Secure DFT-Ordered Luminance Method for Parallel Transmission Image-Sensor Based VLC

A secure method is proposed for paralleltransmission (PT) image-sensor (IS) based visible light communication, where M luminance signals in one-dimensional order produced by inverse discrete Fourier transform (IDFT) are mapped in a two-dimensional plane transmitted in free space between liquid crystal display (LCD) and IS. Each position in the one-dimensional order is preassigned to a region on the twodimensional plane, which is known to both transmitters and receivers. In the secure method, the one-dimensional order of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> DFT-related luminance signals is shuffled, and only the legitimate receiver can restore the original order. To share the original order secretly between authorized transmitter/receiver pairs, we use three integers e, d, and n based on RSA cryptosystem. When a transmitter chooses an integer I between 0 and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>!−1, it uses the Ith order among <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>! ways to rearrange the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> DFT-related luminance signals. For the transmitter to tell I as the ciphered integer u, it calculates the modulo-(M + 1) of u to divide u0, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</i>1,..., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</i>H−1. Then, it inserts a new luminance signal called “mark” at the uhth position in the rearranged order over H consecutive frames. Although all receivers detect the position of “mark” every frame, only the legitimate receiver correctly calculates I, from the mark-detected positions v0, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</i>1,..., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</i>H−1, using the private integer d. Receivers without d must search the original order among M! possible permutations every frame even though they detect all the positions of “mark” correctly. Experimental results show that the luminance value <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> of “mark” exists that receivers can distinguish it from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> DFT-related signals, in the transmission distance of 1.5 meters to seven meters and that the probability is extremely low that receivers without d demodulate the information bits correctly