A Dynamic Hybrid Cryptosystem Using Chaos and Diffie–Hellman Protocol: An Image Encryption Application

Abstract

Images with sensitive content require encryption for storage and transmission. Symmetric schemes can cipher them, while an asymmetric cryptosystem can distribute the secret key safely. For this reason, we propose a dynamic hybrid cryptosystem, which ciphers images and transfers its private keys. It has a symmetric algorithm that applies the Lorenz equations for generating different boxes and permutations in every encryption process and round. Since the secret key concatenates two private numbers, an asymmetric algorithm is included for its key distribution. The proposal uses the Diffie–Hellman protocol with ElGamal for obtaining a seed and building 128 strings. Then, the SHA-512 is applied in each of them a number of times associated with the secret key value in its blockchain representation. The resultant strings are concatenated to conform to the public key. Finally, the tests indicate that the cryptosystem resists differential, linear, algebraic, and brute-force attacks. Its cipher quality is high according to the entropy, correlation, DFT, NPCR, UACI, AC, texture analysis, and goodness of fit test. Additionally, occlusion, additive, multiplicative, and the proposed χ2 noise attacks are simulated on encrypted images. Finally, the sharpness loss is measured with the Similarity Parameter and improved with a filter 5 × 5.

Keywords

• Lorenz equations
• ElGamal system
• chaos
• Hash SHA functions
• dynamic <i>S</i>-box
• dynamic permutation