CashFusion - The Privacy Boost

CashFusion is a privacy protocol that structures transaction inputs and outputs to preserve privacy. It makes it difficult to associate specific inputs with outputs, thereby enhancing financial privacy — a crucial feature for everyday economic use.

Why is Privacy Important?

Privacy in financial transactions is crucial for several reasons:

• Protection from Exploitation: If others can see your financial details, they might exploit this information. For instance, a merchant knowing your total funds could inflate prices or offer unfavorable terms.
• Safety and Security: Without privacy, your financial history could be exposed with every transaction. This makes it easy for malicious actors to target you for scams, theft, or extortion. Imagine buying a coffee and the seller seeing your entire financial history—this could lead to significant risks.
• Financial Autonomy: Privacy ensures that your spending habits, investments, and donations remain confidential. This autonomy is essential for freedom and personal security, as it prevents external interference and judgment.
• Economic Utility: For a currency to be practically useful in an everyday economy, it must safeguard user privacy. If cryptocurrencies are to replace or complement traditional currencies, they must provide robust privacy features to protect users.

CashFusion addresses these concerns by offering a privacy solution for cryptocurrencies, enhancing their practical utility and security.

What is CashFusion?

CashFusion is a privacy protocol designed for UTXO-based blockchains, specifically implemented on Bitcoin Cash (BCH). It allows multiple participants to combine transaction inputs into a single transaction and then split the outputs in a way that obscures the relationships between inputs and outputs. This decentralized, trustless, and permissionless process significantly enhances user privacy.

There are other factors that make CashFusion a powerful privacy tool, which we'll explore in this article. For a deeper dive into CashFusion, visit the CashFusion website.

Understanding the Transaction Structure

Each participant in a CashFusion transaction commits 1..N inputs and 1..M outputs, ensuring that the sum of inputs equals the sum of outputs minus a miner fee. The primary question then becomes: how many combinations are possible for a given number of inputs and outputs?

The number of possible input combinations can be determined using Stirling numbers of the second kind, denoted as S(n, k), which count the ways to partition a set of n objects into k non-empty subsets. Similarly, the number of possible output groupings is calculated in the same way.

Stirling Number Examples

Here are some examples of Stirling numbers, illustrating how they change with the size of the set and the number of subsets:

// Stirling number counts
S(5,1) = 1
S(5,2) = 15
S(5,3) = 25
S(5,4) = 10
S(5,5) = 1
 
S(20,1) = 1
S(20,2) = 524,287
S(20,3) = 580,606,446
S(20,4) = 45,232,115,901
S(20,5) = 749,206,090,500
...
S(20,19) = 190
S(20,20) = 1

As the number of ways to partition the set grows rapidly, particularly in the middle ranges. For instance, with 20 elements and 3 groups, there are 580,606,446 ways to partition the set. This rapid growth in possible combinations enhances CashFusion's effectiveness as a privacy tool.

Use the widget below to calculate any Stirling numbers of the second kind. The max elements is 100,000 to prevent the page from crashing.

Example Calculation

Consider a basic transaction with 4 inputs and 2 outputs:

inputs = S(4, 2) + S(4,1) = 7 + 1 = 8
outputs = S(2, 2) + S(2,1) = 1 + 1 = 2
totalCombinations = inputs * outputs = 8 * 2 = 16
 
"Possible combinations count = 16"

When a transaction has N inputs and M outputs, the maximum number of participants is the smaller of the two numbers (i.e., min(N, M)). Each possible number of participants needs to be considered to calculate the total number of combinations. The overall combination count is the product of the sums of Stirling numbers for inputs and outputs across all participant counts.

So with 4 inputs and 2 outputs, there are 16 possible combinations.

Real-world Example

Using the Fusion Stats on the Redteam Cash website, we can examine a real CashFusion transaction. Let's take a look at 7de74e138 - Transaction on Blockchair

This transaction has 77 inputs and 63 outputs, implying between 1 and 63 participants. The number of possible combinations is astronomical:

inputSum = S(77,1) + S(77,2) + ... + S(77, 63) = 7.03e+82
outputSum = S(63,1) + S(63,2) + ... + S(63, 63) = 8.67e+63
totalCombinations = inputSum * outputSum = 6.10e+146

Given these vast numbers, it's clear that checking all possible combinations is computationally infeasible. Next we'll explore how long it would take to check all these combinations.

You can use the tool below to calculate the number of possible combinations for any number of inputs and outputs and see how rapidly the number increases.

How long to check?

So, 6.10e+146 is a big number, but how big is it really? How long would it take to check all these possible combinations?

For example, if a modern computer can check 100 million combinations per second, it would take:

timeInSeconds = 6.10e+146 / 100,000,000 = 6.10e+137 seconds
timeInYears = 6.10e+137 / (60 * 60 * 24 * 365) = 1.93e+129 years

This is approximately 1.4e+121 times longer than the age of the universe. Therefore, it’s safe to say that it’s not feasible to check all these possible combinations.

