Citation :

Erdwin Owuma Ngwawe, Tsitsi Zengeya, 2025. "Post-Quantum Cryptography Algorithms and Implementation Challenges" International Journal of Computer Science & Information Technology  Volume 1, Issue 2: 14-24.

Abstract :

Quantum computer poses a very high threat to the current cryptographic measures we are practicing to protect our digital infrastructure. In particular, the best known public-key algorithms (such as RSA for encryption, and ECDSA for digital signatures), are broken by a quantum computer using Shor's algorithm. But quantum algorithms like Shor's algorithm don't care. This security grows even worse as quantum computing advances. Yet, we need to find cryptography which does not get broken out-of-the-box when quantum computers arrive. Post-Quantum Cryptography (PQC) is encryption that can use quantum, but it must be secure against the attack of a quantum computer and also must be safe with classical computer. This study is a significant contribution to broaching the algorithmic frameworks used in Post-Quantum Cryptography (PQC), including lattice-based, code based, multivariate and hash-based methods.

References :

[1] Shor, P. W. (1994). Quantum Computation: Discrete Logarithms & Factoring In Proc. 35th FOCS.

[2] Grover, L. K. (1996). Quantum mechanical description of an algorithm for database search. In 28th Annual ACM Symposium on Theory of Computing.

[3] Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.) (2009). Post-Quantum Cryptography. Springer.

[4] NIST. (2022). Post-Quantum Cryptography Standardization Project. https://csrc.nist.gov/Projects/post-quantum-cryptography

[5] Alkim, E., Ducas, L., Pöppelmann, T., Schwabe, P. (2016). Post-Quantum Key Exchange – A New Hope. USENIX Security.

[6] Bos, J. W., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J. M., … & Whyte, W. (2018). CRYSTALS-Kyber. IEEE European Symposium on Security and Privacy.

[7] Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J. M., Schwabe, P. & Stehlé, D. (2018). CRYSTALS-Dilithium. IEEE Euro S&P.

[8] Bernstein, D. J., et al. (2009). Security of the McEliece cryptosystem and its variants; PQCrypto.

[9] Hülsing, A., et al. (2013). SPHINCS: Practical stateless hash-based signatures. EUROCRYPT.

[10] Open Quantum Safe Project. https://openquantumsafe.org

[11] NSA. (2022). CNSA Suite 2.0. https://www.nsa.gov

[12] ENISA. (2021). New Current Benchmark Review on Post-Quantum Cryptography.

[13] Lyubashevsky, V., Peikert, C., and Regev, O. (2010). New constructions for ideal lattices and application to learning with errors over rings. EUROCRYPT.

[14] Peikert, C. (2016). A decade of lattice cryptography. Foundations and Trends® in Theoretical Computer Science.

[15] Bernstein, D., & Lange, T. (2017). Post-quantum cryptography. Nature, 549(7671), 188–194.

[16] Chen, L., et al. (2016). Report on Post-Quantum Cryptography. NISTIR 8105.

[17] NIST. (2022). FIPS 203: Module-Lattice-Based Key-Encapsulation Mechanism: ML-KEM (Draft).

[18] NIST. (2022). FIPS 204: Module-Lattice-Based Digital Signature Algorithm: ML-DSA (Draft).

[19] NIST. (2023). FIPS 205 - Stateless Hash-Based Digital Signature Algorithm: SLH-DSA (Draft).

[20] Aranha, D. F., Paterson, K. G. (2016). On the Security of Hybrid Key Exchange Protocols. ASIACRYPT.

[21] Campagna, M. et al. (2020). Hybrid Post-Quantum TLS. IETF Draft.

[22] Schwabe, P., Stoffelen, K. (2016). All the AES you need. Selected Areas in Cryptography.

[23] Hoffstein, J., Pipher, J., & Silverman, J. H. (1998). NTRU: A Ring-based Public Key Cryptosystem. ANTS.

[24] Courtois, N. T. (2001). Secure and Efficient Zero-Knowledge Authentication. PKC.

[25] Beullens, W. (2021). Rainbow Shattered in a Weekend. Cryptology ePrint Archive.

[26] Regev, O. (2005). Lattices, Learning with Errors, Random Linear Codes and Cryptography. STOC.

[27] Goldreich, O., Goldwasser, S., & Halevi, S. (1997). Lattice reduction problems and public-key cryptosystems. CRYPTO.

[28] Hoffstein, J., Howgrave-Graham, N. (2003). NTRUEncrypt: Alive after all these years. PQCrypto.

[29] Sendrier, N. (2011). Cryptography from Code: Current State and Perspectives. IEEE Security & Privacy.

[30] Hülsing, A., Rijneveld, J., Schwabe, P. SPHINCS+. Submission to NIST PQC.

[31] ETSI. (2020). Quantum Safe Cryptography and Security. ETSI TR 103 619.

[32] Steinfeld, R., et al. (2012). Secure against keyword guessing attacks. PKC.

[33] PQClean GitHub Repository. https://github.com/PQClean/PQClean

[34] Bindel, N., et al. (2021). Hybrid Key Encapsulation Mechanisms. IACR.

[35] Hülsing, A., Butin, D. (2018). XMSS: Extended Hash-Based Signatures. RFC 8391.

[36] Chen, M. S., et al. (2020). Quantum cryptanalysis: Progress and challenges. ACM Computing Surveys.

[37] Derler, A., Krenn, S., Slamanig, D. (2018). Post-quantum zero-knowledge proofs. PQCrypto.

[38] Misoczki, R., et al. (2013). MDPC-McEliece: New McEliece Variants. ISIT.

[39] Albrecht, M. R., et al. (2017). LWE, NTRU, and SIS Problems: Estimates. Cryptology ePrint Archive.

[40] Overbeck, R., Sendrier, N. (eds.) (2009). Code-based cryptography. In Post-Quantum Cryptography.

[41] Bernstein, D. J., Lange, T., Niederhagen, R. (2011). Dual EC: A Standardized Backdoor. CHES.

[42] D'Anvers, J. P., et al. (2021). SABER: Module-LWR Based Key Exchange. PQCrypto.

[43] Kales, D., et al. (2020). Secure MPC with Post-Quantum Guarantees. IEEE S&P.

[44] Boneh, D., Kim, S. (2019). Quantum Resilient Zero-Knowledge Systems. ePrint Archive.

[45] Naehrig, M., et al. (2011). Can Homomorphic Encryption be Practical? ACM Cloud.

[46] Chen, H., et al. (2019). On Deploying Quantum-Resistant Authentication. IEEE Comm. Mag.

[47] Fluhrer, S. (2017). Quantum-safe key encapsulation in TLS. Internet-Draft.

[48] Lindner, R., Peikert, C. (2011). Better key sizes for LWE-based encryption. CT-RSA.

[49] Lepoint, T., Naehrig, M. (2014). A Comparison of Homomorphic Encryption Schemes. EUROCRYPT.

[50] IETF Crypto Forum Research Group. (2023). Quantum-Ready Internet Protocols. Draft.

Keywords :

Case Studies, Commercial Enclaves, Energy Efficiency And Sustainability Cryptographic Security Key Exchange Digital Signatures Lattice-Based Cryptography Quantum Computing Post-Quantum Cryptography Cryptographic Algorithms.