Parameter security characterization of knapsack public-key crypto under quantum computing

Knapsack public-key encryption schemes are based on the knapsack problem, which is NP-complete. Merkle-Hellman knapsack encryption scheme was the first concrete realization of a public-key encryption scheme. As its secure basis is superincreasing knapsack problem, it has been demonstrated to be insecure. Many variations have subsequently been proposed, whose knapsack vector density are less than 1. 3 L -lattice basis reduction algorithm is a polynomial-time algorithm for finding a reduced basis when given a basis for a lattice. In 1991, Schnorr and Euchner presented and improved algorithm.In 1992, Coster et al gave an algorithm for low density knapsack problem based on lattice basis reduction algorithm.If the density of the knapsack is less than 0.9408, the knapsack problem can be solved with high probability. Thus most variations of the Merkle-Hellman scheme are insecure. However, there is not an efficient algorithm for solving knapsack problem, and the complexity of the