Is 100 million per second an accurate representation of the speed of modern computers? Even if modern computers or supercomputers were drastically faster, it wouldn't significantly reduce the time required to check all combinations.

Here's a simple tool to show this. You can adjust the number of inputs, outputs, and the number of combinations checked per second.

Key Privacy Features of CashFusion

As we have seen, the number of possible combinations in a CashFusion transaction grows rapidly with the number of inputs and outputs, making it computationally infeasible to trace funds through exhaustive searches. In addition to this combinatorial complexity, several other features of CashFusion significantly enhance its privacy:

• Variable Input and Output Amounts: Each input in a CashFusion transaction is paired with an output amount that is slightly less to account for miner fees. This discrepancy ensures that the sum of input amounts does not perfectly match the sum of output amounts, adding an additional layer of obfuscation. Each participant pays their share of the miner fee, which varies and further enhances privacy.

• Range Pools: CashFusion mitigates the reduction in valid combinations due to varying input and output sizes by using different pools for different ranges of amounts. By categorizing transactions into specific ranges, CashFusion ensures that inputs and outputs of similar magnitudes are grouped together, preserving the anonymity set and complicating the analysis for potential attackers.

• Multiple Rounds: CashFusion transactions can be processed in multiple rounds, where the outputs of one round are used as the inputs for subsequent rounds. This multi-layered approach significantly enhances privacy by continuously mixing and rematching inputs and outputs, making it increasingly difficult to trace the origins and destinations of funds.

• Decentralized Coordination: CashFusion operates in a decentralized manner, with no central party controlling the mixing process. This trustless setup ensures that no single participant can compromise the privacy of the transaction, as all participants independently verify and approve the transaction details.

• Large Anonymity Sets: By allowing multiple participants to combine their inputs and outputs in a single transaction, CashFusion creates large anonymity sets. The larger the number of participants, the greater the anonymity provided, as it becomes increasingly difficult to determine which inputs and outputs belong to whom.

• TOR Requirement: For enhanced privacy, CashFusion uses TOR (The Onion Router) to anonymize network traffic. By routing communications through multiple nodes, TOR obscures the origin and destination of data, protecting users from network-level surveillance and ensuring that transaction details remain private.

• Reduction of UTXOs: CashFusion can reduce the number of UTXOs (Unspent Transaction Outputs) a user has by fusing them together. This consolidation not only enhances privacy but also simplifies the management of funds and can reduce transaction fees over time compared to other structures that do not consolidate UTXOs.

Downsides and Weaknesses of CashFusion

While CashFusion offers significant privacy enhancements, it is not without its downsides and weaknesses:

• Complexity and Resource Intensive: The process of mixing transactions and creating large anonymity sets can be resource-intensive, requiring significant computational power and time, especially for transactions with many inputs and outputs. Additionally, implementing CashFusion can be complex, and wallets need to adopt it to make it accessible for everyday users. This complexity can deter some users from adopting CashFusion.

• Transaction Fees: CashFusion transactions can incur higher fees due to the additional computational resources required to process them. However, on Bitcoin Cash (BCH), transaction fees remain very low compared to other blockchains.

• Network Congestion: As more users adopt CashFusion, the network could experience congestion, leading to slower transaction times and higher fees. However, the larger block sizes on BCH help mitigate this issue.

• Potential for Deanonymization: Despite its robust privacy features, CashFusion is not immune to advanced deanonymization techniques. Sophisticated attackers with sufficient resources might still find ways to trace transactions, especially if there are patterns or anomalies in the transaction data.

• Coordination Requirement: CashFusion still requires a pool operator to coordinate the mixing process. While the protocol itself is decentralized and trustless, the reliance on a pool operator introduces a potential point of failure and requires users to trust that the operator will act in the best interest of privacy.

• Not a Standalone Solution: CashFusion is a powerful tool for enhancing privacy, but it should be used in conjunction with other privacy measures. Relying solely on CashFusion without considering other aspects of privacy, such as secure wallets and best practices for handling cryptocurrencies, may not provide complete protection.

CashFusion is just one tool in the broader landscape of cryptocurrency privacy. Users should be aware of its limitations and combine it with other privacy-enhancing techniques to achieve the highest level of security.

Disclaimer

While we've made every effort to ensure the accuracy of the mathematical calculations and explanations in this article, some details may be imperfect. We welcome feedback and corrections from our readers to improve the content.

Resources and Further Reading

For more information on CashFusion and related topics, check out these resources:

• Analyzing the combinatorial math of CashFusion
• More CashFusion math
• CashFusion website
• Fusion Stats
• Stirling numbers of the second kind
• Electron Cash Wallet
• TX::Watch

Conclusion

This article introduced CashFusion and explored the math behind its privacy-enhancing capabilities. If you have any questions or wish to learn more about specific aspects of cryptocurrency, please message us on X.

If you enjoyed this article, consider supporting us with a donation.