Abstract
Key exchange enables two or more entities to agree on an identical key. In post-quantum, the construction of ring learning with error (RLWE) based key exchange provides a strong provable secure, and efficient solution. The resistance against signal leakage and key mismatch attacks is essential for developing secure RLWE-based key exchange mechanisms for the quantum era. RLWE-based key exchange schemes are developed in recent years, however, most of them found vulnerable to attacks or have higher computational costs. We have analyzed the existing contributions and defined a mechanism to achieve a computationally efficient and secure solution. To improve security and reduce computing overhead, we are introducing a new key exchange technique to attain efficiency and security against signal leakage and key mismatch attacks. Our scheme is proven secure by the random oracle model (ROM). Moreover, we have provided a performance evaluation of computation cost competing with other existing key exchange techniques.

Similar content being viewed by others
Data availability
Not applicable.
References
Stallings, W.: Cryptography and Network Security, 4/E. Pearson Education India (2006)
Zhao, Z., Ma, S., Qin, P.: Password authentication key exchange based on key consensus for iot security. Clust. Comput. 26(1), 1–12 (2023)
Hellman, M.: New directions in cryptography. IEEE Trans. Inform. Theory 22(6), 644–654 (1976)
Jing, Z., Gu, C., Yu, Z., Shi, P., Gao, C.: Cryptanalysis of lattice-based key exchange on small integer solution problem and its improvement. Clust. Comput. 22(1), 1717–1727 (2019)
Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th annual symposium on foundations of computer science, IEEE, pp. 124–134 (1994)
Soni, L., Chandra, H., Gupta, D.S., Keval, R.: Quantum-resistant public-key encryption and signature schemes with smaller key sizes. Clust. Comput. 2, 1–13 (2022). https://doi.org/10.1007/s10586-022-03955-y
Tang, Y., Ba, Y., Li, L., Wang, X., Yan, X.: Lattice-based public-key encryption with conjunctive keyword search in multi-user setting for iiot. Clust. Comput. 25(4), 2305–2316 (2022)
Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. J. ACM (JACM) 60(6), 1–35 (2013)
Ding, J., Xie, X., Lin, X.: A simple provably secure key exchange scheme based on the learning with errors problem. Cryptology ePrint Archive (2012)
Harn, L., Mehta, M., Hsin, W.-J.: Integrating Diffie–Hellman key exchange into the digital signature algorithm (dsa). IEEE Commun. Lett. 8(3), 198–200 (2004)
Zhang, J., Zhang, Z., Ding, J., Snook, M., Dagdelen, Ö.: Authenticated key exchange from ideal lattices, In: Annual international conference on the theory and applications of cryptographic techniques, Springer, pp. 719–751 (2015)
Bos, J.W., Costello, C., Naehrig, M., Stebila, D.: Post-quantum key exchange for the tls protocol from the ring learning with errors problem. In: IEEE symposium on security and privacy. IEEE 2015, 553–570 (2015)
Alkim, E., Ducas, L., Pöppelmann, T., Schwabe, P.: Post-quantum key exchange-a new hope. In: USENIX security symposium, Vol. 2016 (2016)
Bos, J., Costello, C., Ducas, L., Mironov, I., Naehrig, M., Nikolaenko, V., Raghunathan, A., Stebila, D.: Frodo: Take off the ring! practical, quantum-secure key exchange from lwe, In: Proceedings of the 2016 ACM SIGSAC conference on computer and communications security, pp. 1006–1018 (2016)
Fluhrer, S.: Cryptanalysis of ring-lwe based key exchange with key share reuse, Cryptology ePrint Archive (2016)
Ding, J., Saraswathy, R., Alsayigh, S., Clough, C.: How to validate the secret of a ring learning with errors (rlwe) key, Cryptology ePrint Archive (2018)
Gao, X., Ding, J., Li, L., Liu, J.: Practical randomized rlwe-based key exchange against signal leakage attack. IEEE Trans. Comput. 67(11), 1584–1593 (2018)
Wang, K., Jiang, H.: Analysis of two countermeasures against the signal leakage attack, in: International Conference on Cryptology in Africa, Springer, pp. 370–388 (2019)
Regev, O.: The learning with errors problem. Invited Survey CCC 7(30), 11 (2010)
Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. J. ACM (JACM) 60(6), 1–35 (2013)
Steinfeld, R., Sakzad, A., Zhao, R.K.: Titanium: proposal for a nist post-quantum public-key encryption and kem standard. NIST PQC Round 1, 4–12 (2017)
