Risk Equation Derivation
Mathematical Derivation of Risk Equations
The mathematical framework for assessing the risk associated with relay families within the Anyone Network is critical for understanding the probability of network compromise due to relay concentration within a single family. This appendix provides a detailed explanation of the equations used to calculate these risks and the simplifications applied for practical implementation.
Basic Definitions and Formula
Probability Calculation for Multiple Hops within One Family
This formula calculates the probability by first determining the likelihood that the first two hops are not within the family and then subtracting this value from 1.
Simplification and Approximation
Graphical Analysis and Validation
Application and Boost Calculation
Conclusion
The mathematical construction of risk equations provides a robust basis for implementing security measures in the Anyone Network. By utilizing these calculations, the network can effectively manage and mitigate risks associated with relay family concentrations, ensuring a secure and reliable decentralized network environment. This appendix serves as a reference point for understanding the theoretical underpinnings and practical applications of risk assessments within the Anyone Networkās operational framework.
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