Main Article Content
In this work, we propose a new directed digital signature scheme over a group ring whose security relies on the hardness of the discrete logarithm problem and the factorization search problem. This scheme is efficient as it requires very few operations for both signing and verifying signatures. Furthermore, the security of the proposed scheme is examined.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
- Authors keep the rights and guarantee the Journal of Innovative Applied Mathematics and Computational Sciences the right to be the first publication of the document, licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License that allows others to share the work with an acknowledgement of authorship and publication in the journal.
- Authors are allowed and encouraged to spread their work through electronic means using personal or institutional websites (institutional open archives, personal websites or professional and academic networks profiles) once the text has been published.
R. Alvarez, F-M. Martinez, J-F. Vicent and A. Zamora, A new public key cryptosystem based on matrices, in: Proc. WSEAS Int. Conf. on Inform. Security and Privacy, 2007, 36–39.
J. J. Climent, P. R. Navarro and L. Tortosa, Key exchange protocols over noncommutative rings The case of End(Zp × Zp2), International Journal of Computer Mathematics, 89(13-14) (2012), 1753–1763.
W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Transactions on Information Theory, 22(6) (1976), 644–654.
M. Eftekhari, A Diffie–Hellman key exchange protocol using matrices over non-commutative rings, Journal of Groups, Complexity, Cryptology, 4(1) (2012), 167–176.
M. Eftekhari, Cryptanalysis of some protocols using matrices over group rings, in: Proc. Int. Conf. on Cryptology in Africa, Lecture Notes in Computer Science, 10239 (2017), 223–229.
T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Transactions on Information Theory, 31(4) (1985), 469–472.
S. Goldwasser, S. Micali and R. L. Rivest, A digital signature scheme secure against adaptive chosen-message attacks, SIAM Journal on Computing, 17(2) (1988), 281–308.
I. Gupta, A. Pandey and M. K. Dubey, A key exchange protocol using matrices over group ring, Asian-European Journal of Mathematics, 12(05) (2019), 1950075.
D. Kahrobaei, C. Koupparis and V. Shpilrain, Public key exchange using matrices over group rings, Journal of Groups, Complexity, Cryptology, 12(1) (2013), 97–115.
C. H. Lim and P.J. Lee, Modified Maurer-Yacobi’s scheme and its applications, in: Proc. Int. Workshop on the Theory and Application of Cryptographic Techniques, Lecture Notes in Computer Science, 718 (1982), 308–323.
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, Advances in Mathematics of Communications, 9(2)(2015), 247–253.
A. Myasnikov, V. Shpilrain and A. Ushakov, Non-commutative Cryptography and Complexity of group-theoretic Problems, Math. Surveys Monogr., Vol. 177, Am. Math. Soc., Providence, RI, USA, 2011.
R. W. K. Odoni, V. Varadharajan and P. W. Sanders, Public key distribution in matrix rings, Electronics Letters , 20(9) (1984), 386–387.
D. S. Passman, The Algebraic Structure of Group Rings, Wiley, New York, NY, USA, 1977.
R. L. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, 21(2) (1978), 120–126.
J. H. Silverman, Fast multiplication in finite fields GF(2N), in: Proc. Int. Workshop on Cryptographic Hardware and Embedded Systems, Lecture Notes in Computer Science, 1717 (1999), 122–134.
N. R. Wagner and M. R. Magyarik, A public-key cryptosystem based on the word problem, in: Proc. Workshop on the Theory and Application of Cryptographic Techniques, Lecture Notes in Computer Science, 196 (1984), 19–36.
S. Wei, A new digital signature scheme based on factoring and discrete logarithms, In: Chen, K. (eds) Progress on Cryptography. The International Series in Engineering and Computer Science, 769 (2004), 107–111.