Tightly Secure Public-Key Cryptographic Schemes from One-More Assumptions

查看全文 作　　者：Ge [1,2,3]Wu;Jian-Chang [4]Lai;Fu-Chun [2]Guo;Willy [2]Susilo;Fu-Tai [5]Zhang 机构地区：[1]School of Cyber Science and Engineering,Southeast University,Nanjing 211189,China;[2]Institute of Cybersecurity and Cryptology,School of Computing and Information Technology University of Wollongong,Wollongong 2522,Australia;[3]Purple Mountain Laboratories,Nanjing 211111,China;[4]School of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350117,China;[5]School of Computer Science and Technology,Nanjing Normal University,Nanjing 210023,China 出　　处：《Journal of Computer Science & Technology》索引2019年第34卷第6期,共14页 基　　金：This work was supported by the National Natural Science Foundation of China under Grant Nos.61672289,61972094,61802195,and 61902191;the Natural Science Foundation of Jiangsu Province under Grant No.BK20190696;the Purple Mountain Laboratories。 摘　　要：A tightly secure cryptographic scheme refers to a construction with a tight security reduction to a hardness assumption,where the reduction loss is a small constant.A scheme with tight security is preferred in practice since it could be implemented using a smaller parameter to improve efficiency.Recently,Bader et al.(EUROCRYPT 2016)have proposed a comprehensive study on the impossible tight security reductions for certain(e.g.,key-unique)public-key cryptographic schemes in the multi-user with adaptive corruptions(MU-C)setting built upon non-interactive assumptions.The assumptions of one-more version,such as one-more computational Diffie-Hellman(n-CDH),are variants of the standard assumptions and have found various applications.However,whether it is possible to have tightly secure key-unique schemes from the one-more assumptions or the impossible tight reduction results also hold for these assumptions remains unknown.In this paper,we give affirmative answers to the above question,i.e.,we can have efficient key-unique public-key cryptographic schemes with tight security built upon the one-more assumptions.Specifically,we propose a digital signature scheme and an encryption scheme,both of which are key-unique and have tight MU-C security under the one-more computational Diffie-Hellman(n-CDH)assumption.Our results also reflect from another aspect that there indeed exists a gap between the standard assumptions and their one-more version counterparts. 关 键 词：public-key CRYPTOGRAPHY MULTI-USER setting TIGHT security one-more ASSUMPTION