A Mathematical Perspective on Post-Quantum Cryptography

In 2016, the National Institute of Standards and Technology (NIST) announced an open competition with goal finding standardizing suitable algorithms for quantum-resistant cryptography. This study presents a detailed, mathematically oriented overview round-three finalists NIST’s post-quantum cryptography standardization consisting lattice-based key encapsulation mechanisms (KEMs) CRYSTALS-Kyber, NTRU SABER; code-based KEM Classic McEliece; signature schemes CRYSTALS-Dilithium FALCON; multivariate-based scheme Rainbow. The above-cited algorithm descriptions are precise technical specifications intended cryptographic experts. Nevertheless, documents not well-suited general interested mathematical audience. Therefore, main focus is put on algorithms’ corresponding algebraic foundations, in particular LWE problems, lattices, linear codes multivariate equation systems aim fostering broader understanding concepts behind