The "Elliptic" matrices and a new kind of cryptography

Resumen

In [17], A. Chillali et al introduce a new cryptographic method based on matrices over a finite field Fpn , where p is a prime number. In this paper, we will generate this method in a new group of square block matrices based on an elliptic curve, called "elliptic" matrices.

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Citas

R. Avanzi, H. Cohen, C. Doche, G. Frey, T. Lange, K. Nguyen and F. Vercauteren, Handbook of elliptic and hyperelliptic cryptography. Chapman and Hall/CRC (2006).

I. F. Blake, G. Seroussi and N. P. Smart, Elliptic Curves in Cryptography. Cambridge (1999). DOI: https://doi.org/10.1017/CBO9781107360211

I. F. Blake, G. Seroussi and N. P. Smart, Advances in Elliptic Curve Cryptography. Cambridge (2005). DOI: https://doi.org/10.1017/CBO9780511546570

C. Boyd & A. Mathuria, Protocols for Authentication and Key Establishment, Information Security and Cryptography Series, Springer-Verlag, Heidelberg, (2003). DOI: https://doi.org/10.1007/978-3-662-09527-0

A. Chillali, Cryptography over elliptic curve of the ring Fq[e], e4 = 0, World Acad. of Sci. Eng. & Technol. 78 (2011) 848-850.

J. J. Climent, P. R. Navarro and L. Tortosa, Key exchange protocols over non-commutative rings. The case of End Zp × Zp2, Int. J. Comput. Math. 89(1314) (2012) 1753-1763. DOI: https://doi.org/10.1080/00207160.2012.696105

M. Eftekhari, A Diffie-Hellman key exchange protocol using matrices over non-commutative rings, Groups Complex. Cryptol. 4(1) (2012) 167-176. DOI: https://doi.org/10.1515/gcc-2012-0001

M. Eftekhari, Cryptanalysis of some protocols using matrices over group rings, in Int. Conf. on Cryptology in Africa: Progress in Cryptology - AFRICACRYPT 2017, Lecture Notes in Computer Science, Vol. 10239 (Springer, 2017). DOI: https://doi.org/10.1007/978-3-319-57339-7_13

S. D. Galbraith, Mathematics of public key cryptography. Cambridge University Press (2012). DOI: https://doi.org/10.1017/CBO9781139012843

D. Hankerson, A. Menezes and S. Vanstone, Guide to elliptic curve cryptography. Springer (2004).

D. Kahrobaei, C. Koupparis and V. Shpilrain, Public key exchange using matrices over group rings, Groups Complex. Cryptol. 5(1) (2013) 97-115. DOI: https://doi.org/10.1515/gcc-2013-0007

A. J. Menezes and Y. H. Wu, The discrete logarithm problem in GL(n, q), ARS Combinatoria. 47 (1997) 23-32.

G. Micheli, Cryptanalysis of a non-commutative key exchange protocol, Adv. Math. of Comm. 9(2) (2015) 247-253. DOI: https://doi.org/10.3934/amc.2015.9.247

R. Odoni, V. Varadharajan and P. Sanders, Public key distribution in matrix rings, Electron. Lett. 20(9) (1984) 386-387. DOI: https://doi.org/10.1049/el:19840267

A. P. Stakhov, The ‘golden’ matrices and a new kind of cryptography, Chaos, Solitons and Fractals 32 (2007) 1138-1146. DOI: https://doi.org/10.1016/j.chaos.2006.03.069

L. C. Washington, Elliptic Curves, Number Theory and Cryptography, 2nd edn. CRC Press (2008).

M. Zeriouh, A. Chillali and A. Boua, Cryptography Based on the Matrices, Bol. Soc. Paran. Mat (2019) 75-83 DOI: https://doi.org/10.5269/bspm.v37i3.34542

Publicado
2022-12-29
Sección
Articles