What is the Double-Spending Problem?

The double-spending problem is a potential issue in digital cash systems, where the same funds are simultaneously paid to two recipients. Without proper countermeasures, the problem cannot be fully resolved by protocol alone, as users have no way to verify whether the funds they received have already been spent elsewhere.

In the realm of digital cash, it is essential to ensure that specific monetary units cannot be duplicated. If Alice can receive 10 monetary units, copy and paste them 10 times, and then possess 100 monetary units, the entire system would collapse. Similarly, if she can send the same 10 monetary units to both Bob and Carol simultaneously, the system would also fail. Therefore, appropriate mechanisms must be in place to prevent such scenarios and ensure the proper functioning of digital currencies.

How to Prevent the Double-Spending Problem?

Centralized Approach

A centralized approach is easier to implement than decentralized solutions. It typically requires a supervisor to manage the system and control the issuance and distribution of monetary units. David Chaum's eCash is an example of a centralized solution to the double-spending problem.

Banks can use blind signatures to issue cash-like digital assets to users (enabling anonymous peer-to-peer transactions). Cryptographer David Chaum detailed this in his 1982 paper, "Blind Signatures for Untraceable Payments."

In this scenario, if a user, Dan, wishes to receive $100 in digital cash, he must first notify the bank. If his account has sufficient balance, the bank generates random numbers (multiple if the denominations are smaller). Suppose five random numbers are generated, each worth $20. To prevent the bank from tracking specific monetary units, Dan obscures the data by adding blind factors to each random number.

He then submits this data to the bank, which deducts $100 from his account and signs the messages, certifying that each of the five pieces of information is redeemable for $20. Dan can now use the bank-issued digital cash. He visits Erin's restaurant and spends $40.

Dan can remove the blind factors, revealing the random numbers associated with each digital cash "note," which serve as unique identifiers (akin to serial numbers). He discloses two of these numbers to Erin, who must immediately redeem the funds with the bank to prevent Dan from spending them elsewhere. The bank verifies the signatures' validity and, if correct, deposits $40 into Erin's account.

The used "notes" are then destroyed. If Erin wishes to use her balance similarly, she must issue new notes.

The Chaumian eCash mechanism is highly valuable for private transactions. However, eCash itself lacks resilience. Since the bank is a centralized node, a system failure would lead to total collapse. The bank-issued notes have no intrinsic value; their worth derives solely from the bank's willingness to exchange them for dollars. Customers are at the bank's mercy, relying on its credibility to manage funds. This is precisely the problem cryptocurrencies aim to solve.

Decentralized Approach

Preventing double-spending in an ecosystem without oversight is more challenging. Participants with equal rights must coordinate under the same rules to prevent fraud and incentivize honest behavior.

The Bitcoin whitepaper's most significant innovation was its solution to the double-spending problem. Satoshi Nakamoto proposed a groundbreaking data structure now known as the blockchain.

A blockchain is essentially a database with unique properties. Network participants (called nodes) run specialized software to synchronize their database copies. This allows the entire network to audit transaction history back to the genesis block. Since the blockchain is publicly viewable, detecting and preventing fraudulent activities—such as attempted double-spending—becomes easier.

When a user broadcasts a transaction, it is not immediately added to the blockchain. It must first be mined into a block. Thus, only after a block is added to the chain can the recipient confirm the transaction's validity. Otherwise, if the sender spends the same tokens elsewhere, the recipient risks losing the funds.

Once a transaction is confirmed, token ownership is reassigned to the new user and verified by the entire network, making double-spending impossible. For this reason, many recommend waiting for multiple confirmations before accepting payment. Each subsequent block significantly increases the effort required to modify or rewrite the chain (e.g., in a 51% attack).

Let’s return to the restaurant scenario. Dan revisits the restaurant and notices a "We Accept Bitcoin" sticker. Craving the same meal, he orders it again, paying 0.005 BTC.

Erin provides Dan with a public address for the transfer. Dan broadcasts the transaction—essentially a signed message declaring that the 0.005 BTC he owns now belongs to Erin. Without delving into details, anyone can verify Dan's signed transaction to confirm his ownership and authority to send the tokens.

However, as mentioned earlier, the transaction is only valid once confirmed in a block. Accepting an unconfirmed transaction is like accepting $40 in eCash without immediate bank redemption—the sender could spend the funds elsewhere. Thus, Erin should wait for at least six block confirmations (~1 hour) before accepting Dan's payment.

Double-Spending in Bitcoin

Bitcoin is meticulously designed to prevent double-spending attacks, at least when the protocol is used as intended. That is, if someone awaits block confirmation for a transaction, the sender cannot easily reverse it. Reversing a transaction would require "rewriting" the blockchain, demanding immense hash power.

However, some double-spending attacks target users who accept unconfirmed transactions. For small purchases, merchants may not wait for transactions to be mined. A busy fast-food restaurant might not tolerate the time required for network processing. Thus, if a merchant enables "instant" payments, they risk double-spending. A buyer could pay for a burger and immediately send the same funds back to their own address. If the latter transaction has a higher fee, it might confirm first, invalidating the initial payment.

There are three common double-spending attacks:

1. 51% Attack: A single entity or group gains control of over 50% of the hash rate, enabling them to delete or alter transaction order. Such attacks are highly unlikely on Bitcoin but have occurred on other networks.

2. Race Attack: The attacker broadcasts two conflicting transactions using the same funds, with only one confirmed. The goal is to invalidate the payment by having their preferred transaction validated (e.g., sending funds to their own address). Race attacks typically involve the recipient accepting an unconfirmed transaction.

3. Finney Attack: The attacker pre-mines a transaction into a block but delays broadcasting it. Instead, they spend the same tokens in another transaction before releasing the pre-mined block, invalidating the payment. Finney attacks require specific event sequences and depend on the recipient accepting unconfirmed transactions.

As seen, merchants can significantly reduce risk by patiently waiting for block confirmations, avoiding double-spending victimization.

Conclusion

Users can exploit double-spending attacks to manipulate peer-to-peer electronic cash systems, spending the same funds multiple times for unfair gain. Historically, unresolved double-spending issues hindered progress in this field.

Fortunately, blind signatures emerged as a notable solution in centralized finance. Later, proof-of-work and blockchain technology gave rise to Bitcoin—a robust decentralized currency—inspiring thousands of cryptocurrency projects.