# 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.

Download#### 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