Define Chaos in Cyber Risk Valuations

A few years ago, I embarked on a fascinating research journey aimed at removing subjectivity from risk assessment by applying chaos theory and different analysis techniques. I aimed to challenge the reliance on standard risk processes that heavily depend on assessors' opinions and experiences in cyber risk. After dusting off my research, I have reignited my passion and commitment to sharing my findings as I progress.

Risk assessment needs a universal rulebook, with organizations like the Department of Energy (DOE), the National Institute of Standards and Technology (NIST), and numerous other standards offering their recommendations. However, despite the various guidelines available, they often rely on the same subjective approach. Only a limited number of analysis methodologies can offer a detailed and precise risk assessment for the security of Information Systems.

Risk analysis in information security has historically been challenging due to the perceived complexity and uncertainty in assessing risks. Many organizations rely on risk methodologies that oversimplify the calculation of likelihood, leading to a failure in exposing all the complexities of risk factors. This subjectivity in assessments leaves significant areas of risk that need to be addressed. For instance, an Information system comprises multiple assets, including hardware, software, data, users, location, and infrastructure. Threat agents such as untrained users, user errors, hackers, and business competitors can exploit vulnerabilities in the system. While organizations assign value to their information systems and implement countermeasures, simplistic likelihood calculations often fail to capture accurate risk exposure.

Calculated risk is paramount in information systems security risk management, especially as the world becomes more interconnected through machine learning and cloud service providers. Skillful analysis and reporting on vulnerabilities within an organizational network are increasingly critical. Risk analysis is about defining a comprehensive security structure to safeguard known vulnerabilities from unknown threat agents. It encompasses policies, determined risk support, and the implementation of security mitigation programs.

Probability and chaos play significant roles in understanding and managing risk. Nonlinear dynamical systems offer a way to model complex behavior, including IT risk management. Chaos can be detected using Liapunov exponents, which measure sensitivity to initial conditions and provide a means to quantify the unpredictable and complex behavior in a system. Applying chaos theory and random parameters to cyber risk involves mathematical modeling to assess the likelihood of events or scenarios. Negative probabilities, as seen in quantum mechanics, can be used based on conditional probabilities. Understanding the convolution of non-negative definite functions helps grasp the relationship between variables contributing to risks.

The geometric structure of chaos, including attractors of dynamical systems, plays a crucial role in risk management. Attractors represent stable patterns in chaotic systems, visually depicting the system's evolution over time. Fractal geometry, popularized by B. Mandelbrot, has contributed to understanding attractors in chaotic systems and their role in risk management. By utilizing Liapunov exponents and attractors, security professionals can gain insights into risk's complex and unpredictable nature and make informed decisions to mitigate risk in their IT infrastructure.

Chaos theory, while lacking a universally accepted mathematical definition, offers valuable insights into understanding complex systems. Liapunov exponents, a widely used method, provide a means to measure chaos by quantifying the exponential divergence of nearby states within a system. Applying Chaos theory holds significance in vulnerability assessments within the realm of cybersecurity. By leveraging Liapunov exponents, we gain a deeper understanding of risk behavior over time. However, it is essential to note that predicting outcomes in complex systems becomes increasingly challenging as time progresses due to the emerging exponential separation rates.

By harnessing the power of chaos theory, we can gain a deeper understanding of the consequences associated with compromised systems. It transcends financial losses and encompasses the often-overlooked aspect of reputational damage.

It is disheartening to see how many organizations perceive cyber risk analysis as a mere checkbox activity for compliance, overlooking its true potential as a proactive tool to identify and address potential issues throughout the entire organization. However, organizations must prioritize conducting comprehensive risk analyses to uncover actual and potential threats and identify vulnerabilities within their security systems. Organizations can effectively reduce future risk exposure and mitigate the subjective aspects commonly associated with cyber security assessments by adopting a mathematical hybrid risk assessment approach, such as leveraging Chaos theory.

In their pursuit of success, organizations prioritize fulfilling mission-critical tasks in areas where they possess expertise. Naturally, they strive to mitigate risks and leverage positive business developments. Effective management of business risks, including security risks, is fundamental to sustainable business growth and resilience.