A bit-plane encryption algorithm for RGB image based on modulo negabinary code and chaotic system

Abstract

This paper proposes a new color image encryption algorithm based on modulo negabinary code (MNBC-IEA), which treats a color pixel as one 24-bit unsigned integer rather than three 8-bit unsigned integers, and it makes the 24-bit-planes dependent on each other. We first provide a new coding scheme of unsigned integers called modulo negabinary code (MNBC), and we construct its encoding and decoding algorithm. Next, we use MNBC to design the substitution algorithm for color image encryption. MNBC-IEA consists of the enhanced MNBC, a random cyclic shift (RCS), and a diffusion procedure. The RCS procedure is composed of the RCSs in three directions, and it treats a color image as a cuboid. Hence, the permutation process can cause the 24-bit-planes to affect each other in addition to scrambling the bit positions. The enhanced MNBC can change the grayscale values via a process that encodes a 28-bit unsigned integer consisting of a 24-bit pixel value and a 4-bit key into the MNBC. The diffusion procedure includes exclusive OR and modulo arithmetic such that plaintext pixels, ciphertext pixels, and keystreams are related to each other. The final experiments indicate that our algorithm can encrypt a color image into a random binary sequence and resist various statistical, differential, and brute-force attacks.