Parameter security characterization of knapsack public-key crypto under quantum computing
This work addresses security vulnerabilities in knapsack public-key cryptosystems for cryptography applications, but it is incremental as it builds on existing quantum algorithms.
The paper tackles the security of knapsack-based cryptography under quantum attacks by analyzing a quantum algorithm for the knapsack problem over Z_r, finding that security requires r < O(2^n) to resist such attacks, and applies this to assess the Chor-Rivest public-key crypto.
In order to research the security of the knapsack problem under quantum algorithm attack, we study the quantum algorithm for knapsack problem over Z_r based on the relation between the dimension of the knapsack vector and r. First, the oracle function is designed based on the knapsack vector B and S, and the quantum algorithm for the knapsack problem over Z_r is presented. The observation probability of target state is not improved by designing unitary transform, but oracle function. Its complexity is polynomial. And its success probability depends on the relation between n and r. From the above discussion, we give the essential condition for the knapsack problem over Z_r against the existing quantum algorithm attacks, i.e. r<O(2^n). Then we analyze the security of the Chor-Rivest public-key crypto.