# Problem-Solution Essay

###### tags: `ILACS`

## Draft

### Introduction

The Quantum computer is the next major milestone of the modern computer industry. But despite the technological innovation, some people are starting to worry about the superior computation power that quantum computers provide would become the nightmare of our network security. How is the masterpiece of an engineer turning into the doomsday of modern cryptography? And how should we avoid such a disaster? In this essay, we will first briefly mention the background knowledge of the existing encryption method. And secondly, point out the threat of quantum computers. Then lastly, give the solution to the challenge.

### Background

Although modern cryptography were originally been used for military purpose. Nowadays it is already been widely used in our daily life. Imagine our morning time, we might check the mailbox, weather conditions, and online newsletter. All of these connections or Wi-Fi networks are encrypted. Without encryption, we could only transmit so-called 'plain text' to the internet. So our password, mail, bank information, and credit card number would become visible to everyone in between transmissions. That is why we need cryptography to protect our data.

### How do Cryptographic Works 101

We could simply categorize cryptographic methods into two types: symmetric and non-symmetric. The main difference between them is the secret key used in the encryption and decryption process. In the symmetric method, we use the exact same key to encrypt and decrypt. The good part is that they are relatively fast. But there is a drawback, and that is because the symmetric cipher required the same key to decrypt. But on the Internet, there is no way to 'tell' the receiver which secret key to decrypt the data. Therefore we need another secure method to exchange the secret key before we actually talk to each other with a symmetrically encrypted channel. That is where non-symmetric cipher has been used. As the name suggests, a non-symmetric cipher uses not one but a pair of keys to encrypt or decrypt data. The two keys often are referred to as 'public key' and 'private key'. The rule is simply when we use the public key to encrypt something, we must use the private key to decrypt it. Or vice versa, when we use a private key to protect data, then we have to use the public key to unlock it. The tricky part is that we can easily generate public keys with the private key. It means if we have the private key then we can calculate the corresponding public key. But if we only have the public key, then it will be extremely hard even impossible to retrieve the original private key. So we can send our public key without protecting it. Everyone else can use the public key to encrypt the message they want to send back to us. And the encrypted message could not be unlocked by our private key. But non-symmetric encryption and decryption need more calculations than symmetric ones. So we often use the non-symmetric cipher to protect the secret key for the symmetric cipher at the beginning of a secured connection. Then we could use the symmetric cipher to secure the entire connection. All of those operations are finished in a few milliseconds when we open a webpage, watch Netflix, or send an e-mail.

### Now we are in danger

But the standard of protection that supports our daily life faced a new challenge. As the theory of quantum computers more mature. Experts are starting to worry about the once unbreakable encryption method will be in danger. Especially for the non-symmetric cipher. As mathematical magic behind the public key and the private key of non-symmetric is the so-called 'trap door function'. One example is prime number and semiprime. Semiprime is the product of a prime number. For example, 3 and 5 are prime number, their product 15 is a semiprime. We can easily multiply 3 and 5 to get 15, but hard to reverse that operation if the number is big enough. Like the product of 109 multiply 113 will be 12317, if we want to find the factor of 12317, then we will need to divide it by every possible factor. This process is time-consuming even for the modern computer. As we expand the length of the number, the time required to crack the key will close to infinite. But as the quantum computer concept has been developed. In the theory, quantum physics could simulate or calculate multiple possibilities at the same time (Marinescu, 2005). Such a parallelism ability makes quantum computers suited to solve a complex problem that may only be done by trying out every possible situation on conventional hardware. Including factoring the prime number of semiprime. In order to find the private key of mainstream non-symmetric cipher like RSA-2048, which uses 617 decimal digits as semiprime, would require a quantum computer equipped with 4096 qubits or quantum bits to break it (Kirsch Mentor & Chow, 2015). Plus IBM revealed its first commercial quantum computer. And improved version has 433 qubits. Even promise the future version will have more than 4158 qubits in 2025 (IBM, 2022). This means in 2025, IBM may have the technology to be able to break the RSA-2048. It is more and more clear that the end of the current standard has come. There is no doubt we need a new generation of security before the arrival of the quantum era.

### Post-Quantum Cryptography

Before the quantum computer totally destroyed our security system. Experts and the government are actually starting work on the solution. In 2016 the NIST or the National Institute of Science and Technology launch a project called Post-Quamtum Cryptography or the PQC (NIST, 2017). The essential goal of the project is to find a replacement algorithm that can resist the attack by a quantum computer. To achieve this, the NIST raised a competition initially, but they quickly decided to stimulate the cooperation between cryptographers rather than compete with each other (Moody, 2021). After 6 years and more than 80 submissions, the NIST finally announced the selected algorithms in 2022 and starting finalized the standard (NIST, 2022). It means we should be safe even after the quantum era hit. But there is one more thing. Because of the storage space become cheaper and cheaper. This is possible to store the encrypted data from today. Then try to decrypt them after quantum computers are available. Especially for high-value targets like mega corporations or governments, the risk of these attacks is much higher than for normal people. So they do need to adapt the post-quantum encryption algorithm as soon as possible.

### Conclusion

To be concluded, quantum computers indeed once threatened the security standard. But thank the hard work of experts and governments. The next generation of encryption will be able to defend the attack from both quantum and conventional computers better than ever.

## Reference

### [NIST Announces First Four Quantum-Resistant Cryptographic Algorithms](https://www.nist.gov/news-events/news/2022/07/nist-announces-first-four-quantum-resistant-cryptographic-algorithms)

### [The NIST Post-Quantum Crypto “Competition”](https://csrc.nist.gov/CSRC/media//Projects/Post-Quantum-Cryptography/documents/asiacrypt-2017-moody-pqc.pdf)

### [Post-Quantum Cryptography](https://csrc.nist.gov/projects/post-quantum-cryptography)

### [Quantum Computing: The Risk to Existing Encryption Methods](https://www.cs.tufts.edu/comp/116/archive/fall2015/zkirsch.pdf)

### [The promise of quantum computing and quantum information theory - quantum parallelism](https://ieeexplore.ieee.org/abstract/document/1419938)

sci-hub: https://sci-hub.mksa.top/10.1109/ipdps.2005.430

### [IBM Unveils 400 Qubit-Plus Quantum Processor and Next-Generation IBM Quantum System Two](https://newsroom.ibm.com/2022-11-09-IBM-Unveils-400-Qubit-Plus-Quantum-Processor-and-Next-Generation-IBM-Quantum-System-Two)