Security of public key cryptosystems based on Chebyshev Polynomials

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 cryptosystem 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 discussi...

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Pina Bergamo, Paolo D'Arco, Alfredo De Santis, Ljupco Kocarev
• Keywords: CORR 2004, Education, Nice Chaotic Properties, Public Key Cryptosystems, Real Numbers