Proposed Development of NTRU Public Key Encryption


  • Marwah Aearaby Sayyid Directorate of Education in Wasit



The 1996 proposal by Hoffstein, Pfeiffer, and Silverman for the NTRU public key encryption system provides a quick and useful substitute for factorization- or discrete logarithm-based classical programs. It rovides approximate security against quantum computing assaults and earoptimal asymptotic efficiency, in contrast to these latter approaches. The security analysis of the system involves examining naturally occurring computational and statistical challenges that are defined on finite polynomial rings. Current advancements in the broader field of latticebased cryptography, include security studies and applications of NTRU and its variations. These advancements include the creation of multilinear.


Download data is not yet available.


"~rste NTRU survey.pdf". May 2014. [Online]. Available:

R. Steinfeld. "NTRU cryptosystem: Recent developments and emerging mathematical problems in finite polynomial rings". Aug 2014. [Online]. Available:

A. P. Premnath. "Application of NTRU Cryptographic Algorithm for securing SCADA communication". Mar 2023. [Online]. Available:

S. Singh and S. Padhye. "Generalisations of NTRU cryptosystem". Nov 2016. [Online]. Available:

L. Miao, X. Zhou, H. Xu and L. Shuai. "A Group-based NTRU-like Public-key Cryptosystem for IoT". Jun 2019. [Online]. Available:

A. Nitaj. "The Mathematics of the NTRU Public Key Cryptosystem". Jul 2016. [Online]. Available:

Savvas, Ilias K., D. Poulakis, Makris, Georgios C., Sabani, Maria E. and G. Garani. "Evaluation and Comparison of Lattice-Based Cryptosystems for a Secure Quantum Computing Era". Jan 2023. [Online]. Available:

"The Mathematics of the NTRU Public Key Cryptosystem". Jul 2016. [Online]. Available:

"Success_Jimoh_Internship_Report". Dec 2021. [Online]. Available:

A. Al-Khasawneh, A. Chefranov, Joel J. P. C. Rodrigues, Y. Daraghmi, N. Hamad and A. Ibrahim. "NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks". Aug 2020. [Online]. Available:

D. Nunez, J. Lopez and I. Agudo. "NTRUReEncrypt: An efficient proxy re-encryption scheme based on NTRU". Apr 2015. [Online]. Available:

"1". May 2020. [Online]. Available:

Maria E. Sabani, Ilias K. Savvas, Dimitrios Poulakis, Georgia Garani and Georgios C. Makris. "Evaluation and Comparison of Lattice-Based Cryptosystems for a Secure Quantum Computing Era". Jun 2023. [Online]. Available:

"NTRU: A ring-based public key cryptosystem". Jul 2006. [Online]. Available:

"Towards Secure Classical-Quantum Systems". Apr 2023. [Online]. Available:

"High-speed key encapsulation from NTRU". Aug 2017. [Online]. Available:

G. Garani, Ilias K. Savvas, D. Poulakis, Maria E. Sabani and Georgios C. Makris. "Evaluation and Comparison of Lattice-Based Cryptosystems for a Secure Quantum Computing Era". Jun 2023. [Online]. Available:

"Post-quantum cryptography - Wikipedia". Jan 2024. [Online]. Available:

Santiago Sanchez-Solano, Eros Camacho-Ruiz, Macarena C. Martinez-Rodriguez and Piedad Brox. "Multi-Unit Serial Polynomial Multiplier to Accelerate NTRU-Based Cryptographic Schemes in IoT Embedded Systems". Mar 2022. [Online]. Available:

R. Bhatia and K. Munjal. "A systematic review of homomorphic encryption and its contributions in healthcare industry". Aug 2023. [Online]. Available:

"i". Nov 2022. [Online]. Available:

Ahmed, Hassan I. Sayed, Abdallah, Mohamed S., Aslan, Heba K., G. Elkabbany and Y. Cho. "Lightweight Computational Complexity Stepping Up the NTRU Post-Quantum Algorithm Using Parallel Computing". (accessed Jan 23, 2024). [Online]. Available:


"Compact and efficient KEMs over NTRU lattices". Apr 2024. [Online]. Available:

"NTRU Prime: reducing attack surface at low cost". Aug 2017. [Online]. Available:

A. Karbasi. "ILTRU: An NTRU-Like Public Key Cryptosystem Over Ideal Lattices". Jan 2015. [Online]. Available:

C. Lee, J. H. Cheon and J. Jeong. "An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low-level encoding of zero". Aug 2016. [Online]. Available:

P. Brox, S. Sanchez-Solano, Martinez-Rodriguez, Macarena C. and E. Camacho-Ruiz. "Timing-Attack-Resistant Acceleration of NTRU Round 3 Encryption on Resource-Constrained Embedded Systems". Jun 2023. [Online]. Available:

Juliet N. Gaithuru and M. Bakhtiari. "Insight into the operation of NTRU and a comparative study of NTRU, RSA and ECC public key cryptosystems". Dec 2014. [Online]. Available:

"NTRU - Wikipedia". Sep 2023. [Online]. Available:

A. Thompson, G. Arome, B. K. Alese and H. C. Ukwuoma. "Post-quantum cryptography-driven security framework for cloud computing". Jan 2022. [Online]. Available:

C. Gentry and M. Szydlo. "Cryptanalysis of the Revised NTRU Signature Scheme". Apr 2002. [Online]. Available:

"Post-quantum cryptography Algorithm's standardization and performance analysis". Sep 2022. [Online]. Available:

M. Perepechaenko and R. Kuang. "A novel homomorphic polynomial public key encapsulation algorithm". Oct 2023. [Online]. Available:

"hubfs files ntru-orig.pdf". Jun 2005. [Online]. Available:

J. Liao, C. Kuang, W. Liang, N. Xiong, L. Chen, K. Li, S. Li and Y. Chen. "Post-Quantum Security: Opportunities and Challenges". Nov 2023. [Online]. Available:

"Computational Cryptography: Algorithmic Aspects of Cryptology [1 ed.] 1108795935, 9781108795937 - EBIN.PUB". (accessed Jan 23, 2024). [Online]. Available:

"CRYPTOGRAPHY". May 2021. [Online]. Available:

J. Hermans, B. Preneel and F. Vercauteren. "Speed records for NTRU". Dec 2010. [Online]. Available:

D. Xiao, A. Wang and Y. Yu. "Lattice-based cryptosystems in standardisation processes: A survey". Mar 2023. [Online]. Available:




How to Cite

Sayyid, M. A. (2024). Proposed Development of NTRU Public Key Encryption . JOURNAL OF ADVANCES IN MATHEMATICS, 23, 49–60.