After the great expansion of internet, communications tends to be lifeblood, at the same time data protection became more critical issue, so the need to secure transfer channel is being more urgent, this goal achieved by applying one or more of data protection techniques. Steganography one of the most suitable solution for this problem, due to the good specification of concealing secret file inside cover image, in such way there is nobody even suspects the existence of transferred file. The main challenge in steganography methods is how to make balance between the quality of file that will be used to conceal the secret and the size of the secret file. Also there are another factors should be considered, which are, robustness and security against attacks. In this study Fibonacci numbers have been exploited to achieve these goals. Fibonacci numbers used to decompose the cover file into 12-bitplanes instead of 8-bitplanes produced by binary decomposition, the four extra layers will increase the capacity of cover image. The resulted 12-bitplanes, has special statistical nature in terms of distribution of black regions (zero values) and white regions (one values). This statistical nature has been exploited by modifying the binary representation of secret message to make matching between the representation of secret message and cover image to reduce the impact of embedding process on the resulted file (stego-image). By applying Fibonacci decomposition to the cover image, better results have been achieved in terms of Peak Signal to Noise Ratio(PSNR) which indicates the ability of embed more secret size with maintaining the quality of stego-image, also the security and robustness has been evaluated by applying chi-square attack, the result for this attacks show that Fibonacci LSB method is withstanding for such attack
