An improved RSA image encryption algorithm using 1-D logistic map

The need to have a more secured ways of protecting sensitive images in this modern age of technology has become necessary for ensuring that such images sent via the insecure public network called the Internet are protected from attacks. To this end, various image encryption algorithms have been proposed by many researchers and RSA image encryption algorithm is one of them. Studies on RSA image encryption algorithm reveal that some images when encrypted using the algorithm, gives encrypted images that do expose some features of the plain images on visual inspection no matter the size of primes used. This is due to the fact that digital images have high redundancy and high correlation of image data that make RSA algorithm image dependent. Cryptanalysis has been a major source of concern (in particular the brute-force attack) when designing a cryptosystem since it is assumed that the cryptanalyst knows exactly the design and working of the cryptosystem under study except the secret key. Thus, making the secret key access much more difficult to the cryptanalyst makes the encryption algorithm a more reliable one. In view of these, an improved RSA image encryption algorithm using 1-D logistic map was proposed. The proposed scheme has two stages. In the first stage, the plain-image is shuffled using the chaotic properties of the map and in the second stage; the shuffled image is encryption using the RSA algorithm. The proposed algorithm and the RSA algorithm were tested on two standard test gray scale images: cameraman.tif and clock.tif using four different set of keys. Security analysis such as histogram analysis and correlation coefficient analysis were also carried out on the results obtained from the two methods. The results of the analysis show that the proposed scheme is more secured and stronger against the brute-force attack ( encrypted image which does not reveals any hint about the plain image to the attacker and also its key space has double: the two primes, initial condition and control parameter) than the RSA image encryption scheme.