Post-Quantum Encryption Algorithms: Securing Communications in the Quantum Age. Part 1.
Introduction
In the era of digital communication, encryption plays a crucial role in protecting confidential information from prying eyes. However, with the development of quantum computing, this process has become a serious threat to the security of modern cryptographic algorithms. Traditional encryption algorithms, such as RSA and ECC, are vulnerable to attacks from quantum computers, which can easily solve the mathematical problems on which these algorithms are based. This has forced humanity to develop encryption algorithms that can provide secure communication channels resilient to quantum attacks.
Post-quantum encryption algorithms use mathematical problems that are difficult to solve for both classical and quantum computers. They are based on various mathematical concepts, such as lattice-based cryptography, code-based cryptography, isogeny-based cryptography, and others.
In this article, we will provide a superficial overview of post-quantum encryption algorithms, examine their key features, and discuss some of the most widely used schemes. We will also discuss the potential applications of quantum cryptography in real-world scenarios and their importance in ensuring the security of our digital communications in the face of quantum threats.
Description of the problem of quantum computing and cryptography
Quantum computers use a fundamentally different approach to computing than classical computers. Classical computers use bits, which can be in one of two states, 0 or 1, to perform calculations. Quantum computers, on the other hand, use quantum bits, or qubits, which can exist in a superposition of the 0 and 1 states simultaneously. This allows a quantum computer to solve certain problems significantly faster than classical computers.
These tasks include factoring large numbers, optimizing complex systems, modeling quantum systems, and others. In fact, the use of quantum computers to solve these problems threatens modern encryption methods.
However, quantum computers are still in the early stages of development, and their construction and use remain complex and expensive. Despite this, they promise significant progress in solving complex problems and improving many areas of science and technology in the future.
Features of post-quantum encryption algorithms
Post-quantum encryption algorithms are currently in the research and development stage, and there are currently no standard post-quantum encryption algorithms that can be used at present. However, there are already several promising directions that are being studied, and which could become post-quantum encryption algorithms in the future.
One direction is the use of quantum keys, which are generated using a quantum protocol called “BB84”. Quantum keys are created using photons that are transmitted between two users, and can be used to create a secure communication channel. Even if someone tries to intercept the photons, they will change and become unusable as an encryption key.
Another direction is the use of lattice-based signatures. These signatures are based on mathematical problems related to lattices that quantum computers cannot solve quickly. Such signatures can be used to protect data in the future from quantum computers.
Research is also being conducted on the use of error-correcting codes (so-called McEliece codes), which quantum computers cannot easily decrypt. In the future, these codes could become an important tool for protecting information from quantum attacks.
Of course, these post-quantum encryption algorithms are still in the research stage and are not yet a standard for information protection. However, their development and study are important for ensuring security in the future when quantum computers become more common.
Overview of some post-quantum encryption algorithms
a. Lattice-based cryptography:
One of the most promising approaches to post-quantum cryptography is lattice-based cryptography. Lattice-based cryptography is based on the mathematical concept of lattices, which are a type of discrete mathematical structure. Lattice-based cryptography uses the difficulty of certain lattice problems to provide security.
One of the most widely used lattice-based encryption schemes is the NTRUEncrypt scheme. NTRUEncrypt is based on the shortest vector problem in lattices. The security of NTRUEncrypt is based on the difficulty of finding the shortest non-zero vector in a lattice.
Another lattice-based encryption scheme is the Ring-LWE (Learning With Errors) scheme. The Ring-LWE scheme is based on the hardness of solving the Ring-LWE problem, which involves finding a secret polynomial that is multiplied by a random matrix and added to a noisy polynomial.
b. Code-based cryptography:
Code-based cryptography is based on the use of error-correcting codes. One of the most widely used code-based encryption schemes is the McEliece cryptosystem. The McEliece cryptosystem is based on the hardness of decoding certain types of linear error-correcting codes. The security of the McEliece cryptosystem is based on the difficulty of finding the generator matrix of the code.
c. Hash-based cryptography:
Hash-based cryptography is based on the use of hash functions. One of the most widely used hash-based signature schemes is the Merkle Signature Scheme (MSS). The MSS is based on the Merkle-Damgård construction, which is used to create a one-time signature from a hash function. The security of the MSS is based on the difficulty of finding two different messages that have the same hash value.
d. Multivariate cryptography:
Multivariate cryptography is based on the use of systems of polynomial equations. One of the most widely used multivariate encryption schemes is the Rainbow signature scheme. The Rainbow signature scheme is based on the Rainbow system of polynomial equations. The security of the Rainbow signature scheme is based on the difficulty of solving the Rainbow system of polynomial equations.
Application of post-quantum algorithms in real conditions
While post-quantum encryption algorithms are still in development, they have already started to be tested and implemented in real-world applications. For example, the National Institute of Standards and Technology (NIST) has been running a competition to select post-quantum encryption algorithms that will be recommended for standardization.
Another example is Google’s experiment with the New Hope encryption algorithm. In 2016, Google implemented the New Hope encryption algorithm in its experimental Canary build of Chrome. The New Hope encryption algorithm is a lattice-based encryption scheme that is designed to be resistant to attacks by quantum computers. While the experiment was small-scale and short-lived, it demonstrated that post-quantum encryption algorithms can be implemented in real-world applications.
Conclusion
The development of quantum computers is posing a significant threat to the security of our communications. Traditional cryptographic algorithms, such as RSA and ECC, which are widely used for encrypting data and establishing secure communication channels, are vulnerable to attacks by quantum computers. To address this challenge, researchers have been working on developing new encryption algorithms that are resistant to quantum attacks. These algorithms are collectively referred to as post-quantum encryption algorithms.
There are several approaches to developing post-quantum encryption algorithms, including lattice-based cryptography, code-based cryptography, hash-based cryptography, and multivariate cryptography. While post-quantum encryption algorithms are still in development, they have already started to be tested and implemented in real-world applications.
As quantum computing technology continues to advance, it is essential to have secure communication systems that can withstand attacks by quantum computers. Post-quantum encryption algorithms offer a promising solution to this challenge and are likely to play an increasingly important role in securing our communications in the quantum age.
