Public Key Cryptosystems Based on Chaotic-Chebyshev Polynomials

Due to rapid developments in limits and possibilities of communications and information transmissions, there is a growing demand of cryptographic techniques, which has spurred a great deal of intensive research activities in the study of cryptography. This paper describes a public key encryption based on chebyshev polynomials [1]. We discuss the algorithm for textual data and present the cryptanalysis which can be performed on this algorithm for the recovery of encrypted data [2]. We also describe a simple hashing algorithm for making this algorithm more secure, and which can also be used for digital signature [3]. The main scope of this paper is to propose an extension of this algorithm to images and videos and making it secure using multilevel scrambling and hash. Software implementations and experimental results are also discussed in detail.

[1]  Kehar Singh,et al.  Fully phase encryption using fractional Fourier transform , 2003 .

[2]  Jian Zhang,et al.  Image Encryption Method Based on Chaotic Map , 2007, 2007 2nd IEEE Conference on Industrial Electronics and Applications.

[3]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[4]  Alfredo De Santis,et al.  Security of public-key cryptosystems based on Chebyshev polynomials , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  L. Kocarev.  Chaos-based cryptography: a brief overview , 2001 .

[6]  Xiaofeng Liao,et al.  A novel key agreement protocol based on chaotic maps , 2007, Inf. Sci..

[7]  K. Ganesan,et al.  Look-up Table Based Chaotic Encryption of Audio Files , 2006, APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems.

[8]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[9]  Naveen K. Nishchal,et al.  Fully phase encrypted memory using cascaded extended fractional Fourier transform , 2003, SPIE Optics + Photonics.

[10]  Ljupco Kocarev,et al.  Public-key encryption based on Chebyshev maps , 2003, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03..