Analysis and design of stream ciphers
Analysis and design of stream ciphers
A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Binary sequences derived from ML-sequences over rings I: periods and minimal polynomials
Journal of Cryptology
The interpolating random spline cryptosystem and the chaotic-map public-key cryptosystem
The interpolating random spline cryptosystem and the chaotic-map public-key cryptosystem
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
A novel key agreement protocol based on chaotic maps
Information Sciences: an International Journal
Using time-stamp to improve the security of a chaotic maps-based key agreement protocol
Information Sciences: an International Journal
Finding the differential characteristics of block ciphers with neural networks
Information Sciences: an International Journal
New Stream Cipher Designs: The eSTREAM Finalists
New Stream Cipher Designs: The eSTREAM Finalists
Color image encryption based on one-time keys and robust chaotic maps
Computers & Mathematics with Applications
Secure group key agreement protocol based on chaotic Hash
Information Sciences: an International Journal
On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$
IEEE Transactions on Computers
New directions in cryptography
IEEE Transactions on Information Theory
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Recently Kocarev and Tasev [20] proposed to use Chebyshev polynomials over real numbers to design a public key algorithm by employing the semigroup property. Bergamo et al. [4] pointed out that the public key algorithm based on Chebyshev polynomials working on real numbers is not secure and devised an attack which permits to recover the corresponding plaintext from a given ciphertext. Later Kocarev et al. [19] generalized the Chebyshev polynomials from real number fields to finite fields and finite rings to make the public key algorithm more secure and practical. However, we analyzed the period distribution of the sequences generated by the Chebyshev polynomials over finite fields [21]. When the modulus N is prime, we found this algorithm was also not secure and proposed an attack on this algorithm over finite fields. We then proposed some schemes to improve the security. In this paper, we further analyze in detail the period distribution of the sequences generated by Chebyshev polynomials over the integer ring Z"N when N is composite. It turns out that the period distribution is poor if N is not chosen properly and there are many small periods, which are not secure in the sense of cryptology. Based on these findings, we devise an attack on the public key algorithm based on Chebyshev polynomials over the integer ring Z"N. We also propose some suggestions to avoid this attack.