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Abstract
NTRU is a latticebased publickey cryptosystem that has been selected as one of the Round III finalists at the NIST PostQuantum Cryptography Standardization. Compressing the key sizes to increase efficiency has been a longstanding open question for latticebased cryptosystems. In this paper we provide a solution to three seemingly opposite demands for NTRU cryptosystem: compress the key size, increase the security level, optimize performance by implementing fast polynomial multiplications. We consider a specific variant of NTRU known as NTRUNTT. To perform polynomial optimization, we make use of the NumberTheoretic Transformation (NTT) and hybridize it with the Karatsuba Algorithm. Previous work done in providing 2part Hybridized NTTKaratsuba Algorithm contained some operational errors in the product expression, which have been detected in this paper. Further, we conjectured the corrected expression and gave a detailed mathematical proof of correctness. In this paper, for the first time, we optimize NTRUNTT using the corrected Hybridized NTTKaratsuba Algorithm. The significance of compressing the value of the prime modulus q lies with decreasing the key sizes. We achieve a 128bit postquantum security level for a modulus value of 83,969 which is smaller than the previously known modulus value of 1,061,093,377, while keeping n constant at 2048.
Original language  English 

Title of host publication  Proceedings of the 8th International Conference on Information Systems Security and Privacy 
Publisher  SciTePress 
Pages  143151 
Number of pages  9 
ISBN (Print)  9789897585531 
Publication status  Accepted/In press  2021 Dec 9 
Event  8th International Conference on Information Systems Security and Privacy, ICISSP 2022  Online Streaming Duration: 2022 Feb 9 → 2022 Feb 11 
Conference
Conference  8th International Conference on Information Systems Security and Privacy, ICISSP 2022 

City  Online Streaming 
Period  2022/02/09 → 2022/02/11 
Subject classification (UKÄ)
 Computer Science
Keywords
 PostQuantum Cryptography, Latticebased Cryptography, Ringlearning with Errors Problem, NTRU Algorithm, Number Theoretic Transformation, Hybridized NTTKaratsuba Algorithm, Key Size
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SMARTY: Säkra mjukvaruuppdateringar för den smarta staden
Hell, M., Magnusson, B., Gehrmann, C., Paladi, N., Karlsson, L., Sönnerup, J., Johnsson, B. A., Hedin, G., Nordahl, M., Pagnin, E., Kundu, R. & Åkesson, A.
Swedish Foundation for Strategic Research, SSF
2018/03/01 → 2023/02/28
Project: Research