Roşca, M., Sakzad, A., Stehlé, D., Steinfeld, R.: Middle-product learning with errors, In: Advances in Cryptology–CRYPTO 2017: 37th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 20–24, 2017, Proceedings, Part III, Springer, pp. 283–297 (2017)
Hamburg, M.: Module-lwe key exchange and encryption: The three bears, Tech. rep., Technical report, National Institute of Standards and Technology, 2017 (2018)
Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J.M., Schwabe, P., Seiler, G., Stehlé, D.: Crystals-kyber: a cca-secure module-lattice-based kem. In: IEEE European symposium on security and privacy (EuroS &P). IEEE 2018, 353–367 (2018)
Langlois, A., Stehlé, D.: Worst-case to average-case reductions for module lattices. Des. Codes Cryptogr. 75(3), 565–599 (2015)
Kirkwood, D., Lackey, B.C., McVey, J., Motley, M., Solinas, J.A., Tuller, D.; Failure is not an option: Standardization issues for post-quantum key agreement. In: Workshop on Cybersecurity in a Post-Quantum World, p. 21 (2015)
Ding, J., Branco, P., Schmitt, K.: Key exchange and authenticated key exchange with reusable keys based on rlwe assumption, Cryptology ePrint Archive (2019)
Feng, Q., He, D., Zeadally, S., Kumar, N., Liang, K.: Ideal lattice-based anonymous authentication protocol for mobile devices. IEEE Syst. J. 13(3), 2775–2785 (2018)
Dabra, V., Bala, A., Kumari, S.: Lba-pake: lattice-based anonymous password authenticated key exchange for mobile devices. IEEE Syst. J. 15(4), 5067–5077 (2020)
Ding, R., Cheng, C., Qin, Y.: Further analysis and improvements of a lattice-based anonymous pake scheme. IEEE Syst. J. 16(3), 5035–5043 (2022)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)
Pursharthi, K., Mishra, D.: On the security of ring learning with error-based key exchange protocol against signal leakage attack, Security and Privacy e310
Ding, J., Alsayigh, S., Lancrenon, J., Snook, S.R.V.M.: Provably secure password authenticated key exchange based on rlwe for the post-quantum world. In: Topics in Cryptology–CT-RSA 2017: The Cryptographers’ Track at the RSA Conference 2017, San Francisco, CA, USA, February 14–17, 2017, Proceedings, Springer, 2017, pp. 183–204
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the fortieth annual ACM symposium on Theory of computing, 2008, pp. 197–206 (2008)
Micciancio, D., Regev, O.: Worst-case to average-case reductions based on gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007)
Zhang, Y., Chen, J., Huang, B.: An improved authentication scheme for mobile satellite communication systems. Int. J. Satell. Commun. Netw. 33(2), 135–146 (2015)
Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-lwe and security for key dependent messages. In: Advances in Cryptology–CRYPTO 2011: 31st Annual Cryptology Conference, Santa Barbara, CA, USA, August 14-18, 2011. Proceedings 31, Springer, pp. 505–524 (2011)
Abdalla, M., Fouque, P.-A., Pointcheval, D.: Password-based authenticated key exchange in the three-party setting. In: International workshop on public key cryptography, Springer, pp. 65–84 (2005)
Islam, S.H.: Provably secure two-party authenticated key agreement protocol for post-quantum environments. J. Inform. Secur. Appl. 52, 102468 (2020)
Ding, J., Alsayigh, S., Saraswathy, R., Fluhrer, S., Lin, X., Leakage of signal function with reused keys in rlwe key exchange. In: IEEE international conference on communications (ICC). IEEE 2017, 1–6 (2017)
Longa, P.: Post-quantum cryptography lwe (learning with errors) library, https://github.com/microsoft/LWE_Library.git (2017)
Peikert, C.: Lattice cryptography for the internet, in: Post-Quantum Cryptography: 6th International Workshop, PQCrypto 2014, Waterloo, ON, Canada, October 1-3, 2014. Proceedings 6, Springer, pp. 197–219 (2014)
Dabra, V., Bala, A., Kumari, S.: Reconciliation based key exchange schemes using lattices: a review. Telecommun. Syst. 77, 413–434 (2021)
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing Interest
The authors have not disclosed any competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Pursharthi, K., Mishra, D. A computationally efficient and randomized RLWE-based key exchange scheme. Cluster Comput 27, 1599–1610 (2024). https://doi.org/10.1007/s10586-023-04032-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10586-023-04032-8