No classical cryptographic algorithm has been proven to be completely secure against attacks by large-scale quantum computers. The reason is that quantum computers have the potential to break many of the widely used classical cryptographic algorithms that rely on the computational hardness of certain mathematical problems.
For example, widely used public-key encryption algorithms like RSA and elliptic curve cryptography (ECC) are based on the difficulty of factoring large numbers and solving the elliptic curve discrete logarithm problem, respectively. However, Shor's algorithm, a quantum algorithm discovered in 1994, has the potential to solve these problems efficiently on a large-scale, fault-tolerant quantum computer.
The security of classical cryptographic algorithms against quantum attacks is typically analyzed using post-quantum cryptography, which focuses on developing cryptographic algorithms that are resistant to attacks by both classical and quantum computers. These algorithms are designed to be secure even in the presence of powerful quantum computers.
Post-quantum cryptographic algorithms are typically based on mathematical problems that are believed to be hard for both classical and quantum computers. Examples include lattice-based cryptography, code-based cryptography, multivariate polynomial cryptography, and hash-based cryptography, among others. However, the security of these post-quantum algorithms is based on assumptions about the hardness of these mathematical problems, and they have not been proven to be unconditionally secure like some classical cryptographic algorithms.
The ongoing research in post-quantum cryptography aims to develop and analyze cryptographic algorithms that are believed to be resistant to attacks by both classical and quantum computers. The goal is to provide a new generation of cryptographic primitives that can withstand the advent of large-scale quantum computers.