- BITCOIN ANALYSIS

# How Bitcoin’s Cryptography fares with Quantum’s Prowess

- Concerns grow over quantum’s ability to soon break bitcoin’s cryptography.
- Quantum computers are becoming powerful enough to factor large prime numbers, a critical component of bitcoin’s public cryptography.
- Quantum computing is a key risk to bitcoin as a cybersecurity threat.
- Taproot, a bitcoin update aims to make all public keys visible on the blockchain, further increasing bitcoin’s quantum vulnerability

## Report

Investors and technologists alike share concerns that quantum computers will soon be able to break bitcoin’s cryptography. The concern is warranted, as quantum computers become increasingly adept at factoring large prime numbers, a critical component of bitcoin’s public-key cryptography.

For starters, bitcoin’s current ECDSA cryptography largely depends on the security and protection of computing large prime numbers quickly, which is something quantum computers specialise in. Namely, the most powerful quantum computers solve prime number cryptography 100 million times faster than conventional computer hardware, which served as the backbone for bitcoin’s initial security design.

Bitcoin’s cryptography relies on ecliptic curve digital signature algorithm (ECDSA), which manages and determines private/public key pairing. Public keys employ a hash function to create your bitcoin’s public address. This is what you send and receive funds with. This public key itself was meant to be shared with other users. Whereas private keys are used to sign and validate transactions, and thus are 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” is dependent on the inability of any classical computer to easily factor large prime numbers.

Currently, ECDSA, bitcoin’s cryptography, generates a 256 byte string that is compressed to a 32 byte string. The 32 byte string represents 64 possible characters in the range of 0-9 or A-F. And each of the possible 64 characters can hold 16 different combinations. So there are 16^64 possible combinations. So if every person in the world, say 8 billion people, attempted to break the encryption using hardware computing, the mathematical odds of any person cracking the encryption is highly unlikely:

`100 * (8,000,000,000/16^64)= 6.90^e-66`

Multiplying this number by the cumulative computation power, say 153 million, on 2 November, results in 0.46 billion years. This is the projected time it would take hardware computing to crack ECDSA cryptography. Additionally, the time increases when factoring in the growing 2^160 possible bitcoin addresses with each bitcoin address having 2^58 possible private key combinations. As a result, the mathematical proof ensures that any one user would need more than the 10 minutes bitcoin requires to secure the network and highlights the protective features of ECSDA cryptography relative to bitcoin’s hardware computing capability at inception.

Fast forward to 2021 and a 2300 qubit quantum computer could break ECDSA cryptography. While a classical computer can reduce any factor problem to a matter of order-finding, it cannot solve the order-finding problem itself. Quantum computers are exceptionally effective at solving this order-finding problem. With Shor’s algorithm, any quantum computer above 2300 qubits can break bitcoin’s ECDSA cryptography.

Moore’s law serves as a reference to the rate of growth in quantum computing. Named after Intel’s co-founder Gordon Moore, Moore’s law states that computing power will double roughly every two years. This law is particularly useful in relation to the increase quantum computing has experienced in the past decade. For example, in late 2006, the first 12 qubit quantum computer was introduced by researchers at the Institute for Quantum Computing. Eleven years later, 2018 saw the introduction of IBM’s 50 qubit computer. Relatively speaking, the 50 qubit can perform with more than two million more processing power than its 2006 12 qubit counterpart.

For reference, the United States projects the year 2030 as the earliest target date for quantum computing to break the cryptographic threshold. The key takeaway is that almost every cryptography that is widely used to secure data remission, from bitcoin’s network to government intelligence, will be vulnerable. Surely, the intricate power of quantum computing will force blockchain ecosystems to adopt cryptography solutions more suitable to function within the circumstance of the time.

Interestingly enough, public keys may soon be made public again. Taproot, a bitcoin update that aims to make bitcoin transactions more flexible, is scheduled to go live in November and will make public keys visible. By doing so, Taproot increases bitcoin’s quantum vulnerability.

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