Fast algorithms of public key cryptosystem based on Chebyshev polynomials over finite field

Journal of China Universities of Posts and Telecommunications

Volumn 18, Issue 2, 2011, Pages 86-93

  Li, Zhi Hui ^a   Cui, Yi Dong ^a   Xu, Hui Min ^a  

^a BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

algorithm; Chebyshev polynomial; running time; square root

Indexed keywords

CHARACTERISTIC POLYNOMIALS; CHEBYSHEV POLYNOMIAL; CHEBYSHEV POLYNOMIALS; EIGENVALUES; EXECUTION SPEED; FAST ALGORITHMS; FINITE FIELDS; GENERIC ALGORITHM; MATRIX; MATRIX ALGORITHMS; MODIFIED ALGORITHMS; PUBLIC KEY CRYPTOSYSTEMS; RUNNING TIME; SOFTWARE IMPLEMENTATION; SQUARE ROOT;

COMPUTER PROGRAMMING; EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; OPTIMIZATION; POLYNOMIALS; PUBLIC KEY CRYPTOGRAPHY;

ALGORITHMS;

EID: 79955618398     PISSN: 10058885     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1005-8885(10)60049-0     Document Type: Article

References (16)

1. L Kocarev Chaos-based cryptography: A brief overview IEEE Circuits and Systems Magazine 1 3 2001 6 21 (Pubitemid 33778221)
2. NK Pareek, V Patidar, KK Sud A random bit generator using chaotic maps International Journal of Network Security 10 1 2010 32 38
3. B He, LY Luo, D Xiao A method for generating S-box based on iterating chaotic maps Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition) 22 1 2010 89 93 (in Chinese).
4. L Kocarev, Z Tasev Public-key encryption based on Chebyshev maps Proceedings of the International Symposium on Circuits and Systems (ISCAS'03), Vol 3, May 25-28, 2003, Bangkok, Thailand 2003 IEEE Computer Society Los Alamitos, CA, USA 28 31
5. P Bergamo, P D'Arco, AD Santis Security of public-key cryptosystems based on Chebyshev polynomials IEEE Transactions on Circuits and Systems I: Regular Papers 52 7 2005 1382 1393 (Pubitemid 41078438)
6. Fee G J, Monagan M B. Cryptography using Chebyshev polynomials. Proceedings of the Maple Summer Workshop (MSW'04), Jul 11-14, 2004, Burnaby, Canada. 2004: 15p.
7. Kocarev L, Tasev Z, Amato P, et al. Encryption process employing chaotic maps and digital signature process. United States Patent 6892940. 2005.
8. L Kocarev, J Makraduli, P Amato Public-key encryption based on Chebyshev polynomials Circuits, Systems, and Signal Processing 24 5 2005 497 571
9. HZ Ning, Y Liu, DQ He Public key encryption algorithm based on Chebyshev polynomials over finite fields Proceedings of the 8th International Conference on Signal Processing (ICSP'06): Vol 4, Nov 16-20, 2006, Beijing, China 2006 IEEE Piscataway, NJ, USA 4
10. T Elgamal A public key cryptosystem and a signature scheme based on discrete logarithms IEEE Transactions on Information Theory 31 4 1985 469 472
11. JB Lima, RM Campello de Souza, D Panario Security of publickey cryptosystems based on Chebyshev polynomials over prime finite fields Proceedings of the IEEE International Symposium on Information Theory (ISIT'08), Jul 6-11, 2008, Toronto, Canada 2008 IEEE Piscataway, NJ, USA 1843 1847
12. DH Wang, HZ Yang, FS Yu A new key exchange scheme based on Chebyshev polynomials Proceedings of the Congress on Image and Signal Processing (CISP'08), May 27-30, 2008, Sanya, China 2008 IEEE Piscataway, NJ, USA 124 127
13. DH Wang, ZG Hu, ZJ Tong An identity authentication system based on Chebyshev polynomials Proceedings of the 1st International Conference on Information Science and Engineering (ICISE'09), Dec 26-28, 2009, Nanjing, China 2010 IEEE Piscataway, NJ, USA 1648 1650
14. XY Wang, JF Zhao An improved key agreement protocol based on chaos Communications in Nonlinear Science and Numerical Simulation 15 12 2010 4052 4057
15. AJ Menezes, PC Van Oorschot, SA Vanstone Handbook of applied cryptography 1997 CRC Press New York, NY, USA
16. S Muller On the Computation of square roots in finite fields Designs, Codes and Cryptography 31 3 2004 301 312