Skip to main content
Log in

On Authentication Schemes Using Polynomials Over Non Commutative Rings

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

Authentication is a term very important for data communication security. We see many frauds due to authentication failure. The problem manifolds when communication is over insecure channel. Entity authentication is a term which involves proof of sender’s identity and very useful in various applications like in banking sector and various other client server mechanisms. Availability of quantum computers increases the vulnerability of breaking old protocols. Researchers are finding new platforms to overcome this problem and one such example is non commutative polynomial rings [NCPR]. In 2012, M.R.Vallauri [MRV], in his paper suggested an authentication protocol using NCPR. He has proved security analysis under the assumption that polynomial symmetrical decomposition problem (PSDP) is hard. In this paper we show that the protocol suggested by him is breakable without solving PSDP. We also provide corrected protocol to overcome this problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

Code availability

Not applicable.

References

  1. A.J. Menezes, P.C.V. Oorschot, S.A. Vanstone: Handbook of applied cryptography. fifth edition, CRC press Inc, USA ISBN: 9780849385230, 2001

  2. W. Stallings Cryptography and network security, principles and practices. Seventh edition, Prentice Hall, 2005, ISBN-13:978-0134444284, ISBN-10:0134444280

  3. Buchanan, W., & Woodward, A. (2017). Will quantum computers be the end of public key encryption? Journal of Cyber Security Technology, 1(1), 28–43.

    Article  Google Scholar 

  4. Pritchard, F. L. (1996). The ideal membership problem in non-commutative polynomial rings. Journal of symbolic computation, 22(1), 27–48. https://doi.org/10.1006/jsco.1996.0040.

    Article  MathSciNet  MATH  Google Scholar 

  5. M.R.Valluri, Authentication schemes using polynomials over non-commutative rings, International journal on cryptology and information security, volume 2, number 4, 2012, 51–58, available at https://wireilla.com/papers/ijcis/V2N4/2412ijcis06.pdf accessed on 03 November 2020.

  6. Z. Shaikh, P. Garg, Single and multi trusted third party: comparison, identification and reduction of malicious conduct by trusted third party in secure multiparty computing protocol, Advances in computer science, engineering & applications. [Part of the advances in intelligent systems and computing book series (volume 167)], 2012, 295–304 https://doi.org/10.1007/978-3-642-30111-7_28

  7. Rizvi, S., Cover, K., & Gates, C. (2014). A trusted third-party (TTP) based encryption scheme for ensuring data confidentiality in cloud environment. Procedia computer science, 36, 381–386. https://doi.org/10.1016/j.procs.2014.09.009.

    Article  Google Scholar 

  8. M. Lepinski, S. Micali, A. Shelat, Fair zero knowledge, Theory of cryptography conference [Part of the lecture notes in computer science book series (LNCS, volume 3378)], 2005, 245–263 https://doi.org/10.1007/978-3-540-30576-7_14

  9. R. Cramer, I. Damgård, Efficient zero-knowledge proofs of knowledge without intractability assumptions, International workshop on public key cryptography [Part of the lecture notes in computer science book series (LNCS, volume 1751)], 2000, 354–372 https://doi.org/10.1007/978-3-540-46588-1_24

  10. I. A. Gheyas, A.E. Abdallah, Detection and prediction of insider threats to cyber security: a systematic literature review and meta-analysis, Big data analytics , volume 1, article number 6, 2016, 1–29 https://doi.org/10.1186/s41044-016-0006-0

  11. M.B. Salem, S.Hershkop, S.J. Stolfo, A survey of insider attack detection research, Insider attack and cyber security [Part of the advances in information security book series (ADIS, volume 39)], 2008, 69–90 https://doi.org/10.1007/978-0-387-77322-3_5

  12. H. Gao, C. Bodei, P. Degano, H.R. Nielson, A formal analysis for capturing replay attacks in cryptographic protocols, Annual asian computing science conference [Part of the lecture notes in computer science book series (LNCS, volume 4846)], 2007, 150–165 https://doi.org/10.1007/978-3-540-76929-3_15

  13. W.C. Yan, S.H. Heng, B.M. Goi, Off-line keyword guessing attacks on recent public key encryption with keyword search schemes, International conference on autonomic and trusted computing [Part of the lecture notes in computer science book series (LNCS, volume 5060)], 2008, 100–105 https://doi.org/10.1007/978-3-540-69295-9_10

  14. H. Jung, H.S. Kim, Secure hash-based password authentication protocol using smart cards, International conference on computational science and its applications. [Part of the lecture notes in computer science book series (LNCS, volume 6786)], 2011, 593–606 https://doi.org/10.1007/978-3-642-21934-4_48

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Varun Shukla.

Ethics declarations

Conflicts of interest

No conflicts of interests exist.

Availability of data and material

The data is self generated.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shukla, V., Chaturvedi, A. & Misra, M.K. On Authentication Schemes Using Polynomials Over Non Commutative Rings. Wireless Pers Commun 118, 185–193 (2021). https://doi.org/10.1007/s11277-020-08008-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-020-08008-4

Keywords

Navigation