On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$

2010 ◽  
Vol 59 (10) ◽  
pp. 1392-1401 ◽  
Author(s):  
Xiaofeng Liao ◽  
Fei Chen ◽  
Kwok-wo Wong
Keyword(s):  
Finite Field ◽  
Chebyshev Polynomials ◽  
Public Key

Cryptanalysis of Multiplicative Coupled Cryptosystems Based on the Chebyshev Polynomials

2016 ◽  
Vol 26 (07) ◽  
pp. 1650112 ◽  
Author(s):  
Ali Shakiba ◽  
Mohammad Reza Hooshmandasl ◽  
Mohsen Alambardar Meybodi
Keyword(s):  
Finite Field ◽  
Chebyshev Polynomials ◽  
Public Key ◽  
Floating Point ◽  
Real Numbers ◽  
Public Key Cryptosystems ◽  
Floating Point Arithmetic ◽  
Security Models ◽  
Point Arithmetic

In this work, we propose a class of public-key cryptosystems called multiplicative coupled cryptosystem, or MCC for short, as well as discuss its security within three different models. Moreover, we discuss a chaotic instance of MCC based on the first and the second types of Chebyshev polynomials over real numbers for these three security models. To avoid round-off errors in floating point arithmetic as well as to enhance the security of the chaotic instance discussed, the Chebyshev polynomials of the first and the second types over a finite field are employed. We also consider the efficiency of the proposed MCCs. The discussions throughout the paper are supported by practical examples.

On Public-Key Encryption Scheme Based on Chebyshev Maps

2011 ◽  
Vol 268-270 ◽  
pp. 1110-1114
Author(s):  
Lin Hua Zhang ◽  
Xiu Li Mao ◽  
Wan Yu Duan
Keyword(s):  
Theoretical Analysis ◽  
Chebyshev Polynomials ◽  
Experimental Results ◽  
Public Key ◽  
Encryption Scheme ◽  
Public Key Encryption ◽  
Public Key Cryptosystems

Due to the exceptionally desirable properties, Chebyshev polynomials have been recently proposed for designing public key cryptosystems. However, some proposed schemes were pointed out to be insecure and unpractical. In this paper, we analyze their defects, discretize the Chebyshev maps, generalize properties of Chebyshev polynomials and design an improved scheme. Theoretical analysis shows that it possesses higher security than RSA and experimental results shows it can be implemented easily.

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