithm is demonstrated through the implementation on medical images using XILINXISE and ModelSim.