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NTRU is a lattice-based public-key cryptosystem that has been selected as one of the Round III finalists at the NIST Post-Quantum Cryptography Standardization. Compressing the key sizes to increase efficiency has been a long-standing open question for lattice-based 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 NTRU-NTT. To perform polynomial optimization, we make use of the Number-Theoretic Transformation (NTT) and hybridize it with the Karatsuba Algorithm. Previous work done in providing 2-part Hybridized NTT-Karatsuba 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 NTRU-NTT using the corrected Hybridized NTT-Karatsuba Algorithm. The significance of compressing the value of the prime modulus q lies with decreasing the key sizes. We achieve a 128-bit post-quantum 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.
|Title of host publication
|Proceedings of the 8th International Conference on Information Systems Security and Privacy
|Number of pages
|Published - 2022
|8th International Conference on Information Systems Security and Privacy, ICISSP 2022 - Online Streaming
Duration: 2022 Feb 9 → 2022 Feb 11
|8th International Conference on Information Systems Security and Privacy, ICISSP 2022
|2022/02/09 → 2022/02/11
Subject classification (UKÄ)
- Computer Science
- Post-Quantum Cryptography, Lattice-based Cryptography, Ring-learning with Errors Problem, NTRU Algorithm, Number Theoretic Transformation, Hybridized NTT-Karatsuba Algorithm, Key Size
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- 1 Active
2018/03/01 → 2024/12/31