# A Probabilistic Model of the Bitcoin Blockchain

## TL;DR

This paper introduces a comprehensive probabilistic model of the Bitcoin Blockchain, capturing transaction dependencies and entity attributes, and evaluates privacy implications and behavioral patterns using real blockchain data.

## Contribution

It presents a novel probabilistic graphical model of the Bitcoin Blockchain, including hidden entity attributes and transaction behaviors, with empirical evaluation on real data.

## Key findings

- The model captures complex transaction dependencies.
- Asymptotic bounds on privacy properties are derived.
- Behavioral patterns of transaction-to-transaction activity are identified.

## Abstract

The Bitcoin transaction graph is a public data structure organized as transactions between addresses, each associated with a logical entity. In this work, we introduce a complete probabilistic model of the Bitcoin Blockchain. We first formulate a set of conditional dependencies induced by the Bitcoin protocol at the block level and derive a corresponding fully observed graphical model of a Bitcoin block. We then extend the model to include hidden entity attributes such as the functional category of the associated logical agent and derive asymptotic bounds on the privacy properties implied by this model. At the network level, we show evidence of complex transaction-to-transaction behavior and present a relevant discriminative model of the agent categories. Performance of both the block-based graphical model and the network-level discriminative model is evaluated on a subset of the public Bitcoin Blockchain.