Abstract
In the present paper, we propose a secured scheme of digital signature connecting both conjugacy problem and discrete logarithm problem based on non-commutative group generated over a finite field. For this, we define a non-commutative group over matrices with the elements of finite field such that conjugacy and discrete logarithm problems can be executed together proficiently. By doing so, we can formulate the signature structures using conjugacy and discrete logarithm through non commutative group. In some domains, the above combination reduces to completely in discrete logarithm problem. This digital signature scheme more elemental over F* q(x) = G Ln (Fq). Here the security of the signature protocol depending on complexity of the problems associated with conjugacy and discrete logarithm. The security analysis and intermission of proposed protocol of digital signature is presented with the aid of order of complexity, existential forgery and signature repudiation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
W. Diffie, M. Hellman, New directions in cryptography. IEEE Trans. Inf. Theory IT-2.2(6), 644–654 (1976)
J. Kang, J.W. Han, J.H. Cheon, S.J. Lee, K.H. Ko, S.J. Lee, C. Park, New public key crypto system using braid groups. Lect. Notes Comput. Sci. 1880, 166–183 (2000)
D. Moon, K.C. Ha, S. Cho, Y.-O. Kim, Key exchange protocol using matrix algebras and its analysis. J. Korean Math. Soc.
A. Raulynaitis, E. Sakalauskas, P. Tvarijonas, key agreement protocol using conjugacy and discrete logarithm problems in group representation level. Informatica 18(1), 115–124 (2007)
Los Alamitos, Network and System Security. IEEE Computer Society, CA, USA (2009), pp. 443–446
Text Book: Cryptography and network security by MR. AtulKahate
http://www.iacr.org (International Association for Cryptographic Research—website)
D. Poulakis, A Variant of Digital Signature Algorithm Designs, Codes and Cryptography, vol. 51(1) (2009), pp. 99–104
N.M.F. Tahat, E.S. Ismail, R.R. Ahmad, A new digital signature scheme based on factoring and Discrete logarithms. J. Math. Stat. 4(4), 222–225 (2008)
C.Y. Yang, M.S. Hwang, S.F. Tzeng, A new digital signature scheme based on factoring and discrete logarithm. IJCM 81(1), 9–14 (2004)
Z. Shao, Security of a new digital signature scheme based on factoring and discrete logarithms. IJCM 82(10), 1215–1219 (2005)
Z. Shao, Signature schemes based on factoring and discrete logarithms, in Computers and Digital Techniques, IEEE Proceedings-, vol. 145. IET (2002), pp. 33–36
G.S.G.N. Anjaneyulu, P.V. Reddy, U.M. Reddy, Secured digital signature scheme using polynomials over non-commutative division semi ring. IJCSNS 8(8), (2008)
G.S.G.N. Anjaneyulu, U.M. Reddy Secured directed digital signature over non-commutative division semirings and allocation of experimental registration number. IJCSI 9(5), 3 (2012)
A.J. Menezes, Y.-H. Wu, The discrete logarithm problem in G Ln (Fq); ARS Combinatorica 47, 23–32 (1997)
S. Wei, A new digital signature scheme based on factoring and discrete logarithms, in Progress on Cryptography (2004), pp. 107–111
S. Alam, A. Jamil, A. Saldhi, M. Ahamad, Digital image authentication and encryption using digital signature, in ICACEA (2015), pp. 332–336
N.A. Moldovyan, D.N. Moldovyan, A new hard problem over non commutative finite groups for cryptographic protocols. Lect. Notes Comput. Sci. 6258, 183–194 (2010)
D. Boneh, A. Joux, P.Q. Nguyen, Why textbook Elgamal and RSA encryption are insecure, in Lecture Notes in Computer Science, vol. 1976 (2000), pp. 30–44
V. Retakh, S. Gelfand, I. Gelfand, R. Wilson, Quasideterminants. Adv. Math. 193, 56–141 (2005)
M. Eftekhari, A Diffie-Hellman key exchange protocol using matrices over non abelian ring. http://arXiv1209.6144v1[cs.CR] (2012)
B. Leclerc, V. Retakh, J.-Y. Thibon, A. Lascoux, D. Krob, I. Gelfand, Non commutative symmetric functions. Adv. Math. 112(2), 218–348 (1995)
V. Shpilrain, D. Grigoriev, Authentication from matrix conjugation, groups, complexity, cryptology, vol. 1, pp. 199–205 (2009)
B. Lynn, D. Boneh, H. Shacham, Short signatures from the Weil pairing, in Proceedings of Asia Crypt 2001, LNCS, vol. 2248 (Springer, 2001), pp. 533–551
D. Pointcheval, T. Okamoto, The gap-problems: a new class of problems for the security of cryptographic schemes, in Proceedings of PKC 2001, LNCS, vol. 1992 (Springer, 2001), pp. 104–118
A. Lincoln, Electronic signature laws and the need for uniformity in the global market, 8 J. Small & Emerging Bus. L. 67 (2004)
T.J. Smedinghoff, R.H. Bro, Moving with change: electronic signature legislation as a vehicle for advancing e-commerce. 17 J. Marshall J. Computer & Info. L. 723, 199
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Narendra Mohan, L., Anjaneyulu, G. (2017). A Secured Digital Signature Using Conjugacy and DLP on Non-commutative Group over Finite Field. In: Satapathy, S., Bhateja, V., Udgata, S., Pattnaik, P. (eds) Proceedings of the 5th International Conference on Frontiers in Intelligent Computing: Theory and Applications . Advances in Intelligent Systems and Computing, vol 516. Springer, Singapore. https://doi.org/10.1007/978-981-10-3156-4_47
Download citation
DOI: https://doi.org/10.1007/978-981-10-3156-4_47
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-3155-7
Online ISBN: 978-981-10-3156-4
eBook Packages: EngineeringEngineering (R0)