散在群的最小对数签名
Minimal Logarithmic Signatures for Sporadic Groups
摘要：
对数签名作为有限群分解的一种特殊形式，在秘密密钥密码系统如PGM和公钥密码系统如MST 1、MST 2和MST 3中被用作密钥的主要组成部分。具有最短长度的LS被称为最小对数签名（MLS），甚至是加密构造所需要的。MLS猜想指出，每个有限单群都有一个MLS。到目前为止，MLS猜想已经被证明对某些单群族成立。本文将证明一些零星群的最小对数签名的存在性。
英文摘要：
As a special type of factorization of finite groups, logarithmic signature (LS) is used as the main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST1, MST2 and MST3. An LS with the shortest length is called a minimal logarithmic signature (MLS) and is even desirable for cryptographic constructions. The MLS conjecture states that every finite simple group has an MLS. Until now, the MLS conjecture has been proved true for some families of simple groups. In this paper, we will prove the existence of minimal logarithmic signatures for some sporadic groups.
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