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Minimum length key in MST cryptosystems

MST密码系统中极小长度密钥的研究

Abstract

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 MST 1, MST 2 and MST 3. 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-Hölder 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.

创新点

根据有限单群的分类定理,本文利用有限群论、代数群论、射影几何等学科的相关理论给出了剩余四种单群极小对数签名的结构,最终从理论上完成MLS 猜想的证明,为MST 密码系统提供了广阔的应用平台。具体成果如下: (a) 给出了一类经典单群极小对数签名的构造。(b) 给出了一类经典单群—射影特殊酉群极小对数签名的构造。 (c) 构造了所有十类特殊李型群的极小对数签名。 (d) 构造了剩余十三类零散群的极小对数签名。

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Correspondence to Zhiguo Qu.

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Hong, H., Wang, L., Ahmad, H. et al. Minimum length key in MST cryptosystems. Sci. China Inf. Sci. 60, 052106 (2017). https://doi.org/10.1007/s11432-015-5479-3

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Keywords

  • MLS conjecture
  • finite groups
  • (minimal) logarithmic signature
  • minimum length key
  • MST cryptosystems
  • 052106

关键词

  • MLS
  • 猜想
  • 有限群
  • (极小)对数签名
  • 极短长度密钥
  • MST密码系统