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Xiaofeng Liao, Fei Chen, KwokWo Wong, "On the Security of PublicKey Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$," IEEE Transactions on Computers, vol. 59, no. 10, pp. 13921401, October, 2010.  
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@article{ 10.1109/TC.2010.148, author = {Xiaofeng Liao and Fei Chen and KwokWo Wong}, title = {On the Security of PublicKey Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$}, journal ={IEEE Transactions on Computers}, volume = {59}, number = {10}, issn = {00189340}, year = {2010}, pages = {13921401}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2010.148}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  On the Security of PublicKey Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$ IS  10 SN  00189340 SP1392 EP1401 EPD  13921401 A1  Xiaofeng Liao, A1  Fei Chen, A1  KwokWo Wong, PY  2010 KW  Chaos KW  Chebyshev polynomials KW  period distribution KW  publickey cryptography KW  security analysis. VL  59 JA  IEEE Transactions on Computers ER   
[1] M.S. Baptista, "Cryptography with Chaos," Physics Letters A, vol. 240, nos. 1/2, pp. 5054, 1998.
[2] G. Jakimoski and L. Kocarev, "Chaos and Cryptography: Block Encryption Ciphers Based on Chaotic Maps," IEEE Trans. Circuits and Systems I, Regular Papers, vol. 48, no. 2, pp. 163169, Feb. 2001.
[3] K.W. Wong, "A Fast Chaotic Cryptography Scheme with Dynamic LookUp Table," Physics Letters A, vol. 298, pp. 238242, 2002.
[4] D. Xiao, X. Liao, and K.W. Wong, "Improving the Security of a Dynamic LookUp Table Based Chaotic Cryptosystem," IEEE Trans. Circuits and Systems II: Express Briefs, vol. 53, no. 6, pp. 502506, June 2006.
[5] J.M. Amigo, L. Kocarev, and J. Szczepanski, "Theory and Practice of Chaotic Cryptography," Physics Letters A, vol. 366, pp. 211216, 2007.
[6] F. Hwu, "The Interpolating Random Spline Cryptosystem and the ChaoticMap PublicKey Cryptosystem," PhD thesis, Univ. of Missouri, 1993.
[7] R. Tenny, L. Tsimring, L. Larson, and H. Abarbanel, "Using Distributed Nonlinear Dynamics for Public Key Encryption," Physical Rev. Letters, vol. 90, no. 4, p. 047903, 2003.
[8] L. Kocarev and Z. Tasev, "PublicKey Encryption Based on Chebyshev Maps," Proc. 2003 IEEE Int'l Symp. Circuits and Systems, vol. 3, pp. 2831, 2003.
[9] P. Bergamo, P. D'Arco, A. De Santis, and L. Kocarev, "Security of PublicKey Cryptosystems Based on Chebyshev Polynomials," IEEE Trans. Circuits and Systems I: Regular Papers, vol. 52, no. 7, pp. 13821393, July 2005.
[10] G. Maze, "Algebraic Methods for Constructing OneWay Trapdoor Functions," PhD thesis, Univ. of Notre Dame, 2003.
[11] K. Cheong and T. Koshiba, "More on Security of PublicKey Cryptosystems Based on Chebyshev Polynomials," IEEE Trans. Circuits and Systems II: Express Briefs, vol. 54, no. 9, pp. 795799, Sept. 2007.
[12] L. Kocarev, J. Makraduli, and P. Amato, "PublicKey Encryption Based on Chebyshev Polynomials," Circuits, Systems and Signal Processing, vol. 24, no. 5, pp. 497517, 2005.
[13] J.B. Lima, R.M. Campello de Souza, and D. Panario, "Security of PublicKey Cryptosystems Based on Chebyshev Polynomials over Prime Finite Fields," Proc. IEEE Int'l Symp. Information Theory, pp. 18431847, 2008.
[14] W.B. Muller and W. Nobauer, "Some Remarks on PublicKey Cryptosystems," Studia Scientiarum Mathematicarum Hungarica, vol. 16, pp. 7176, 1981.
[15] P.J. Smith and M.J.J. Lennon, "LUC: A New Public Key System," Proc. Ninth IFIP Int. Symp. Computer Security, pp. 103117, 1993.
