Iranian Society of Cryptology The ISC International Journal of Information Security 2008-2045 8 1 2015 12 15 On the design and security of a lattice-based threshold secret sharing scheme 25 38 40678 10.22042/isecure.2016.8.1.2 EN H. R. Amini Khorasgani Information Systems and Security Lab (ISSL), Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran S. Asaad Information Systems and Security Lab (ISSL), Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran H. Pilaram Information Systems and Security Lab (ISSL), Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran T. Eghlidos Electronics Research Institute, Sharif University of Technology, Tehran, Iran M. R. Aref Information Systems and Security Lab (ISSL), Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran Journal Article 2015 07 28 In this paper, we introduce a method of threshold secret sharing scheme (TSSS) in which secret reconstruction is based on Babai's nearest plane algorithm. In order to supply secure public channels for transmitting shares to parties, we need to ensure that there are no quantum threats to these channels. A solution to this problem can be utilization of lattice-based cryptosystems for these channels which requires designing lattice-based TSSSs. We investigate the effect of lattice dimension on the security and correctness of the proposed scheme. Moreover, we prove that for a fixed lattice dimension the proposed scheme is asymptotically correct. We also give a quantitative proof of security from information theoretic viewpoint. https://www.isecure-journal.com/article_40678_756f3d220f584170f0bd50b552fbb76b.pdf