Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
Volume 52, Issue 7, Pages 1382-1393Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2005.851701
Keywords
chaos theory; Chebyshev polynomials; Jacobian elliptic Chebyshev rational map; public-key cryptography
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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.
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