Probabilistic Analysis and Empirical Validation of Patricia Tries in Ethereum State Management

• Main Authors: Kuznetsov, Oleksandr, Yezhov, Anton, Kuznetsova, Kateryna, Domin, Oleksandr
• Format: Journal Article
• Language: English
• Published: 26-08-2024
• Subjects: Computer Science - Cryptography and Security
• DOI: 10.48550/arxiv.2408.14217

This study presents a comprehensive theoretical and empirical analysis of
Patricia tries, the fundamental data structure underlying Ethereum's state
management system. We develop a probabilistic model characterizing the
distribution of path lengths in Patricia tries containing random Ethereum
addresses and validate this model through extensive computational experiments.
Our findings reveal the logarithmic scaling of average path lengths with
respect to the number of addresses, confirming a crucial property for
Ethereum's scalability. The study demonstrates high precision in predicting
average path lengths, with discrepancies between theoretical and experimental
results not exceeding 0.01 across tested scales from 100 to 100,000 addresses.
We identify and verify the right-skewed nature of path length distributions,
providing insights into worst-case scenarios and informing optimization
strategies. Statistical analysis, including chi-square goodness-of-fit tests,
strongly supports the model's accuracy. The research offers structural insights
into node concentration at specific trie levels, suggesting avenues for
optimizing storage and retrieval mechanisms. These findings contribute to a
deeper understanding of Ethereum's fundamental data structures and provide a
solid foundation for future optimizations. The study concludes by outlining
potential directions for future research, including investigations into
extreme-scale behavior, dynamic trie performance, and the applicability of the
model to non-uniform address distributions and other blockchain systems.