Polynomial Time Bounded Distance Decoding near Minkowski's Bound in Discrete Logarithm Lattices

International audienceWe propose a concrete family of dense lattices of arbitrary dimension n in which the lattice Bounded Distance Decoding (BDD) problem can be solved in determin-istic polynomial time. This construction is directly adapted from the Chor-Rivest cryptosystem (IEEE-TIT 1988). The lattice construction needs discrete logarithm computations that can be made in deterministic polynomial time for well-chosen parameters. Each lattice comes with a deterministic polynomial time decoding algorithm able to decode up to large radius. Namely, we reach decoding radius within O(log n) Minkowski's bound, for both 1 and 2 norms

Quantum Algorithms for Attacking Hardness Assumptions in Classical and Post‐Quantum Cryptography

In this survey, the authors review the main quantum algorithms for solving the computational problems that serve as hardness assumptions for cryptosystem. To this end, the authors consider both the currently most widely used classically secure cryptosystems, and the most promising candidates for post-quantum secure cryptosystems. The authors provide details on the cost of the quantum algorithms presented in this survey. The authors furthermore discuss ongoing research directions that can impact quantum cryptanalysis in the future