The cause of the next crypto crash

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The idea that a quantum computer could one day break bitcoin is rapidly gaining traction. This is because quantum computers are becoming powerful enough to accommodate large prime numbers, a critical part of bitcoin public key cryptography.

Quantum computers rely on what is known as the Shors algorithm to achieve this feat. The Shors algorithm considerably reduces the time required to solve factorization problems. It is also tailor-made for quantum computing, as it exploits the “superposition” of states used in quantum computing.

How public key cryptography works

The security behind creating a wallet and signing transactions relies on public key cryptography. What is public key cryptography?

Let’s start by noting that the Bitcoins protocol relies on an Elliptical Curve Digital Signature Algorithm (ECDSA) to create a private key and its corresponding public key. Bitcoin users should be aware of both.

Public keys use a hash function to create the public address of your bitcoins (what you send and receive funds with). This public key itself was intended to be shared with other users. The fact that crypto users feel pressured to hide their public key suggests that the key system is inherently flawed.

Private keys are used to sign and validate transactions, and are therefore kept secret.

While a user’s public key can be mathematically derived from their private key, private keys cannot be derived from public keys. This one-way function depends on the inability of any classical computer to easily factor large prime numbers.

The magic of the Shors algorithm

In 1994, mathematician Peter Shor revealed a quantum algorithm that can actually derive a private key from a public key. Shors’ algorithm achieves this by reducing the number of steps required to find the prime factors of large numbers.

While a classical computer can reduce any factor problem to an order search question, it cannot solve the order search problem itself. Quantum computers, however, are exceptionally good at solving this order finding problem. This is because their acceleration compared to classical algorithms evolves exponentially.

The story continues

With Shors’ algorithm, anyone with a sufficiently powerful quantum computer – around 2300 qubits (source) – can reconstruct a private key from their corresponding public key.

Once a private key is known, an attacker can create a digital signature which is verifiable by its corresponding public key. As you might expect, this allows an attacker to gain access to funds in a user account. Depending on the account, the attacker may also be able to access additional details about the user. Here, identity theft becomes a very real possibility.

Discern who is vulnerable.

In the early days of Bitcoins, a user’s public key served as the receiving address. Therefore, anyone making a bitcoin transaction could easily see the recipient’s public key.

However, crypto experts quickly realized that these paid public key (p2pk) addresses could one day be exploited. In 2010, bitcoin users started replacing their p2pk addresses with pay to pubkey hash (p2pkh) addresses (still in use today).

Not incidentally, reused p2pkh addresses should not be considered secure either. Once someone transfers funds from a p2pkh address, their public key becomes public. As a result, many wallets currently prevent users from reusing an address.

In total, about a quarter of all bitcoin remains in these two types of addresses (p2pk and p2pkh reused). These parts will eventually become very vulnerable to theft, because anyone with a powerful quantum computer will be able to calculate the private key from such an address.

Although most bitcoin investors no longer use p2pk addresses, they still remain vulnerable to them. Once a quantum computer publicly derives a private key from a public key, the price of bitcoin will most likely plummet.

Hacking of transactions

An attacker who can perform a (live) transaction hijacking will have to perform several tasks in a short period of time. After running the Shors algorithm to derive the private key, the attacker must then create, sign and broadcast the conflicting transaction.

All of these steps can be done quickly if a powerful quantum computer is present. The result will be similar to a double spend attack, except that the attacker is the only beneficiary.

An enterprising miner can combine this trade hijacking attack with a selfish mining attack. With sufficient quantum computing power, a miner could create their own secret chain and selectively post blocks on the public chain.

In doing so, the quantum attacker will cause a reorganization of the public chain (a rollback of the chain). In this scenario, the attacker acquires all funds and blocks the rewards contained in all spent transactions – in the now overwritten transactions.

Visibility of the taproot and public key

Bitcoin users looking to keep their transactions private could be blocked by companies like Glassnode and Chain Analysis. These companies access and compile the logs from a mempool of nodes, showing the public keys for each transaction in the process.

Public keys could soon be made public again anyway. A bitcoin upgrade named Taproot aims to make all public keys visible on the blockchain. The basis of this upgrade is to make bitcoin transactions more flexible (such as allowing the use of new types of signature).

By making public keys visible, of course, Taproot will increase the quantum vulnerability of bitcoins. Critics question the rationale for such an upgrade since bitcoin primarily functions as a store of value.

No easy solutions

Given these challenges, it seems justified to require that all bitcoin be transferred to a new p2pkh address. Aside from the legal complications it might cause, it is unlikely to serve as a long-term solution.

Quantum computers will eventually become fast enough to overcome p2pkh protections as well. Instead, the institution of quantum resistant cryptography appears to be the most viable option to meet this challenge.

Quantum Resistant Ledger (QRL) plays a key role in this process. The cryptocurrency incorporates a hash-based, quantum-resistant signature scheme called XMSS (eXtended Merkle Signature Scheme). If necessary, QRL can also update this signature scheme without compromising its security.

However, QRL didn’t just create a stand-alone post-quantum blockchain. He also created enQlave, an ethereum wallet that secures any balance of ether or erc20 tokens against quantum theft. This innovation integrates XMSS signature verification on Ethereum.

Peter Waterland founded QRL after concluding that quantum computers pose a deadly threat to cryptocurrencies.

Concluding Note

Trying to solve these problems before the advent of quantum computers is a bit exhilarating. It is analogous to rebuilding a car engine while the engine is running and going down a hill. At the bottom of the hill the car will go over a cliff if you don’t finish in time. Implementing Taproot is like keeping the throttle open at the same time.

Bitcoin investors who believe quantum computing remains a distant threat risk being blinded by the technology.

Quantum computing has already progressed rapidly, much faster than many scientists had predicted. And since tech companies continue to invest millions of dollars in research and development, nothing can be taken for granted.

For cryptocurrency investors keen to take a proactive approach to blockchain security, solutions that incorporate post-quantum cryptography seem like their best bet in the long run.

Currently, Quantum Resistant Ledger is the only blockchain company credibly moving in this direction. Join the discussion on the future of post-quantum cryptography today on our Discord channel.

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