The Reductions for the Approximating Covering Radius Problem

  • Wenwen Wang
  • Kewei LvEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10631)


We establish the direct connection between \(\text {CRP}\) (Covering Radius Problem) and other lattice problems. We first prove that there is a polynomial-time rank-preserving reduction from approximating \(\text {CRP}\) to \(\text {BDD}^{\rho }\) (Covering Bounded Distance Decoding Problem). Furthermore, we show that there are polynomial-time reductions from \(\text {BDD}^{\rho }\) to approximating \(\text {CVP}\) (Closest Vector Problem) and \(\text {SIVP}\) (Shortest Independent Vector Problem), respectively. Hence, \(\text {CRP}\) reduces to \(\text {CVP}\) and \(\text {SIVP}\) under deterministic polynomial-time reductions.


Lattice Polynomial time reductions Covering Radius Problem Covering Bounded Distance Decoding Problem 



This work was supported by National Natural Key R&D Program of China (Grant No. 2017YFB0802502), the Science and Technology Plan Projects of University of Jinan (Grant No. XKY1714), the Doctoral Initial Foundation of the University of Jinan (Grant No. XBS160100335), the Social Science Program of the University of Jinan (Grant No. 17YB01).


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Business SchoolUniversity of JinanJinanChina
  2. 2.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  3. 3.Data Assurance Communication Security Research CenterChinese Academy of SciencesBeijingChina

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