Skip to main content

An Efficient Forward Secure Authenticated Encryption Scheme with Ciphertext Authentication Based on Two Hard Problems

  • Conference paper
  • First Online:
Advances in Big Data and Cloud Computing

Abstract

Authenticated encryption is a cryptographic technique that concurrently establishes message confidentiality, integrity, authenticity and non-repudiation. In this paper, an efficient authenticated encryption scheme is proposed, based on the hardness of the integer factorization problem and the discrete logarithm problem on conic curves over a ring \(Z_n\). The protocol provides forward secrecy in case the sender’s private keys are compromised and supports public verifiability, as well as, ciphertext authentication by an external verifier, without full decryption. Hence, the protocol can be used for secure data sharing in untrusted cloud environments. Several attack scenarios against the scheme are analysed to confirm its validity as an authenticated encryption protocol. The security criterions are satisfied, as long as either one of the hardness assumptions hold. The scheme is implemented over conic curves, which possess interesting characteristics like effective message encoding and decoding, easily computable point operations and inverses.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Zheng, Y.: Digital signcryption or how to achieve cost (signature & encryption) cost (signature)+ cost (encryption). In: Annual International Cryptology Conference, pp. 165–179. Springer, Berlin Heidelberg (1997). https://doi.org/10.1007/BFb0052234

  2. Zheng, Y., Imai, H.: How to construct efficient signcryption schemes on elliptic curves. Informat. Process. Lett. 68, 227–253. Elsevier (1998). https://doi.org/10.1016/S0020-0190(98)00167-7

  3. Zheng, Y., Imai, H.: Efficient signcryption schemes on elliptic curves. Citeseer (1996). 10.1.1.130.4261

    Google Scholar 

  4. Hwang, R.J., Lai, C.H., Su, F.F.: An efficient signcryption scheme with forward secrecy based on elliptic curve. Appl. Mathemat. Comput. 167, 870–881. Elsevier (2005). https://doi.org/10.1007/s11042-014-2283-9

  5. Toorani, M., Beheshti, A.A.: An elliptic curve-based signcryption scheme with forward secrecy. arXiv preprint arXiv:1005.1856 (2010). https://doi.org/10.3923/jas.2009.1025.1035

  6. Xiang-xue, L., Ke-fei, C., Shi-qun, L.: Cryptanalysis and improvement of signcryption schemes on elliptic curves. Wuhan Univ. J. Nat. Sci. 10(1), 231–234 (2005). https://doi.org/10.1007/BF02828657

    Article  MathSciNet  Google Scholar 

  7. Chow, S.S., Yiu, S.M., Hui, L.C., Chow, K.P.: Efficient forward and provably secure ID-based signcryption scheme with public verifiability and public ciphertext authenticity. In: International Conference on Information Security and Cryptology, pp. 352–369. Springer Berlin Heidelberg (2003). https://doi.org/10.1007/978-3-540-24691-6_26

  8. Mohamed, E., Elkamchouchi, H.: Elliptic curve signcryption with encrypted message authentication and forward secrecy. Int. J. Comput. Sci. Netw. Secur. 9(1), 395–398 (2009)

    Google Scholar 

  9. Elkamchouchi, H., Nasr, M., Ismail, R.: A new efficient strong proxy signcryption scheme based on a combination of hard problems. In: IEEE International Conference on Systems, Man and Cybernetics, SMC 2009. IEEE, pp. 5123–5127 (2009). https://doi.org/10.1109/ICSMC.2009.5346018

  10. Hinek, M.J.: On the security of multi-prime RSA. J. Math. Cryptology 2(2), 117–147 (2008). 0.1515/JMC.2008.006

    Google Scholar 

  11. Ciet, M., Koeune, F., Laguillaumie, F., Quisquater, J.J.: Short private exponent attacks on fast variants of RSA. UCL Crypto Group Technical Report Series CG-2002/4, University Catholique de Louvain (2002). doi:10.1.1.12.9925

    Google Scholar 

  12. Sun, Y., Zhang, J., Xiong, Y., Zhu, G.: Data security and privacy in cloud computing. Int. J. Distrib. Sens. Netw. (2014)