[16] P. Smith and C. Skinner, "A PublicKey Cryptosystem and a Digital Signature System Based on the Lucas Function Analogue to Discrete Logarithms," Advances in Cryptology—Asiacrypt '94, pp. 298306, Springer, 1995.
[17] W.B. Muller and W. Nobauer, "Cryptanalysis of the DicksonScheme," Advances in Cryptology—Eurocrypt '85, pp. 5061, Springer, 1986.
[18] D. Bleichenbacher, W. Bosma, and A.K. Lenstra, "Some Remarks on LucasBased Cryptosystems," Advances in Cryptology—Crypto '95, pp. 386396, Springer, 1996.
[19] C.S. Laih, F.K. Tu, and W.C. Tai, "Remarks on LUC Public Key System," Electronics Letters, vol. 30, no. 2, pp. 123124, 1994.
[20] C.S. Laih, F.K. Tu, and W.C. Tai, "On the Security of the Lucas Function," Information Processing Letters, vol. 53, no. 5, pp. 243247, 1995.
[21] G. Gong and L. Ham, "PublicKey Cryptosystems Based on Cubic Finite Field Extensions," IEEE Trans. Information Theory, vol. 45, no. 7, pp. 26012605, Nov. 1999.
[22] S. Goldwasser and S. Micali, "Probabilistic Encryption and How to Play Mental Poker Keeping Secret All Partial Information," Proc. 14th Ann. Symp. Theory of Computing, pp. 365377, 1982.
[23] S. Goldwasser and S. Micali, "Probablistic Encryption," J. Computer and System Sciences., vol. 28, pp. 270299, 1984.
[24] M. Bellare and P. Rogaway, "Random Oracles Are Practical: A Paradigm for Designing Efficient Protocols," Proc. First Ann. Conf. Computer and Comm. Security, pp. 6273, 1993.
[25] M. Bellare, "PracticeOriented Provable Security," Proc. First Int'l Workshop Information Security (ISW '97), pp. 221231, 1998.
[26] T. Herlestam, "On Functions of Linear Shift Registers," Advances in Cryptology—Eurocrypt '85, pp. 119129, Springer, 1986.
[27] J. Massey, "ShiftRegister Synthesis and BCH Decoding," IEEE Trans. Information Theory, vol. IT15 no. 1, pp. 122127, Jan. 1969.
[28] E. Key, "An Analysis of Structure and Complexity of Nonlinear Binary Sequence Generator," IEEE Trans. Information Theory, vol. 22, no. 6, pp. 732736, Nov. 1976.
[29] M. Ward, "The Arithmetical Theory of Linear Recurring Sequences," Trans. Am. Math. Soc., vol. 35, pp. 600628, 1933.
[30] Z.D. Dai, "Binary Sequences Derived from MLSequences over Rings I: Periods and Minimal Polynomials," J. Cryptology, vol. 5, pp. 193207, 1992.
[31] Z. Dai and M. Huang, "A Criterion for Primitiveness of Polynomials over Z/(2^d)," Chinese Science Bull., vol. 36, p. 892, 1991.
[32] S.W. Golomb, Shift Register Sequences. HoldenDay, 1967.
[33] E.S. Selmer, Linear Recurrence Relations Over Finite Fields. Univ. of Bergen, 1966.
[34] M.B. Nathanson, Elementary Methods in Number Theory. SpringerVerlag, 2000.
[35] R. Lidl and H. Niederelter, Finite Fields, Encycopeida of Mathematics and Its Application. AddisonWesley, 1983.
[36] W. Mao, Modern Cryptography: Theory and Practice, first ed. PrenticeHall, 2003.
[37] R. Needhamand and M. Schroeder, "Using Encryption for Authentication in Large Networks of Computers," Comm. ACM, vol. 21, pp. 993999, 1978.
[38] A.J. Menezes, P.C. van Oorschot, and S.A. Vanstone, Handbook of Applied Cryptography. CRC Press, 1997.
[39] M. Bellare and P. Rogaway, "Optimal Asymmetric Encryption— How to Encrypt with RSA and Rabin," Advances in Cryptology— Eurocrypt '94, pp. 171188, Springer, 1995.