Discrete Logarithmic Factorial Problem and Einstein Crystal Model Based Public-Key Cryptosystem for Digital Content Confidentiality

Abstract

Public-key encryption is extensively used to provide digital data confidentiality and deliver the security features, such as nonrepudiation (digital signature) and secure key exchange. Conventional public-key schemes are based on mathematical problems with inflexible constraints, and the security of digital contents relies on computational complexity. In the era of emerging technologies, most public-key image encryption schemes are susceptible to various threats. We propose a novel public-key encryption in this article with near-ring criteria and provide confidentiality to private data with the microstates of the Einstein crystal model. The virtual oscillator generated by microstates of initial oscillators for the common secrets with the public-key scheme produces unique states to encrypt digital data. The privacy-preserved structure, that mimics the data stream of digital content with the behavior of the improved Einstein crystal model, describes a system in terms of microstates to generate diffusion in the plain data with unique states of a virtual oscillator. The performance and digital forensic evaluations, such as randomness, histogram uniformity, pixels’ correlation, pixels’ similarity, visual strength, pixels’ incongruity, key sensitivity, linear and differential attacks, noise, and occlusion attacks analyses, certify the resistivity of the proposed algorithm against potential threats and provide superior capacity in comparison to existing methodologies to hostile certain attacks.

Keywords

• Discrete logarithmic factors problem
• Einstein crystal model
• information security
• image encryption
• key exchange
• Monte Carlo random walk