    Google Scholar 

  13. Chen, Z.G., Song, X.X.: A public-key cryptosystem scheme on conic curves over \(Z_n\). In: 2007 International Conference on Machine Learning and Cybernetics, vol. 4, pp. 2183–2187. IEEE (2007). https://doi.org/10.1109/ICMLC.2007.4370507

  14. Bellini, E., Murru, N.: An efficient and secure RSA-like cryptosystem exploiting Rdei rational functions over conics. Finite Fields Appl. 39, 179–194 (2016). https://doi.org/10.1016/j.ffa.2016.01.011

    Article  MathSciNet  MATH  Google Scholar 

  15. Zheng Fu, C.: A public key cryptosystem based on conic curves over finite field \(F_p\). ChinaCrypt, pp. 45–49, Science Press (1998)

    Google Scholar 

  16. Zhang, D., Liu, M., Yang, Z.: Zero-knowledge proofs of identity based on ELGAMAL on conic. In: IEEE International Conference on E-Commerce Technology for Dynamic E-Business, pp. 216–223. IEEE (2004). https://doi.org/10.1109/CEC-EAST.2004.77

  17. Tahat, N.M.: A new conic curve digital signature scheme with message recovery and without one-way hash functions. Ann. Univ. Craiova-Math. Comput. Sci. Ser. 40(2), 148–153 (2013)

    MathSciNet  MATH  Google Scholar 

  18. Shi, Y., Xiong, G.Y.: An undetachable threshold digital signature scheme based on conic curves. Appl. Math. Inf. Sci. 7(2), 823–828 (2013). https://doi.org/10.12785/amis/070254

    Article  MathSciNet  Google Scholar 

  19. Song, X., Chen, Z.: An efficient conic curve threshold digital signature. In: Proceedings of the 3rd WSEAS International Conference on Circuits, Systems, Signal and Telecommunications, pp. 149–153 (2009)

    Google Scholar 

  20. Dong, X., Qian, H., Cao, Z.: Provably secure RSA type signature based on conic curve. Wirel. Commun. Mob. Comput. 9(2), 217–225 (2009). https://doi.org/10.1002/wcm.602

    Article  Google Scholar 

  21. Lu, R.X., Cao, Z.F., Zhou, Y.: Threshold undeniable signature scheme based on conic. Appl. Math. Comput. 162(1), 165–177 (2005). https://doi.org/10.1016/j.amc.2003.12.084

    MathSciNet  MATH  Google Scholar 

  22. Dai, Z.D., Ye, D.F., Pei, D.Y., Yang, J.H.: Cryptanalysis of ElGamal type encryption schemes based on conic curves. Electron. Lett. 37(7), 426 (2001). https://doi.org/10.1049/el:20010272

  23. Chaudhry, S.A., Farash, M.S., Naqvi, H., Sher, M.: A secure and efficient authenticated encryption for electronic payment systems using elliptic curve cryptography. Electron. Commer. Res. 16(1), 113–139 (2016). https://doi.org/10.1007/s10660-015-9192-5

    Article  Google Scholar 

  24. Yang, J.H., Chang, Y.F., Chen, Y.H.: An efficient authenticated encryption scheme based on ECC and its application for electronic payment. Inf. Technol. Control 42(4), 315–324 (2013). https://doi.org/10.5755/j01.itc.42.4.2150

    Google Scholar 

Download references

Acknowledgements

This work was funded by Visvesvaraya PhD Scheme for Electronics and IT, Ministry of Electronics and Information Technology, Government of India.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Renu Mary Daniel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Daniel, R.M., Rajsingh, E.B., Silas, S. (2018). An Efficient Forward Secure Authenticated Encryption Scheme with Ciphertext Authentication Based on Two Hard Problems. In: Rajsingh, E., Veerasamy, J., Alavi, A., Peter, J. (eds) Advances in Big Data and Cloud Computing. Advances in Intelligent Systems and Computing, vol 645. Springer, Singapore. https://doi.org/10.1007/978-981-10-7200-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-7200-0_11

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-7199-7

  • Online ISBN: 978-981-10-7200-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics