insight - Lattice-Based Cryptography

### Finding Dense Sub-lattices by Mapping to Low-Energy States of a Hamiltonian and Using Quantum Algorithms

This paper presents a novel approach to solving the K-Densest Sub-lattice Problem (K-DSP) using quantum algorithms by mapping it to a Hamiltonian whose first excited state represents the solution. The authors propose a classical preprocessing step to reduce the search space and bound the required qubits, demonstrating the potential of quantum computation for lattice-based cryptography.

### Efficient and Hardware-Aware Design of Learning with Rounding-based Key Encapsulation Mechanisms

This work proposes a suite of three new lattice-based key encapsulation mechanisms (KEMs) called Scabbard, which are designed to improve the efficiency and hardware-awareness of learning with rounding (LWR)-based cryptographic schemes.

### The Mathematical Foundations of Post-Quantum Cryptography

The security of lattice-based post-quantum cryptography relies on the computational hardness of the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP) in lattices, which are equivalent to sphere packing and sphere covering problems, and can be formulated as arithmetic problems of positive definite quadratic forms.