Security of public-key cryptosystems based on Chebyshev polynomials
Security of public-key cryptosystems based on Chebyshev polynomials
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DOI：
10.1109/tcsi.2005.851701
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发表时间：
2005-07-01
影响因子：
5.1
通讯作者：
Kocarev, L
中科院分区：
文献类型：
--
作者：
Bergamo, P;D'Arco, P;Kocarev, L
最近提出了切比雪夫多项式用于设计公钥系统。事实上，它们具有一些很好的混沌特性，这些特性似乎适合在密码学中使用。此外，它们满足半群性质，这使得实现陷门机制成为可能。在本文中，我们研究了基于此类多项式的公钥密码系统，该系统提供加密和数字签名。该密码系统适用于实数并且非常高效。不幸的是，根据我们的分析，它并不安全。我们描述了一种允许从给定密文恢复相应明文的攻击。如果密码系统用于签名消息，则可以应用相同的攻击来产生伪造品。然后，我们指出，由于上述攻击，沿着密码系统的相同路线设计的其他原语、类似 Diffie-Hellman 的密钥协商方案和身份验证方案也是不安全的。我们通过讨论基于实数构建公钥密码系统的问题和可能性来结束本文。
Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which makes possible implementing a trapdoor mechanism. In this paper, we study a public-key cryptosystem based on such polynomials, which provides both encryption and digital signature. The cryptosystern works on real numbers and is quite efficient. Unfortunately, from our analysis, it comes up that it is not secure. We describe an attack which permits to recover the corresponding plaintext from a given ciphertext. The same attack can be applied to produce forgeries if the cryptosystem is used for signing messages. Then, we point out that also other primitives, a Diffie-Hellman like key agreement scheme and an authentication scheme, designed along the same lines of the cryptosystem are not secure due to the aforementioned attack. We close the paper by discussing the issues and the possibilities of constructing public-key cryptosystems on real numbers.