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In order to research the security of the knapsack problem under quantumalgorithm attack, we study the quantum algorithm for knapsack problem over Z_rbased 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. Theobservation probability of target state is not improved by designing unitarytransform, but oracle function. Its complexity is polynomial. And its successprobability 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 theexisting quantum algorithm attacks, i.e. r<O(2^n). Then we analyze the securityof the Chor-Rivest public-key crypto.

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