基于剩余系统的两个同态加密的不安全性研究

Q3 Mathematics SPIIRAS Proceedings Pub Date : 2019-02-18 DOI:10.15622/SP.18.1.230-262
L. Babenko, A. Trepacheva
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引用次数: 0

摘要

分析了最近提出的两种基于剩余系统的对称同态加密方案的安全性。这两种方案都具有很高的计算效率,因为使用剩余系统自然允许并行计算。因此,它们可能是保护云中的数据的好选择。但据我们所知,缺乏对这些加密方案的安全性分析。应该指出的是,我们所考虑的第一个密码系统已经在文献中被考虑过了。提出了自适应选择明文攻击的基本方案,并给出了攻击成功率的估计。本文对这种攻击进行了分析,并指出在某些情况下它可能无法正常工作。同时提出了更通用的已知明文攻击算法。给出了利用该方法恢复密钥的理论估计和实验中得到的实际估计。第二种密码系统的安全性尚未得到分析,我们填补了已知明文攻击的这一空白。分析了恢复密钥和密码系统参数所需的“明文、密文”对数量之间的依赖关系。此外,还提出了提高安全级别的一些建议。我们分析的最后结论是,这两种密码系统都容易受到已知明文攻击。使用它们加密私人数据可能是危险的。最后需要指出的是,所提出的攻击的关键要素是计算最大公约数的算法。因此,它们的计算复杂度与输入数据的大小呈多项式关系。
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Towards Unsecurity of Two Homomorphic Encryptions Based on Residue System
The security of two recently proposed symmetric homomorphic encryption schemes based on residue system is analyzed. Both schemes have a high computational efficiency since using residue system naturally allows parallelizing computations. So they could be good candidates to protect the data in clouds. But to the best of our knowledge there is a lack of security analysis for these encryption schemes. It should be noted that the first cryptosystem under our consideration was already considered in literature. The sketch of adaptive chosen-plaintext attack was proposed and estimation of its success was given. In this paper the attack is analyzed and it is shown that in some cases it may work incorrectly. Also more general algorithm of known-plaintext attack is presented.  Theoretical estimations of probability to recover the key using it and practical estimations of this probability obtained during the experiments are provided. The security of the second cryptosystem has not been analyzed yet and we fill this gap for known-plaintext attack.  The dependency between the number of «plaintext, ciphertext» pairs required to recover the key and parameters of the cryptosystem is analyzed. Also some recommendations for increasing the security level are provided. The final conclusion of our analysis is that both cryptosystems are vulnerable to known-plaintext attack. And it may be dangerous to encrypt private data using them. Finally it should be noted that the key element of the proposed attacks is the algorithm of computing the greatest common divisor. So their computational complexity depends polynomially on the size of input data.
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来源期刊
SPIIRAS Proceedings
SPIIRAS Proceedings Mathematics-Applied Mathematics
CiteScore
1.90
自引率
0.00%
发文量
0
审稿时长
14 weeks
期刊介绍: The SPIIRAS Proceedings journal publishes scientific, scientific-educational, scientific-popular papers relating to computer science, automation, applied mathematics, interdisciplinary research, as well as information technology, the theoretical foundations of computer science (such as mathematical and related to other scientific disciplines), information security and information protection, decision making and artificial intelligence, mathematical modeling, informatization.
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