Quantum computers work by exploiting the principles of quantum mechanics, which allows them to perform certain calculations much faster than classical computers. However, this poses a potential threat to the security of cryptographic systems that are currently used to protect sensitive data such as financial transactions, personal information, and military secrets.

**How quantum computers work and how cryptography can resist them:**

Quantum bits (qubits): Unlike classical bits, which can only exist in two states (0 or 1), qubits can exist in multiple states at once. This allows quantum computers to perform many calculations simultaneously, which is the basis of their speed advantage.

Quantum gates: Quantum gates are used to manipulate the state of qubits to perform mathematical operations. These gates include operations such as the Hadamard gate, CNOT gate, and phase gate.

Quantum algorithms: Quantum algorithms are used to solve certain types of problems much faster than classical algorithms. For example, Shor’s algorithm can factor large numbers into their prime factors, which is the basis for many cryptographic systems. This means that a quantum computer could potentially break these systems, which rely on the difficulty of factoring large numbers to protect information.

Post-Quantum Cryptography: Cryptographers are working on developing new cryptographic systems that are resistant to attacks by quantum computers. These systems are known as Post-Quantum Cryptography (PQC). PQC includes schemes based on lattice-based cryptography, code-based cryptography, hash-based cryptography, and others. These schemes are believed to be resistant to attacks by quantum computers, even if they become widely available.

**More about Post-Quantum Cryptography: **

The current cryptographic systems, such as RSA and ECC, are based on mathematical problems that are believed to be difficult to solve for classical computers. However, quantum computers have the potential to break these systems by using algorithms such as Shor’s algorithm that can factor large numbers and compute discrete logarithms much faster than classical computers. Therefore, PQC is becoming an important area of research to ensure that sensitive data remains secure in the future.

One of the most promising PQC systems is lattice-based cryptography. The basis of lattice-based cryptography is the hardness of the shortest vector problem (SVP) and the closest vector problem (CVP) in lattices. Lattices are geometric structures that can be defined by a set of points in n-dimensional space. The SVP and CVP problems involve finding the shortest or closest vector in a lattice, respectively.

In lattice-based cryptography, public and private keys are generated based on lattice problems. The public key is generated by transforming a random lattice basis into a reduced basis using the LLL algorithm. The private key is a secret short vector that can be used to transform the reduced basis back to the original basis. To encrypt a message, it is first converted into a lattice point and then added to a random multiple of the public key. To decrypt the message, the private key is used to recover the original lattice point, which can then be decoded back into the original message.

Another PQC system is code-based cryptography, which is based on error-correcting codes. The security of code-based cryptography is based on the hardness of decoding a linear code. In code-based cryptography, the public key is a generator matrix of a linear code, and the private key is the knowledge of the decoding algorithm. To encrypt a message, it is first encoded using the generator matrix and then multiplied by a random matrix. To decrypt the message, the private key is used to decode the encoded message.

Hash-based cryptography is another PQC system that is based on the collision resistance of cryptographic hash functions. The security of hash-based cryptography is based on the fact that it is computationally difficult to find two messages that have the same hash value. In hash-based cryptography, the public key is a fixed hash function, and the private key is the knowledge of the message that hashes to a given value. To encrypt a message, it is first hashed and then combined with a random value. To decrypt the message, the private key is used to find the original message that hashes to the given value.

PQC has been a topic of research for many years, and many cryptographic systems have been proposed. However, there are still many challenges that need to be addressed before PQC can be widely adopted. One challenge is the speed of the PQC systems. Many PQC systems are much slower than the current cryptographic systems, which can affect their usability in practical applications. Another challenge is the lack of standardization. Unlike the current cryptographic systems, there is no widely accepted standard for PQC systems. This can make it difficult to compare and evaluate different PQC systems.

### What awaits bitcoin once quantum computers are present?

Bitcoin has come a long way since its inception in 2009. Over the years, it has faced a lot of criticism and skepticism, but it has also managed to gain a lot of attention and support. One of the most significant events in Bitcoin’s history is the halving, which is a pre-programmed event that reduces the block reward by half every four years. The latest halving occurred in May 2020, and it has brought up questions about the future of Bitcoin.

The halving is significant because it reduces the rate at which new Bitcoins are created, making it more scarce and valuable over time. This reduction in supply can create a supply and demand imbalance that can cause the price to rise. In the past, the halving has been followed by significant price increases, but it’s important to note that past performance is not a guarantee of future results.

Another factor that could impact the future of Bitcoin is the development of Post-Quantum Cryptography (PQC). As previously mentioned, PQC is a field of cryptography that focuses on developing cryptographic algorithms that are resistant to attacks by quantum computers. Quantum computers have the potential to break many of the current cryptographic systems, including those used by Bitcoin.

However, the development of PQC could provide a solution to this problem. PQC systems, such as lattice-based cryptography, code-based cryptography, and hash-based cryptography, are designed to be resistant to attacks by quantum computers. If these PQC systems can be successfully integrated into Bitcoin, it could make it more resistant to attacks by quantum computers and ensure the security of Bitcoin in the future.

In addition to PQC, there are other developments in the Bitcoin ecosystem that could impact its future. For example, the Lightning Network is a second-layer scaling solution that allows for faster and cheaper transactions on the Bitcoin network. The Lightning Network has the potential to make Bitcoin more user-friendly and scalable, which could increase its adoption and value.

Furthermore, the increasing institutional interest in Bitcoin could also impact its future. Many large corporations and financial institutions are now investing in Bitcoin, which could increase its legitimacy and value. However, it’s important to note that the regulation of Bitcoin is still a grey area, and it’s unclear how it will be treated by governments and regulatory bodies in the future.