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Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

A generalization of ElGamal signature variants over elliptic curves

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pp. 1–15Vol. 28Issue 1February 2025DOI: 10.47974/JDMSC-1637 Crossmark XML
Received:
08 Sep 2021
Accepted:
03 Mar 2022
Published Online:
28 Feb 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1637
Pages:
1–15

Abstract

The ElGamal signature is a scheme invented by Taher Elgamal in 1984 based on the problem of the discrete logarithm. In our day, there are several variants of this signature. In this paper, we will present the version of many variants schemes of ElGamal over elliptic curves. We will give some examples.

Keywords

Subject Classifications

94A6014H52

References

[1] J. Buchmann, Introduction to Cryptography, Springer Science & Business Media (2013).
[2] W. Diffie and M. Hellman, “New directions in cryptography,” IEEE Trans. Inf. Theory, vol. 22, no. 6, pp. 644–654 (1976).
[3] T. ElGamal, “A public key cryptosystem and a signature scheme based on discrete logarithms,” IEEE Trans. Inf. Theory, vol. 31, no. 4, pp. 469–472 (1985).
[4] L. C. Guillou and J. J. Quisquater, “A ‘paradoxical’ identity-based signature scheme resulting from zero-knowledge,” in Proc. Advances Cryptol., pp. 216–231, Springer-Verlag (1990).
[5] D. Hankerson, A. J. Menezes, and S. Vanstone, Guide to Elliptic Curve Cryptography, Springer Science & Business Media (2006).
[6] J. Hoffstein, J. Pipher, and J. H. Silverman, An Introduction to Mathematical Cryptography, Springer (2008).
[7] P. Horster, M. Michels, and H. Peterson, “Generalized ElGamal signatures for one message block,” Citeseer (1994).
[8] M. Ihia and O. Khadir, “Amelioration of ElGamal digital signature schemes,” Int. J. Inf. Sec., vol. 42, pp. 117–126 (2019).
[9] N. Koblitz, A Course in Number Theory and Cryptography, 2nd ed., Springer-Verlag (1994).
[10] N. Koblitz, Algebraic Aspects of Cryptography, vol. 3 of Algorithms and Computation in Mathematics, Springer-Verlag (1998).
[11] N. Koblitz, “Elliptic curve cryptosystems,” Math. Comput., vol. 48, no. 177, pp. 203–209 (1987).
[12] D. W. Kravitz, “Digital signature algorithm,” Google Patents, US Patent 5, 231, 668, July 27 (1993).
[13] A. J. Menezes, P. C. Van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press (1996).
[14] V. S. Miller, “Use of elliptic curves in cryptography,” in Conf. Theory Appl. Cryptogr. Tech., pp. 417–426 (1985).
[15] O. M. Rabin, “Digitalized signatures and public-key functions as intractable as factorization,” Massachusetts Institute of Technology, Cambridge Lab for Computer Science (1979).
[16] R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM, vol. 21, no. 2, pp. 120–126 (1978).
[17] D. R. Stinson, Cryptography: Theory and Practice, Chapman and Hall/CRC (2005).
[18] L. C. Washington, Elliptic Curves: Number Theory and Cryptography, CRC Press (2008).
[19] N. Mehibel and M. Hamadouche, “A new enhancement of elliptic curve digital signature algorithm,” J. Discrete Math. Sci. Cryptogr., vol. 23, no. 3, pp. 743–757 (2020).
[20] D. M. Kuryazov, “Development of electronic digital signature algorithms with compound modules and their cryptanalysis,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 4, pp. 1085–1099 (2021).

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