Abstract
An Elliptic Curve Cryptography (ECC) is used on the Noncommutative Cryptographic (NCC) principles. The security and strengths of the manuscript are resilient on these two cryptographic assumptions. The claims on the Noncommutative cryptographic scheme on monomials generated elements is considered be based on hidden subgroup or subfield problems that strengthen this manuscript, where original assumptions are hidden and its equivalents semiring takes part in the computation process. In relation to the same, the research gap is well designed on Dihedral orders of 6 and 8, but our contributions are in security- and length-based attacks enhancement over Dihedral order 12, reported in work done. We modeled the said strategies and represent the ideal security concerns for applications.
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References
W. Diffie, M.E. Hellman, New directions in cryptography. IEEE Trans. Inf. Theory 22, 644–654 (1976). https://doi.org/10.1109/TIT.1976.1055638
V.S. Miller, Use of elliptic curves in cryptography. Adv. Cryptol. 218, 417–426 (1986), dl.acm.org/citation.cfm?id=704566
N. Koblitz, Elliptic curve cryptosystems. Math Comput. 48, 203–209 (1987). https://doi.org/10.1090/S0025-5718-1987-0866109-5
P.W. Shor, Algorithms for quantum computation: discrete logarithms and factorings, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science (1994), pp. 124–134. https://doi.org/10.1109/sfcs.1994.365700
A. Kitaev, Quantum measurements and the Abelian stabilizer problem, in Electronic Colloquium on Computational Complexity (1996), http://eccc.hpi-web.de/eccc-reports/1996/TR96-003/index.html
S.H. Paeng, K.C. Ha, J.H. Kim, S. Chee, C. Park, New public key cryptosystem using finite non abelian groups. Lect. Notes Comput. Sci. 2139, 470–485 (2001)
A. Joux, K. Nguyen, Separating decision Diffie-Hellman from Diffie-Hellman in cryptographic groups. Cryptology ePrint Archive, Report 2001/003 (2001), http://eprint.iacr.org/
C. Cocks, An identity based encryption scheme based on quadratic residues. Lect. Notes Comput. Sci. 2260, 360–363 (2001)
S.S. Magliveras, D.R. Stinson, T.V. Trung, New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups. J. Cryptol. 15(4), 285–297 (2002)
K.H. Ko, D.H. Choi, M.S. Cho, J.W. Lee, New signature scheme using conjugacy problem. IACR Cryptology ePrint Archive 2002:168 (2002)
D. Grigoriev, I.V. Ponomarenko, On non-abelian homomorphic public-key cryptosystems. J. Math. Sci. (2002), cs.CR/0207079, arXiv:cs/0207079
J. Proos, C. Zalka, Shor’s discrete logarithm quantum algorithm for elliptic curve. Quantum Inf. Comput. 3, 317–344 (2003), http://dl.acm.org/citation.cfm?id=2011531
E. Lee, Braid groups in cryptology. ICICE Trans. Fundam. E87-A(5), 986–992 (2004)
D. Grigoriev, I. Ponomarenko, Constructions in public-key cryptography over matrix groups (2005), CoRR, abs/math/0506180, arXiv:math/0506180
M. Rotteler, Quantum algorithm: a survey of some recent results. Inf. Forensic Entw. 21, 3–20 (2006), http://link.springer.com/content/pdf/10.1007%2Fs00450-006-0008-7.pdf
Z. Cao, X. Dong, L. Wang, New public key cryptosystems using polynomials over noncommutative rings. Int. J. Cryptol. Res. 9, 1–35 (2007), https://eprint.iacr.org/2007/009.pdf
J. Kubo, The dihedral group as a family group, in Quantum Field Theory and Beyond, ed. by W. Zimmermann, E. Seiler, K. Sibold (World Science Publication, Hackensack, NJ, 2008), pp. 46–63, http://www.worldscientific.com/worldscibooks/10.1142/6963
P.V. Reddy, G.S.G.N. Anjaneyulu, D.V.R. Reddy, M. Padmavathamma, New digital signature scheme using polynomials over noncommutative groups. Int. J. Comput. Sci. Netw. Secur. 8, 245–250 (2008), http://paper.ijcsns.org/07_book/200801/20080135.pdf
D.N. Moldovyan, N.A. Moldovyan, A new hard problem over noncommutative finite groups for cryptographic protocols, in Lecture Notes in Computer Science, vol. 6258 (Springer, Heidelberg, New York, 2010), pp. 183–194
A.D. Myasnikov, A. Ushakov, Cryptanalysis of matrix conjugation schemes. J. Math. Cryptol. 8, 95–114 (2014). https://doi.org/10.1515/jmc-2012-0033
K. Svozil, Non-contextual chocolate balls versus value indefinite quantum cryptography. Theoret. Comput. Sci. 560, 82–90 (2014)
G. Kumar, H. Saini, Novel noncommutative cryptography scheme using extra special group. Secur. Commun. Netw. 2017, 1–21 (2017)
M. Uno, M. Kano, Visual cryptography schemes with dihedral group access structure, in Proceedings of ISPEC’07 (Springer, 2007), pp. 344–359, http://dl.acm.org/citation.cfm?id=1759542
Z. Cao, New Directions of modern cryptography, in Noncommutative Cryptography (CRC Press, 2013)
B.C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Springer, New York, 2003), http://link.springer.com/book/10.1007%2F978-0-387-21554-9
D. Ruinskiy, A. Shamir, B. Tsaban, Length-based cryptanalysis: the case of Thompson’s group. J. Math. Cryptol. 1, 359–372 (2007). https://doi.org/10.1515/jmc.2007.018
A.D. Myasnikov, A. Ushakov, Length based attack and braid groups: cryptanalysis of Anshel-Anshel-Goldfeld key exchange protocol, in Lecture Notes in Computer Science, vol. 4450 (Springer, Heidelberg, 2007), http://link.springer.com/chapter/10.1007%2F978-3-540-71677-8_6
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Kumar, G., Saini, H. (2020). An ECC with Probable Secure and Efficient Approach on Noncommutative Cryptography. In: Jain, L., Tsihrintzis, G., Balas, V., Sharma, D. (eds) Data Communication and Networks. Advances in Intelligent Systems and Computing, vol 1049. Springer, Singapore. https://doi.org/10.1007/978-981-15-0132-6_1
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