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Journal of Discrete Mathematical Sciences and Cryptography cover
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.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

An efficient ID-based cryptographic encryption based on group ring

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pp. 1851–1866Vol. 27Issue 6September 2024DOI: 10.47974/JDMSC-1871 Crossmark XML
Received:
05 Apr 2023
Published Online:
16 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1871
Pages:
1851–1866

Abstract

For most of the traditional IBEs (identity-based encryptions), security totally relies on the safekeeping of private keys. In case the private key is exposed, all the previously generated ciphertext need to be reissued. Due to increased usage of unprotected devices or mobiles, the key exposure is frequent. Therefore, it is important to mitigate the threat originated due to the key exposure in case of IBE. To deal with this issue, in this paper, we construct a novel IBE based on group ring that also provides forward security. We show that the security of our novel IBE is based on the hardness of discrete logarithm problem in group ring. Moreover, against the chosen plaintext attack, we show that it is semantically secure in random oracle model. Finally, we compare our IBE with several other existing IBEs in terms of execution cost. 

Keywords

Subject Classifications

(2010) 94A6020C05

References

[1] D. J. Bernstein, J. Buchmann, E. Dahmen, Post quantum cryptography, Springer (2009).
[2] D. Boneh, X. Boyen, Secure identity based encryption without random oracles, CRYPTO 2004, in: LNCS, 3152, Springer-Verlag, Berlin, 443-459 (2004).
[3] D. Boneh, X. Boyen, Efficient selective-id secure identity based encryption without random oracles, EUROCRYPT 2004, in: LNCS, 3027, Springer-Verlag, Berlin, 223-238 (2004).
[4] D. Boneh, M. K. Franklin, Identity-based encryption from the Weil pairing, SIAM J. Comput., 32(3), 586-615 (2003).
[5] D. Boneh, R. Canetti, S. Halevi, J. Katz, Chosen-ciphertext security from identity-based encryption, SIAM J. Comput., 36(5), 1301-1328 (2003).
[6] C. Cocks, An identity based encryption scheme based on quadratic residues, in: International conference on cryptography and coding, in: LNCS, 2260, Springer-Verlag, 360-363 (2001).
[7] S. Cui, P. Duan, C. W. Chan, An identity based encryption scheme with batch verifications, in: Proceedings of the Ist ACM international conference on scalable information systems, 2260, Hong Kong, pp. 22 (2006).
[8] E. Fujisaki, T. Okamoto, Secure integration of asymmetric and symmetric encryption schemes, Crypto-99, in: LNCS, 1666, Springer-Verlag, Berlin, 537-554 (1999).
[9] N. Goel, I. Gupta, M. Dubey, B. K. Dass, Undeniable signature scheme based over group ring, AAECC, 27, 523-535 (2016).
[10] S. Heng, K. Kurosawa, k-Resilient identity-based encryption in the standard model, IEICE Trans. Fundam., E89CA(1), 39-46 (2006).
[11] J. Hoffstein, J. Pipher, J. H. Silverman, An introduction of mathematical cryptography, Springer (2008).
[12] B. Hurley, T. Hurley, Group ring cryptography, Int. J. Pure Appl. Math., 69(1), 67-86 (2011).
[13] S. Inam, R. Ali, A new ElGamal-like cryptosystem based on matrices over groupring, Neural Comput. & Applic., doi: 10.1007/s00521-016-2745-2.
[14] E. Kiltz, Y. Vahlis, CCA2 secure IBE: standard model efficiency through authenticated symmetric encryption, in: CT-RSA, in: LNCS, 4964, Springer-Verlag, 221-239 (2008).
[15] Ö. Küsmü, T. Hanoymak, A novel public-key encryption scheme based on Bass cyclic units in integral group rings, J. Discret. Math. Sci. Cryptogr., 25(2), 579-589 (2022).
[16] W. C. Lee, K. C. Liao, Constructing identity-based cryptosystems for discrete logarithm based cryptosystems, J. Netw. Comput. Appl., 22, 191-199 (2004).
[17] B. Lynn, Authenticated ID-based encryption, cryptology, ePrint Archive, Report2002/072, 2002, http://eprint.iacr.org/2002/072.
[18] C. Meshram, An efficient ID-based cryptographic encryption based on discrete logarithm problem and integer factorization problem, Inf. Process. Lett., 115, 351-358 (2015).
[19] C. Meshram, S. Meshram, An IND-ID-CPA secure ID-based cryptographic protocol using GDLP and IFP, Informatica, 28(3), 471-484 (2017).
[20] C. P. Milies, S. K. Sehgal, An Introduction to group rings, Kluwer (2002).
[21] G. Mittal, S. Kumar, S. Narain, S. Kumar, Group rings based public key cryptosystems, J. Discret. Math. Sci. Cryptogr., 25(6), 1683-1704 (2022).
[22] G. Mittal, S. Kumar, S. Kumar, A quantum secure ID-based cryptographic encryption based on group rings, Sadhana, 47, 1-16 (2022).
[23] A. Shamir, Identity-based cryptosystems and signature schemes, CRYPTO’84, in: LNCS, 196, Springer-Verlag, 47-53 (1984).
[24] J. Sun, C. Zhang, Y. Zhang, Y. Fang, An identity-based security system for user privacy in vehicular adhoc networks, IEEE Trans. Parallel Distrib. Syst., 27(9), 1227-1239 (2010).
[25] B. Waters, Efficient identity-based encryption without random oracles, CRYPTO 2005, in: LNCS, 3494, Springer-Verlag, Berlin, 114-127 (2005).

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