Lattice Sieving via Quantum Random Walks

Lattice-based cryptography is one of the leading proposals for post-quantum cryptography. The Shortest Vector Problem (SVP) arguably most important problem cryptanalysis lattice-based cryptography, and many schemes have security claims based on its hardness. best quantum algorithm SVP due to Laarhoven [] runs in (heuristic) time \(2^{0.2653d + o(d)}\). In this article, we present an improvement over Laarhoven’s result that has a running \(2^{0.2570 d o(d)}\) where lattice dimension. We also time-memory trade-offs quantify amount memory random access our algorithm. core idea replace Grover’s used key part sieving by walk which add layer local sensitive filtering.