A Nonhomogeneous Poisson Process Modeling for Double Spending Problems of Bitcoin Blockchain

以非齊次卜瓦松模型探討比特幣區塊鍊雙重支付問題

呂易錦(Yi-Chin Lu) ； 馬瀰嘉(Mi-Chia Ma) ； 林億雄(Yi-Hsiung Lin)

《智慧科技與應用統計學報》 18卷1期 (2020/08) Pp. 47-60

摘要

Bitcoin is the most expensive cryptocurrency in the world. It uses the technology of blockchain which functions on the Internet. This system is secured and works by solving the proof of work algorithm that is called mining. This technology uses the Internet to add time-stamp on all online payment transactions, and incorporates an ever-extending proof of work chain as the transaction record. Unless all the proofs of work are updated, the formed transaction records cannot be changed. The double spending problem can be regarded as a race between the attacker and honest nodes. A successful attack happens when the attacker mines blocks faster than the honest nodes do. In this article, we model the cumulative occurrences using a nonhomogeneous Poisson process with two different intensity functions, a power law process and a log linear process. The parameters are estimated by a maximum likelihood method based on real-world data that have not been previously published. We collected observed data from https://btc.com/block, and simulated cumulative occurrences of the attacker and honest nodes respectively in order to find out the empirical probability. It shows that the probability of a successful attack is 0.003 after 36 hours. It is safer for a transaction to wait for 48 hours. It is against the bitcoin protocol that a transaction is not regarded as valid until the transaction is 6 blocks deep. This research provides us better understanding of the probability of a double spending attack, therefore the bitcoin community may institute new and better policies on the basis of our research.

關鍵字

Intensity function ； empirical probability ； nonhomogeneous Poisson process ； proof of work

並列摘要

比特幣是世界上最昂貴的加密貨幣，它是在互聯網上的區塊鏈技術，比特幣系統的安全性是透過稱為挖礦的工作量證明演算法來解決。該技術利用網路對線上支付的全部交易，加上時間戳記和併入不斷延伸的工作量證明鍊條作為交易紀錄，除非更新全部的工作量證明，形成的交易紀錄將無法更改。雙重支付問題可以看作是攻擊者和誠實節點之間的競賽，當攻擊者的挖礦速度比誠實節點快時，攻擊就會成功。在本研究中，使用兩個不同強度函數的非齊次卜瓦松過程：冪法則過程和對數線性過程，對累積事件進行建模。我們從比特幣礦池數據服務網站下載資料，根據以前未發佈的實際數據進行模擬，模擬參數是透過最大概似估計法估算的，我們分別模擬攻擊者和誠實節點的累積發生次數，以計算經驗機率。模擬顯示交易後36小時會成功攻擊的機率為0.003，交易後48小時會成功攻擊的機率小於0.001，這與比特幣協議提出交易後有6個區塊鍊加入時就能確認交易的結果不同。這項研究使我們對雙重支付攻擊的可能性有更進一步的了解，可做為比特幣社群未來制訂新政策的依據。

並列關鍵字

強度函數 ； 經驗機率 ； 非齊次卜瓦松過程 ； 工作量證明