We will explore the potential threats that quantum computers may pose to Bitcoin and the countermeasures being taken.

A qubit can exist in a state of both 0 and 1 simultaneously, allowing for complex calculations to be processed much faster than with classical computers. Thanks to this property, quantum computers have the potential to revolutionize various fields such as cryptography, drug development, and climate modeling.

To explain, consider the following.

For example, a simple multiplication problem like 1103X1117=1232051 does not take long to solve. However, factoring 1232051 is very difficult because both 1103 and 1117 are prime numbers. While computers can multiply quickly, determining that a large number is the product of two primes takes an enormous amount of time.

Multiplication is like going straight. If I know the two numbers, I just follow the path. But what about factoring? There is one starting point, but countless endpoints seem to exist. I may have to try every possible case to determine which number to divide by, whether that number is prime or composite, and whether it can be divided at all.

This is precisely why we say in computer science or cryptography that 'factoring is hard.'

Both humans and computers find division more challenging than multiplication. This is the point on which current security system algorithms are structured. This structure makes hacking difficult and helps us exchange data securely.

Even with today's computers, it takes an incredibly long time to hack these algorithms. For instance, in 1994, it took 8 months to factor a 129-digit number (426 bits) known as RSA129, even when connecting over 1,600 workstations in parallel using algorithms.

If using this algorithm, factoring a 250-digit number (829 bits) would take 800,000 years, and a 1,000-digit number would take 102.5 billion years. This is many times longer than the age of the universe.

However, as mentioned earlier, quantum computers can perform these calculations almost instantaneously, rendering current security algorithms obsolete. Our CD keys also use factoring algorithms, allowing for infinite replication of CD keys. In 2011, quantum computers were only able to factor 21, but the pace of development in the computer field often surpasses the imagination of scholars in this area.

In addition to the factoring problem, many cryptographic algorithms are based on the discrete logarithm problem, which can also be solved by quantum computers. Therefore, once quantum computers are practically implemented, most cryptographic algorithms developed to date will become useless. Bitcoin is based on a distributed ledger technology called blockchain.

Blockchain stores transaction records in blocks linked together like a chain, with all participants verifying and maintaining it. The security of Bitcoin primarily relies on two cryptographic techniques:

Public Key Cryptography: Bitcoin addresses are generated based on public keys, and private keys are used to sign transactions. This process uses ECDSA (Elliptic Curve Digital Signature Algorithm).

Hash Functions: Each block in the blockchain contains the hash value of the previous block, maintaining the integrity of the blockchain. Bitcoin uses the SHA-256 hash function.

Threats from Quantum Computers

The advancement of quantum computers poses a serious threat to the security of cryptocurrencies like Bitcoin.

Decoding ECDSA Signatures

Bitcoin protects transaction signatures using ECDSA. Quantum computers can quickly solve the discrete logarithm problem using Shor's Algorithm. This means that an attacker could infer the private key from the public key. If the private key is leaked, the attacker can forge all transactions signed with that key.

Vulnerability of the SHA-256 Hash Function

Quantum computers can attack hash functions using Grover's Algorithm. Grover's Algorithm reduces the time to find collisions in hash functions to the square root of the original time. This could impact the mining process of Bitcoin and the integrity of the blockchain.

Countermeasures

The Bitcoin community and developers are exploring various measures to respond to the threats posed by quantum computers. The main countermeasures include:

Post-Quantum Cryptography

Post-quantum cryptography is the field of developing encryption algorithms that are strong against quantum computers. Bitcoin is currently researching transitioning its encryption methods to post-quantum cryptography, which can enhance security against quantum computer attacks.

Strengthening Hash Functions

Bitcoin is considering various methods to strengthen the security of the SHA-256 hash function. For example, introducing stronger hash functions or increasing the length of the hash function can enhance security.

Multi-Signature and Distributed Security

Implementing multi-signature technology and distributed security mechanisms is also being considered to maintain the overall system's security even if a single private key is leaked.

However, the Bitcoin community and developers are seeking innovative solutions such as post-quantum cryptography to address these threats.