Strong Cryptography – Is it Easy to Generate and Break a Cryptographic Key?

The motivation for this study is to deepen the understanding of the strength and significance of encryption keys used in asymmetric cryptographic systems, particularly by comparing them with physical and biological magnitudes. Existing literature primarily focuses on the technical aspects of cryptography, such as algorithms and system implementations, but lacks a comprehensive comparison of the scale of cryptographic keys with other scientific measures, leaving a gap in current research.

This paper adopts an interdisciplinary approach, employing mathematical analysis, physical data, and biotechnological models to evaluate the complexity of key generation, primality testing, and the thermodynamic constraints of breaking cryptographic keys. It also analyzes the potential threats posed by emerging computational technologies, such as quantum and DNA computing, and their implications for the security of modern cryptographic systems.

The findings demonstrate that the length and generation processes of cryptographic keys provide a very high level of security, and comparisons with physical and biological magnitudes reveal their immense scale. The study concludes that future cryptography must incorporate new computational paradigms to address the challenges posed by technological advancements.