The digital information is transmitted through different communication channels with ease within no time. The sphere of digital world is evolving and become one of the key aspects of our daily lives. In this regard, confidentially to this digital information which are fundamentally transmitted over insecure line of communication is one of the mandatory concerns. This digital information is placed in different databases available online. In this article, our aim is to perform cryptanalysis of Logarithmic based image encryption scheme and investigate its potential key leakages by utilizing public key to recover its private key. Moreover, we have suggested chaos-based Logarithm scheme which is more secure. The Lorenz system is utilized in an anticipated mechanism which is sensitive to initial conditions and chaotic parameters. The proposed scheme is then authenticated by using available security performance benchmarks. To measure the security against different cryptographic attacks, we utilized the statistical analyses which are entropy and the correlation between the pixels, and the differential analyses which are number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI). In order to resist the brute force attacks, key sensitivity analyses and key space analyses is also performed. The randomness of proposed encryption scheme investigated through entropy and NIST randomness suit tests. An application on digital images is investigated. Also, we have compared our modified confidentiality scheme with existing benchmarks which suggested our encryption technique is quite reasonable for digital multimedia security.
