The problem with popular algorithms currently used in the market is that their security relies on one of three hard mathematical problems:

1. the integer factorization problem,
2. the discrete logarithm problem, or
3. the elliptic-curve discrete logarithm problem

All of these problems could be easily solved on a sufficiently powerful quantum computer running Shor's algorithm or even faster and less demanding (in terms of the number of qubits required) alternatives.

As of 2024, computers lack the processing power to break widely used cryptographic algorithms, cryptographers are designing new algorithms to prepare for Y2Q or Q-Day, the day when current algorithms will be vulnerable to quantum computing attacks. Their work has gained attention from academics and industry through the PQCrypto conference series hosted since 2006, and several workshops on Quantum Safe Cryptography hosted by the European Telecommunications Standards Institute (ETSI), and the Institute for Quantum Computing. The rumored existence of widespread harvest now, decrypt later programs has also been seen as a motivation for the early introduction of post-quantum algorithms, as data recorded now may remain sensitive many years into the future.

In contrast to the threat quantum computing poses to current public-key algorithms, most current symmetric cryptographic algorithms and hash functions are considered to be relatively secure against attacks by quantum computers. While quantum Grover's algorithm does speed up attacks against symmetric ciphers, doubling the key size can effectively block these attacks. Thus post-quantum symmetric cryptography does not need to differ significantly from current symmetric cryptography.

Examples of PQC Approaches

Lattice-based cryptography

Imagine a giant, invisible checkerboard with lots of holes (lattice points) at specific locations. This cryptography uses complex math based on these lattices to scramble and unscramble messages. It is like a super advanced code with a special checkerboard as the key, making it hard to crack even for powerful computers.

Code-based cryptography

This one uses error-checking codes, like the ones used to fix scratches on CDs. It adds a specific pattern of errors to your message in a way that only someone with the right code can fix and read the original message. Decoding without the right code becomes a messy puzzle, keeping your message safe.

Multivariate cryptography

This gets a little trickier. Imagine having multiple complex equations with many variables. In this cryptography, solving the message is like solving a giant system of these equations all at once. The key is knowing the specific way these equations are linked, making it super hard for outsiders to crack the code without that knowledge.

Isogeny-based cryptography

This one deals with special mathematical objects called elliptic curves. Imagine a special kind of curvy line with interesting properties. Isogeny-based cryptography uses these curves and their connections (isogenies) to create complex puzzles. Solving the puzzle requires advanced math and knowledge of these special curves, making it a tough nut to crack for those without the secret key.

These are some of the examples, and many other approaches are also there for Quantum-Safe Cryptography.