Minimum length key in MST cryptosystems  

作　　者：Haibo HONG Licheng WANG Haseeb AHMAD Yixian YANG Zhiguo QU 

机构地区：[1]School of Computer Science and Information Engineering,Zhejiang Gongshang University,Hangzhou 310018,China [2]Information Security Center,State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications,Beijing 100876,China [3]Jiangsu Engineering Center of Network Monitoring,Nanjing University of Information Science&Technology,Nanjing 210044,China

出　　处：《Science China(Information Sciences)》2017年第5期138-148,共11页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 61502048, 61370194, 61373131);NSFC A3 Foresight Program (Grant No. 61411146001);supported by PAPD and CICAEET

摘　　要：As a special factorization category of finite groups, logarithmic signature（LS） is used as the main component of cryptographic keys that operate within secret key cryptosystems such as PGM and public key cryptosystems like M ST1, M ST2 and M ST3. An LS with the shortest length is called a minimal logarithmic signature（MLS） that constitutes of the smallest sized blocks and offers the lowest complexity, and is therefore desirable for cryptographic constructions. However, the existence of MLSs for finite groups should be firstly taken into an account. The MLS conjecture states that every finite simple group has an MLS. If it holds, then by the consequence of Jordan-H¨older Theorem, every finite group would have an MLS. In fact, many cryptographers and mathematicians are keen for solving this problem. Some effective work has already been done in search of MLSs for finite groups. Recently, we have made some progress towards searching a minimal length key for MST cryptosystems and presented a theoretical proof of MLS conjecture.As a special factorization category of finite groups, logarithmic signature（LS） is used as the main component of cryptographic keys that operate within secret key cryptosystems such as PGM and public key cryptosystems like M ST1, M ST2 and M ST3. An LS with the shortest length is called a minimal logarithmic signature（MLS） that constitutes of the smallest sized blocks and offers the lowest complexity, and is therefore desirable for cryptographic constructions. However, the existence of MLSs for finite groups should be firstly taken into an account. The MLS conjecture states that every finite simple group has an MLS. If it holds, then by the consequence of Jordan-H¨older Theorem, every finite group would have an MLS. In fact, many cryptographers and mathematicians are keen for solving this problem. Some effective work has already been done in search of MLSs for finite groups. Recently, we have made some progress towards searching a minimal length key for MST cryptosystems and presented a theoretical proof of MLS conjecture.

关 键 词：MLS conjecture finite groups （minimal） logarithmic signature minimum length key MST cryptosystems 

分 类 号：TN918.1[电子电信—通信与信息系统]