Cryptography that stays secure even when an attacker has a large-scale
quantum computer is called post-quantum (or quantum-resistant)
cryptography. Traditional schemes such as RSA, Diffie-Hellman, and elliptic-curve cryptography rely on problems (integer factorization,
discrete logarithms) that can be solved efficiently by Shor's algorithm on a quantum computer, so they are vulnerable.

Post-quantum schemes are built on mathematical problems for which no
efficient quantum algorithm is known. The main families that the cryptographic community and the NIST Post-Quantum Cryptography Standardization Process-focus on are:

Lattice-based schemes are used for encryption, key-exchange, and signatures. Their security comes from the hardness of the Shortest Vector Problem (SVP) or Learning With Errors (LWE) / Ring-LWE. Representative candidates include Kyber (a key-encapsulation mechanism), Dilithium and Falcon (digital signatures).

Hash-based schemes are primarily for digital signatures. Their security
rests on the difficulty of finding pre-images or collisions in cryptographic hash functions, which remains hard even for quantum computers. Examples include XMSS, LMS, and the stateless SPHINCS+ scheme.

Code-based schemes are used for encryption and key-exchange. They rely on
the difficulty of decoding random linear codes (the syndrome-decoding problem). The classic example is Classic McEliece.

Multivariate-quadratic schemes are mainly for signatures. Their security is based on solving systems of multivariate quadratic equations over finite fields, a problem believed to be hard for both classical and quantum attackers. An example candidate is Rainbow, although it has faced some attacks.

Supersingular isogeny-based schemes are used for key-exchange. The hard problem is computing isogenies between supersingular elliptic curves. SIKE was a prominent candidate, but it was broken in 2022 and is no longer considered viable.

Why these families are considered quantum-resistant: there is currently no known polynomial-time quantum algorithm that solves the underlying hard problems, unlike the integer factorization or discrete-logarithm problems
that break RSA and ECC. Many schemes have security reductions tying their strength to the worst-case hardness of the underlying problem, giving confidence that a breakthrough would need to affect the whole class of problems.

Current status (as of early 2024): NIST is in the final round of standardizing post-quantum algorithms. The algorithms expected to become standards are Kyber (a lattice-based key-encapsulation mechanism), Dilithium (a lattice- based signature scheme), Falcon (another lattice-based signature scheme), SPHINCS+ (a hash-based signature scheme), and Classic McEliece (a code-based encryption/KEM scheme). These will likely replace RSA/ECDSA/ECDH in many protocols once the standards are officially published.

Practical takeaways: for new designs, adopt the NIST-selected algorithms (Kyber, Dilithium, Falcon, SPHINCS+, Classic McEliece) once the standards are finalized. For existing systems, start planning a migration away from RSA/ECDSA/ECDH because future quantum computers could render them insecure. Some deployments already use hybrid approaches, combining a classical algorithm with a post-quantum one to hedge against both current and future threats.

Caveats: Quantum-resistant does not mean provably secure against
all future quantum attacks. It simply means that, today, no known quantum algorithm can break these constructions. Ongoing research may change the landscape, so staying updated on the NIST process and new cryptanalytic results is important.

If you are looking at specific libraries or protocols, check whether they have integrated the NIST-selected primitives-for example, newer versions of OpenSSL, libsodiums experimental modules, or any Proton services that
announce post quantum upgrades.

As requested this article was made. If you have any other topics relating to Sp00knet contact please let me know. I'm at phatstarsociety@proton.me.

Cheers gentlefolks,
-warmfuzzy

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