Weak Keys in MST₁

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• 作者：Jens-Matthias Bohli ; Rainer Steinwandt ; Mar¨ªa Isabel Gonz¨¢lez Vasco and Consuelo Mart¨ªnez
• 关键词：public key cryptography ; cryptanalysis ; group factorizations ; logarithmic signatures ; finite permutation groups
• 刊名：Designs, Codes and Cryptography
• 出版年：2005
• 出版时间：December 2005
• 年：2005
• 卷：37
• 期：3
• 页码：509-524
• 全文大小：155 KB

文摘

The public key cryptosystem MST₁ has been introduced by Magliveras et al. [12] (Public Key Cryptosystems from Group Factorizations. Jatra Mountain Mathematical Publications). Its security relies on the hardness of factoring with respect to wild logarithmic signatures. To identify ‘wild-like’ logarithmic signatures, the criterion of being totally-non-transversal has been proposed. We present tame totally-non-transversal logarithmic signatures for the alternating and symmetric groups of degree ≥ 5. Hence, basing a key generation procedure on the assumption that totally-non-transversal logarithmic signatures are ‘wild like’ seems critical. We also discuss the problem of recognizing ‘weak’ totally-non-transversal logarithmic signatures, and demonstrate that another proposed key generation procedure based on permutably transversal logarithmic signatures may produce weak keys.