The Probabilistic Image Encryption Algorithm Based on Galois Field GF(257)

Abstract

Image encryption technology is an essential measure to protect image information from illegal access. A new probabilistic image encryption algorithm with 480-bit external secret key was proposed in this paper. A chaotic pseudo-random generator is employed to produce the equivalent keys. Then the plain image is covered by the equivalent keys under exclusive or operation to obtain a pending sequence. The pending sequence is transformed into a cipher sequence by arithmetic operations based on GF(257). Finally, the cipher sequence is also covered by the equivalent keys to obtain the cipher image. In the transformation, a 1024-bit pseudo-random number sequence is introduced as the base numbers for the power operation to assist the encryption. The proposed image encryption algorithm has the characteristic of probabilistic encryption. Encrypting the same plain image with the same secret key will result in completely different cipher images. Experiments show that the proposed algorithm has the low time complexity (9.67pi/bit) and space complexity (13.07bit/bit), and high sensitivities on the auxiliary sequence (49.94%), secret key (BACI 26.7698% typically), and plain image (BACI 26.7845% typically), and is a preferred image encryption scheme for commercial and personal image information security.