Image Encryption Algorithm Using Natural Interval Extensions

It is known that chaotic systems have widely been used in cryptography. Generally, floating point simulations are used to generate pseudo-random sequence of numbers. Although, it is possible to find some works on the degradation of chaotic systems due to finite precision of digital computers, little attention has been paid to exploit this limitation to formulate efficient process for image encode. This article proposes a novel image encryption method using natural interval extensions. The sequence of arithmetic operations is different in each natural interval extension. This is what we need to produce two different sequences; the difference between these sequences is used to generate the lower bound error, which has been shown to present satisfactory pseudo-random properties. The approach has been successfully tested using the Chua's circuit as the chaotic system. The secret key has presented good properties for encrypting the Lena image.