New Empirical Traceability Analysis of CryptoNote-Style Blockchains

Abstract

The cascade effect attacks (PETS’ 18) on the untraceability of Monero are circumvented by two approaches. The first one is to increase the minimum ring size of each input, from 3 (version 0.9.0) to 7 in the latest update (version 0.12.0). The second approach is introducing the ring confidential transactions with enhanced privacy guarantee. However, so far, no formal analysis has been conducted on the level of anonymity provided by the new countermeasures in Monero. In addition, since Monero is only an example of leading CryptoNote-style blockchains, the actual privacy guarantee provided by other similar blockchains in the wild remains unknown.

In this paper, we propose a more sophisticated statistical analysis on CryptoNote-style cryptocurrencies. In particular, we introduce a new attack on the transaction untraceability called closed set attack. We prove that our attack is optimal assuming that no additional information is given. In other words, in terms of the result, $\textit{closed set}$ attack is equivalent to brute-force attack, which exhausts all possible input choices and removes those that are impossible given the constraints imposed by the mixins of each transaction.

To verify the impact of our attack in reality, we conduct experiments on the top 3 CryptoNote-style cryptocurrencies, namely, Monero, Bytecoin and DigitalNote, according to their market capitalization. Since the computational cost of performing $\textit{closed set}$ attack is prohibitively expensive, we propose an efficient algorithm, called clustering algorithm, to (approximately) implement our attack. By combining our clustering method with the cascade attack, we are able to identify the real coin being spent in $70.52\%$ Monero inputs, $74.25\%$ Bytecoin inputs, and in $91.56\%$ DigitalNote inputs.

In addition, we provide a theoretical analysis on the identified $\textit{closed set}$ attack, i.e., if every input in a CryptoNote-style blockchain has 3 mixins, and all mixins are sampled uniformly from all existing coins, the success rate of this attack is very small (about $2^{-19}$). Given that $\textit{closed set}$ attack is equivalent to the best possible statistical attack, our findings provide two key insights. First, the current system configuration of Monero is secure against statistical attacks, as the minimum number of mixin is 6. Second, we identify a new factor in improving anonymity, that is, the number of unspent keys. Our analysis indicates that the number of mixins in an input does not need to be very large, if the percentage of unspent keys is high.

A Subset-Based Algorithm

Here we give a naive algorithm to search for all $\textit{closed set}$s through finding all subsets of transaction inputs. Looking head, we use $\mathsf {Cascade\textit{-}Effect(inputs)}$ to denote the function which implements the cascade effect attack. Assume $\mathsf {Remove}$ ($\textit{closed set}{\ } CS$) $\rightarrow$ flag is a function will remove all public-keys contained $\textit{closed set}$ CS from other inputs outside CS, and outputs a variable $flag = true$ if any removing operation happens. The algorithm is given in Algorithm 3 below.