To date, quantum computers have not been used to break widely-used cryptographic algorithms that are considered secure against classical computers. However, it is important to understand that the development of quantum computers poses a potential threat to many existing cryptographic schemes, especially those that rely on the hardness of certain mathematical problems.
Quantum computers have the potential to break certain types of cryptographic algorithms based on integer factorization and the discrete logarithm problem. The most well-known example is Shor's algorithm, which is a quantum algorithm that can efficiently factor large composite numbers and solve the discrete logarithm problem on which some popular cryptographic schemes, such as RSA and Diffie-Hellman, rely.
If large-scale, error-corrected quantum computers become a reality, they could potentially undermine the security of these cryptographic algorithms that are widely used today. This has led to an area of research called post-quantum cryptography, which focuses on developing cryptographic algorithms that are resistant to attacks by both classical and quantum computers.
The goal of post-quantum cryptography is to identify and develop cryptographic schemes that are secure against attacks by quantum computers. These schemes often rely on different mathematical problems that are believed to be hard even for quantum computers. Examples of post-quantum cryptographic schemes include lattice-based cryptography, code-based cryptography, multivariate polynomial cryptography, and more.
While the current generation of quantum computers is not yet capable of breaking widely-used cryptographic algorithms, it is crucial for cryptographic standards and protocols to be prepared for the future when quantum computers become more powerful. The ongoing research in post-quantum cryptography aims to provide a foundation for secure communication and data protection in the post-quantum era.