×
Iovane, G.; Amorosia, A.; Benedetto, E.; Lamponi, G.

An information fusion approach based on prime numbers coming from RSA algorithm and fractals for secure coding. (English) Zbl 1495.94052

J. Discrete Math. Sci. Cryptography 18, No. 5, 455-479 (2015).
Summary: In the present paper we will show a system to realize an innovative cryptographic code that ensures a high level of security using Information Fusion (IF) techniques. In detail, we have decided to merge two codes respectively generated by an algorithm of Cryptographic Public-key and by fractals relations. A companion IF method has been presented with a different use in [G. Iovane et al., ibid. 14, No. 3, 207–225 (2011; Zbl 1495.94053)]. Indeed, in the previous paper it was created an identification access key, while here we wish to generate a highly randomized Cryptography key to be used for encrypting. The choice of using fractals to generate numbers to be fused with codes of Public-Key Cryptography, is due to the randomness of these structures. The idea is to use these features for cryptographic applications such as One-Time-Pad. The presented new modified fusion technique, with respect to [loc. cit.], is called F&NIF (Fractal & Numerical Information Fusion).

Cited in 2 Documents

MSC:

94A60 Cryptography
28A80 Fractals

Keywords:

cryptographic code; public-key cryptography

Citations:

Zbl 1495.94053

Software:

NIST Statistical Test Suite
Cite Review PDF
Full Text: DOI

References:

[1] Iovane, G.; Puccio, L.; Lamponi, G.; Amorosia, A., Electronic access key based on innovative Information Fusion technique involving prime numbers and biometric data, Journal of discrete mathematical sciences and cryptography (2010), Taru Pubblication
[2] Ruggeri, N., Principles of pseudo-random number generation in cryptography, University of Chicaco (2006)
[3] Diffie, W.; Hellman, M. E., Multiuser cryptographic techniques, AFIPS’76: Proceedings of the June 7-10, 1976, national computer conference and exposition, pages 109-112 (1976), New York, NY, USA: ACM, New York, NY, USA
[4] Diffie, W.; Hellman, M. E., New directions in cryptography, IEEE Transactions on Information Theory, 11, 6, 644-654 (1976) · Zbl 0435.94018 · doi:10.1109/TIT.1976.1055638
[5] Pellegrini, A.; Bertacco, V.; Austin, T. M., Fault-based attack of rsa authentication, Design, Automation and Test in Europe (DATE), pages 855-860 (2010)
[6] Devaney, R. L., Caos e Frattali - Matematica dei sistemi dinamici ed applicazioni al calcolatore, Addison-Wesley Italia (1990), Milano
[7] Barnsley, M., Fractals everywhere, Academic Press (1988), Boston · Zbl 0691.58001
[8] Mandelbrot, B. B., The fractal geometry of nature, W.H. Freeman and Company (1982), New York · Zbl 0504.28001
[9] Mandelbrot, B. B., Gli oggetti frattali. Forma, caso e dimensione, Giulio Einaudi Editore, (1987), Torino
[10] Mandelbrot, B. B., Nel mondo dei frattali, Di Renzo Editore (2001), Collana I Dialoghi
[11] Iovane, G.; Tortoriello, F. S., Frattali e geometria dell’universo, Aracne Editrice S.R.L. (2005)
[12] Croydon, David A., “The Hausdorff dimension of a class of random self-similar fractal trees” Adv, Appl. Probab, Volume 39, Number 3, 708-730 (2007) · Zbl 1127.60012 · doi:10.1239/aap/1189518635
[13] Huntress, G. B., Encryption using Fractal Key, United States Patent (2004)
[14] Kumar, S., Public Key Cryptographic System Using Mandelbrot Sets, Military Communications Conference., pages 1-5 (2006)
[15] Alia, M. A.; Samsudin, A. B., A new digital signature scheme based on mandelbrot and Julia fractal sets, American Journal of Applied Sciences, 4, 11, 848-856 (2007) · doi:10.3844/ajassp.2007.848.856
[16] Lian, S.; Chen, X.; Ye, D., Secure fractal image coding based on fractal parameter encryption, Fractal Complex Geometry, Pattern, Scaling in Nature and Society, 17, 2, 149-160 (2009) · Zbl 1177.68244
[17] Rozouvan, V., Modulo image encryption with fractal keys, Optics and Lasers in Engineering, 47, 1, 1-6 (2009) · doi:10.1016/j.optlaseng.2008.09.001
[18] Yoon, E. J.; Yoo, K. Y., Cryptanalysis of a modulo image encryption scheme with fractal keys, Optics and Lasers in Engineering, 48, 7-8, 821-826 (2010) · doi:10.1016/j.optlaseng.2010.02.004
[19] Anand, P. M.R.; Bajpai, G.; Bhaskar, V., Real-time symmetric cryptography using quaternion Julia set, IJCSNS International Journal of Computer Science and Network Security, 9, 3, 20-26 (2009)
[20] Al-Saidi, N. M.G.; Said, M. R.Md., A new approach in cryptographic systems using fractal image coding, Journal of Mathematics and Statistics, 5, 3, 183-189 (2009) · Zbl 1184.94223 · doi:10.3844/jmssp.2009.183.189
[21] Riendeau, J. F.; Ciet, M.; Farrugia, A. J., Method and apparatus for data protection system using geometry of fractals or other chaotic systems, United States Patent Application Publication (2010)
[22] Al-Saidi, N. M.G.; Md, M. R., Said and A.M. Ahmed. Efficiency Analysis for Public Key Systems Based on Fractal Functions, Journal of Computer Science, 7, 4, 526-532 (2011) · doi:10.3844/jcssp.2011.526.532
[23] Dasarathy, B. V., Information fusion - what, where, why, when, and how?, Information Fusion, 2, 2, 75-76 (2001) · doi:10.1016/S1566-2535(01)00032-X
[24] Waltz, E.; Llinas, J., Multisensor Data Fusion, Artech House, Inc., (1990)
[25] Dreher, Fabian; Samuel, Tony, Continuous images of Cantor’s ternary set · Zbl 1305.28019
[26] Curry, Clinton P., Irreducible Julia sets of rational functions, Journal of Difference Equations and Applications, Volume 16, Issue 5 & 6, pages 443-450 (2010) · Zbl 1205.30023 · doi:10.1080/10236190903244857
[27] Shchepin, Evgeny, On fractal Peano curves · Zbl 1124.28011
[28] Rivest, R. L.; Shamir, A.; Adleman, L., A method for obtaining digital signatures and public-key cryptosystems, Commun. ACM, 21, 2, 120-126 (1978) · Zbl 0368.94005 · doi:10.1145/359340.359342
[29] Rukhin, A.; Soto, J.; Nechvatal, J.; Smid, M.; Barker, E.; Leigh, S.; Levenson, M.; Vangel, M.; Banks, D.; Heckert, A.; Dray, J.; Vo, S., A statistical test suite for random and pseudorandom number generators for cryptographic applications, NIST (National Institute of Standards and Technology) (2008)
[30] Curry, Clinton P.; Mayer, John C., Buried Points in Julia Sets, Journal of Difference Equations and Applications, Volume 16, Issue 5 & 6, pages 435-441 (2010) · Zbl 1198.30028 · doi:10.1080/10236190903203861
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.