Image Encryption and Decryption Using Chaotic Maps and Modular Arithmetic

Abstract

In this paper we have proposed a scheme which incorporates the concept of modular arithmetic and chaos theory, for image encryption and decryption. In the proposed scheme, we have used chaos theory to generate the necessary random matrix and used the same for Image encryption. For Decryption, we have used look-up table approach to find the element by element modular inverse of the random matrix and use it for decryption of an encrypted image. Our proposed scheme seems to be robust against various attacks.

Comprehensive Performance Analysis of Chaotic Colour Image Encryption Algorithms Based on its Cryptographic Requirements

“…In this analysis, we investigate issues like key related issues, security analysis and channel issues. Correlation and Histogram analysis were specified in all [2,4,5,6,7,8,12,13,14,15,16,17,18,19,20] the reviewed research articles. NPCR and UACI were carried out by most [2,4,5,6,7,8,12,14,15,16,18] of the research papers in order to prove the efficiency of their algorithms.…”

“…Details like implementation, key related issues, encryption type, resistance against cryptographic and chaos specific attacks are not specified clearly in most of the papers. In some articles, security measures like Mean Absolute Error [8], Mean Square Error [13], Entropy Analysis [4,5,6,12,13,14,15,18], Deviation Measuring Factors [20] and FIPS Test [8] were incorporated. To summarize, if the rules recommended by Gonzalo Alvarez and Shujun Li are followed, a reasonable degree of security and most acceptable features of cryptography can be guaranteed.…”

“…Since then a lot of important concepts like Lyapunov exponents, dimensions and attractors have been introduced. [20,24] In a world of digital image encryption algorithms, there are umpteen number of applications developed with each have advantages / drawbacks over the others. Both cryptography and chaos theory dominate different parts of information security in remarkably different ways.…”

“…Shyamsunder et al [20] proposed encryption and decryption of an image using three different chaotic maps and modular arithmetic with the key space of about 2…”

“…R is the growth rate, and n-generation number. Logistic equation was proposed by Pierre Verhulst in 1845 [20].…”