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

Kundu, Rohon LU ; De Piccoli, Alessandro and Visconti, Andrea (2022) 8th International Conference on Information Systems Security and Privacy, ICISSP 2022 p.145-153
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Post-Quantum Cryptography, Lattice-based Cryptography, Ring-learning with Errors Problem, NTRU Algorithm, Number Theoretic Transformation, Hybridized NTT-Karatsuba Algorithm, Key Size
host publication
Proceedings of the 8th International Conference on Information Systems Security and Privacy
pages
9 pages
publisher
SciTePress
conference name
8th International Conference on Information Systems Security and Privacy, ICISSP 2022
conference location
Online Streaming
conference dates
2022-02-09 - 2022-02-11
external identifiers
  • scopus:85176356214
ISBN
978-989-758-553-1
DOI
10.5220/0010881300003120
project
Säkra mjukvaruuppdateringar för den smarta staden
language
English
LU publication?
yes
id
8750f1d8-8a92-414f-88c9-6eac430dc730
date added to LUP
2022-01-11 17:49:57
date last changed
2024-05-10 07:45:41
@inproceedings{8750f1d8-8a92-414f-88c9-6eac430dc730,
  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.}},
  author       = {{Kundu, Rohon and De Piccoli, Alessandro and Visconti, Andrea}},
  booktitle    = {{Proceedings of the 8th International Conference on Information Systems Security and Privacy}},
  isbn         = {{978-989-758-553-1}},
  keywords     = {{Post-Quantum Cryptography, Lattice-based Cryptography, Ring-learning with Errors Problem, NTRU Algorithm, Number Theoretic Transformation, Hybridized NTT-Karatsuba Algorithm, Key Size}},
  language     = {{eng}},
  pages        = {{145--153}},
  publisher    = {{SciTePress}},
  title        = {{Public Key Compression and Fast Polynomial Multiplication for NTRU using the Corrected Hybridized NTT-Karatsuba Method}},
  url          = {{http://dx.doi.org/10.5220/0010881300003120}},
  doi          = {{10.5220/0010881300003120}},
  year         = {{2022}},
}