Abstract
The generation of pseudo-random numbers (bits) plays a critical role in a large number of applications such as statistical mechanics, numerical simulations, gaming industry, communication or cryptography. The choice of secret keys for cryptographic primitives largely depends on the quality of random numbers used. These random numbers are fundamental tools in the generation of secret keys and initialization variables of encryption for cryptographic application, masking protocols, or for internet gambling. Chaotic Pseudorandom numbers were found to be very efficient in this aspect. The relevance of chaotic pseudorandom sequences in ensuring security in cryptosystems is considered, at the same time reviewing statistical tests required to make such sequences cryptographically secure. This paper intends to review the development of chaotic pseudorandom number generators through the years and the statistical tests they are required to pass as a measure of their randomness.
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References
Addabbo T, Alioto M, Fort A, Rocchi S, Vignoli V (2005) Long Period pseudo random bit generators derived from a discretized chaotic map. IEEE Int Symp Circ Syst 892–895
Akhshani A, Akhavan A, Mobaraki A, Lim SC, Hassan Z (2014) Pseudo random number generator based on quantum chaotic map. Commun Nonlinear Sci Numer Simul 19(1):101–111
Alvarez AME, Fernandez A, Garcia P, Jimenez J (1999) New approach to chaotic encryption. Phys Lett A 263:373–375
Arroyo D, Alvarez G, Li S (2011) Cryptanalysis of a family of self-synchronizing chaotic stream ciphers. Commun Nonlinear Sci Numer Simul 2(16):805–813
Blum L (1986) Pseudo-random number generator. SIAM J Comput 15(2):364–383
Franc M (2013) A Pseudo-random bit generator using three chaotic logistic maps. Theory Appl Model Comput 229–247
Francois M, Grosges T, Barchiesi D, Erra R (2013) A New pseudo-random number generator based on two chaotic maps. Informatic 24(2):181–197
François M, Grosges T, Barchiesi D, Erra R (2014) Pseudo-random number generator based on mixing of three chaotic maps. Commun Nonlinear Sci Numer Simul 19(4):887–895
James F (1990) A review of pseudorandom number generators. Comput Phys Commun 60(3):329–344
Joseph NSPKB (2000) Chaos for stream Cipher. In proc Recent Adv Comput Commun. 35–42
Juan S (1999) Statistical testing of random number generators. Available at http://csrc.nist.gov/rng/rng5.html
Khanzadi H, Eshghi M, Borujeni SE (2014) Image encryption using random bit sequence based on chaotic maps. Arab J Sci Eng 39(2):1039–1047
Knuth DE (1973) The art of computer programming. V 3. Addison-Wesley, Boston, p 829
Kocarev L (2001) Cryptography : a brief overview. Circuits Syst Mag IEEE 1:3
Kurian AP, Puthusserypady S (2008) Self-synchronizing chaotic stream ciphers. Sig Process 88(10):2442–2452
Li YYC, Poh-Han Pei SC (2003) Gnenerating chaotic stream ciphers using chaotic systems Chinese. J Phys 41:6
Makris G, Antoniou I (2012) Cryptography with Chaos. In: 5th Chaotic modelling and simulation international conference, pp 12–15
Maqableh MM (2001) Analysis and design security primitives based on chaotic systems for ecommerce, Durham
MartÃnez-Ñonthe JA, Castañeda-SolÃs A, DÃaz-Méndez A, Cruz-Irisson M, Vázquez-Medina R (2012) Chaotic block cryptosystem using high precision approaches to tent map. Microelectron Eng 90:168–172
Matthews R (1989) On the derivation of a ‘chaotic’ encryption algorithm. Cryptologia 13(1):29–42
Menezes AJ, Van Oorschot PC, Vanstone SA (1996) Applied cryptography. p 794
Merah L, Ali-pacha A, Said NH (2013) A Pseudo random number generator based on the chaotic system of chua’s circuit, and its real time FPGA implementation. 7(55):2719–2734
Merah L, Ali-pacha A, Said NH (2013b) A Pseudo random number generator based on the chaotic system of chua’s circuit, and its real time. FPGA Implementation 7(55):2719–2734
Özkaynak F, Yavuz S (2013) Security problems for a pseudorandom sequence generator based on the Chen chaotic system. Comput Phys Commun 184(9):2178–2181
Patidar V, Pareek NK, Sud KK (2009) A new substitution–diffusion based image cipher using chaotic standard and logistic maps. Commun Nonlinear Sci Numer Simul 14(7):3056–3075
Rhouma R, Solak E, Belghith S (2010) Cryptanalysis of a new substitution–diffusion based image cipher. Commun Nonlinear Sci Numer Simul 15(7):1887–1892
Shujun L, Xuanqin M, Yuanlong C (2001) Pseudo-random bit generator based on couple chaotic systems and its applications in stream-cipher cryptography. In: Progress in cryptology: INDOCRYPT, LNCS. 247:316–329
Silva CP, Young AM (2000) Introduction to chaos-based communications and signal processing. IEEE Aerosp Conf Proc 1:279–299 (Cat. No.00TH8484)
Werndl C, Philosophy A (2009) Are deterministic descriptions and indeterministic descriptions observationally equivalent ? 1–33
Wolfram S (1985) Cryptography with cellular-automata. In: Advances in cryptology–CRYPTO PROC
Xiamin Wang WZ, Zhang J, Fan Y (2010) Chaotic pseudorandom bit generator using n-dimensional nonlinear digital filter. Commun Nonlinear Sci Numer Simul 2:0–3
Xiang T, Liao X, Tang G, Chen Y, Wong K (2006) A novel block cryptosystem based on iterating a chaotic map. Phys Lett A 349(1–4):109–115
Yu W, Cao J (2006) Cryptography based on delayed chaotic neural networks. Phys Lett A 356(4–5):333–338
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Hina, A.D., Said, M.R.M., Banerjee, S. (2015). Chaotic Pseudorandom Sequences and the Security of Cryptosystems. In: Erçetin, Ş., Banerjee, S. (eds) Chaos, Complexity and Leadership 2013. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-09710-7_13
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DOI: https://doi.org/10.1007/978-3-319-09710-7_13
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