quantumresistance

Quantum resistance is a term used to describe phenomena that arise from quantum effects, or to refer to cryptographic algorithms designed to resist quantum attacks. It can denote different concepts in physics and information security, depending on the context.

In physics, quantum resistance refers to the quantization of electrical resistance observed in nanoscale devices. The conductance quantum is G0 = 2e^2/h, and the corresponding resistance quantum is RK = h/e^2 ≈ 25,812 Ω. In a single electronic channel, conductance is an integer multiple of G0, yielding discrete resistance steps. The Landauer–Büttiker formalism expresses conductance as G = (2e^2/h) sum Tn, where Tn are transmission probabilities. In the quantum Hall regime, the Hall resistance is quantized as Rxy = h/(e^2 ν) = RK/ν, with ν an integer. These quantized values reflect the phase-coherent transport of electrons in mesoscopic systems and underlie precise resistance standards in metrology.

In cryptography, quantum resistance (also called post-quantum resistance or quantum-resistant) describes the resilience of a cryptosystem against quantum-enabled adversaries. Shor’s algorithm can break many public-key schemes based on factoring or discrete logarithms, so those systems are not quantum resistant. Post-quantum cryptography seeks alternatives based on lattice problems, code-based, multivariate, hash-based, or isogeny-based hard problems. Standards efforts, such as those coordinated by NIST, aim to select algorithms with strong security guarantees and acceptable performance for widespread deployment. The term thus encompasses distinct notions of robustness to quantum effects or capabilities, depending on the domain.