Date of Award


Publication Type

Master Thesis

Degree Name



Electrical and Computer Engineering

First Advisor

Huapeng Wu



Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.


In the next 10 to 50 years, the quantum computer is expected to be available and quantum computing has the potential to defeat RSA (Rivest-Shamir-Adleman Cryptosystem) and ECC (Elliptic Curve Cryptosystem). Therefore there is an urgentneed to do research on post-quantum cryptography and its implementation. In this thesis, four new Truncated Polynomial Multipliers (TPM), namely, TPM-I, TPM-II, TPM-III, and TPM-IV for NTRU Prime system are proposed. To the best of our knowledge, this is the first time to focus on time-efficient hardware architectures and implementation of NTRU Prime with FPGA. TPM-I uses a modified linear feedback shift register (LFSR) based architecture for NTRU prime system. TPM-II makes use of x^2-net structure for NTRU Prime system, which scans two consecutive coefficients in the control input polynomial r(x) in one clock cycle. In TPM-III and TPM-IV, three consecutive zeros and consecutive zeros in the control input polynomial r(x) are scanned during one clock cycle, respectively. FPGA implementation results are obtained for the four proposed polynomial multiplication architectures and a comparison between the proposed multiplier FPGA results for NTRU Prime system and the existing work on NTRUEncrypt is shown. Regarding space complexity, TPM-I can reduce the area consumption with the least logical elements, although it takes more latency time among the four proposed multipliers and NTRUEncrypt work [12]. TPM-II has the best performance of latency with parameter sets ees401ep1, ees449ep1, ees677ep1 in security levels: 112-bit, 128-bit, and 192-bit, respectively. TPM-IV uses the smallest latency time with the parameter set ees1087ep2 in security level 256, compared to the other three latency time of proposed multipliers. Both TPM-II and TPM-IV have a lower latency time compared to NTRUEncrypt work [12] in different security levels. Note that NTRU Prime has enhanced security in comparison with NTRUEncrypt due to the fact, the former uses a new truncated polynomial ring, which has a more secure structure.