Coin selection by Random Draw according to the Boltzmann distribution

TL;DR

This paper introduces the Boltzmann Draw, a probabilistic coin selection algorithm inspired by statistical physics, which improves efficiency, privacy, and reduces dust in token-based payment systems like cryptocurrencies and CBDCs.

Contribution

The paper presents the Boltzmann Draw algorithm, extending Random Draw with a physics-inspired probabilistic approach, enhancing performance and privacy in coin selection.

Findings

Reduces number of input tokens needed

Limits dust generation and wallet size

Outperforms standard Random Draw and Greedy algorithms

Abstract

Coin selection refers to the problem of choosing a set of tokens to fund a transaction in token-based payment systems such as, e.g., cryptocurrencies or central bank digital currencies (CBDCs). In this paper, we propose the Boltzmann Draw that is a probabilistic algorithm inspired by the principles of statistical physics. The algorithm relies on drawing tokens according to the Boltzmann distribution, serving as an extension and improvement of the Random Draw method. Numerical results demonstrate the effectiveness of our method in bounding the number of selected input tokens as well as reducing dust generation and limiting the token pool size in the wallet. Moreover, the probabilistic algorithm can be implemented efficiently, improves performance and respects privacy requirements - properties of significant relevance for current token-based technologies. We compare the Boltzmann draw to both the standard Random Draw and the Greedy algorithm. We argue that the former is superior to the latter in the sense of the above objectives. Our findings are relevant for token-based technologies, and are also of interest for CBDCs, which as a legal tender possibly needs to handle large transaction volumes at a high frequency.