Public Key Compression and Fast Polynomial Multiplication for NTRU using the Corrected Hybridized NTT-Karatsuba Method

Rohon Kundu, Alessandro de Piccoli, Andrea Visconti

2022

Abstract

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.

Paper Citation

in Harvard Style

Kundu R., de Piccoli A. and Visconti A. (2022). Public Key Compression and Fast Polynomial Multiplication for NTRU using the Corrected Hybridized NTT-Karatsuba Method. In Proceedings of the 8th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP, ISBN 978-989-758-553-1, pages 145-153. DOI: 10.5220/0010881300003120

in Bibtex Style

@conference{icissp22,
author={Rohon Kundu and Alessandro de Piccoli and Andrea Visconti},
title={Public Key Compression and Fast Polynomial Multiplication for NTRU using the Corrected Hybridized NTT-Karatsuba Method},
booktitle={Proceedings of the 8th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP,},
year={2022},
pages={145-153},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010881300003120},
isbn={978-989-758-553-1},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 8th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP,
TI - Public Key Compression and Fast Polynomial Multiplication for NTRU using the Corrected Hybridized NTT-Karatsuba Method
SN - 978-989-758-553-1
AU - Kundu R.
AU - de Piccoli A.
AU - Visconti A.
PY - 2022
SP - 145
EP - 153
DO - 10.5220/0010881300003120