How to Generalize RSA Cryptanalyses
How to Generalize RSA Cryptanalyses
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DOI：
10.1007/978-3-662-49387-8_4
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
Atsushi Takayasu;N. Kunihiro
中科院分区：
文献类型：
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作者：
Atsushi Takayasu;N. Kunihiro
最近，具有模数的RSA变体的安全性，例如，Takagi RSA和素数幂RSA，已经在几篇论文中得到了积极的研究。由于不寻常的复合模量和相当复杂的密钥生成，分析比标准RSA更复杂。本文将目前对标准RSA的最佳攻击方法推广到RSA的变体上，并将其应用于复合整数形式。我们表明，用于攻击标准RSA的格可以转化为格攻击的变种，其中的尺寸是由原格的一个因素。我们相信我们所采取的步骤比以前的研究更自然，为了说明这一点，我们得到了以下结果：Itoh等人提出的Takagi RSA上的小秘密指数攻击的简单证明（CT-RSA 2008）。我们的证明推广了Herrmann和May（PKC 2010）的工作。对Takagi RSA的部分密钥暴露攻击; Ernst等人（Eurocrypt 2005）和Takayasu和Kunihiro（SAC 2014）的工作的推广。我们的攻击改进了Huang et al.（ACNS 2014）的结果。Small secret exponent attacks on the prime power RSA; generalizations of the work of Boneh and Durfee（Eurocrypt 1999）.我们的攻击改进了Sarkar（DCC 2014，ePrint 2015）和Lu等人（Asiacrypt 2015）的结果。对素数幂RSA的部分密钥暴露攻击; Ernst等人的作品的概括。Takayasu和Kunihiro。我们的攻击改进了Sarkar和Lu等人的结果。我们使用的构造技术和策略在概念上比以前的作品更容易理解，因为我们利用了与标准RSA的精确连接。
Recently, the security of RSA variants with moduli, e.g., the Takagi RSA and the prime power RSA, have been actively studied in several papers. Due to the unusual composite moduli and rather complex key generations, the analyses are more involved than the standard RSA. Furthermore, the method used in some of these works are specialized to the form of composite integers.In this paper, we generalize the techniques used in the current best attacks on the standard RSA to the RSA variants. We show that the lattices used to attack the standard RSA can be transformed into lattices to attack the variants where the dimensions are larger by a factor ofof the original lattices. We believe the steps we took present to be more natural than previous researches, and to illustrate this point we obtained the following results:Simpler proof for small secret exponent attacks on the Takagi RSA proposed by Itoh et al. (CT-RSA 2008). Our proof generalizes the work of Herrmann and May (PKC 2010).Partial key exposure attacks on the Takagi RSA; generalizations of the works of Ernst et al. (Eurocrypt 2005) and Takayasu and Kunihiro (SAC 2014). Our attacks improve the result of Huang et al. (ACNS 2014).Small secret exponent attacks on the prime power RSA; generalizations of the work of Boneh and Durfee (Eurocrypt 1999). Our attacks improve the results of Sarkar (DCC 2014, ePrint 2015) and Lu et al. (Asiacrypt 2015).Partial key exposure attacks on the prime power RSA; generalizations of the works of Ernst et al. and Takayasu and Kunihiro. Our attacks improve the results of Sarkar and Lu et al.The construction techniques and the strategies we used are conceptually easier to understand than previous works, owing to the fact that we exploit the exact connections with those of the standard RSA.