密码学报（中英文）2024，Vol.11Issue(4)：895-910,16.DOI:10.13868/j.cnki.jcr.000715
基于循环码的秘密共享方案
Secret Sharing Schemes Based on Cyclic Codes
摘要
Abstract
Error-correcting codes can be used to construct secret sharing schemes.Every linear code can be used to construct a secret sharing scheme.However,it is usually difficult to determine the access structure of the secret sharing scheme based on a linear code.Cyclic codes are a subclass of linear codes and have wide applications in data storage systems,communication systems and consumer electronics due to their efficient encoding and decoding algorithms.Let p be an odd prime and m be a positive integer.Let α be a generator of F*m,0 ≤ e1,e2,e3 ≤ pm-2,s=pm-1/2.Let C(e1,e2,e3)denote the p-ary cyclic code with three nonzeros αe1,αe2,and αe3.This paper presents two classes of optimal quinary cyclic codes C(0,e1,e2)with parameters[5m-1,5m-2m-2,4]by analyzing the number of roots of certain polynomials.Then a connection between p-ary cyclic codes C(0,e1,e2)and C(s,e1+s,e2+s)is given.This connection can be used to obtain optimal p-ary cyclic codesC(1,e,s)from optimal p-ary cyclic codes C(0,1,e).Finally,some secret sharing schemes based on quinary cyclic codes are proposed.Those secret sharing schemes are shown to have good access structures.关键词
五元/循环码/最优/秘密共享方案/有限域Key words
quinary/cyclic codes/optimal/secret sharing schemes/finite fields分类
信息技术与安全科学引用本文复制引用
伍高飞,张玉清..基于循环码的秘密共享方案[J].密码学报（中英文）,2024,11(4):895-910,16.基金项目
国家重点研发计划(2023YFB3106400,2023QY1202) （2023YFB3106400,2023QY1202）
国家自然科学基金重点项目(U2336203,U1836210) （U2336203,U1836210）
海南省重点研发计划(GHYF2022010) （GHYF2022010）
山东大学密码技术与信息安全教育部重点实验室开放课题National Key Research and Development Program of China(2023YFB3106400,2023QY1202) （2023YFB3106400,2023QY1202）
Key Program of National Natural Science Foundation of China(U2336203,U1836210) （U2336203,U1836210）
Key Research and Development Program of Hainan Province(GHYF2022010) （GHYF2022010）
Open Project Program from Key Lab of Cryptologic Technology and Information Security,Ministry of Education,Shandong University （）
