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Faster characteristic three polynomial multiplication and its application to NTRU Prime decapsulation
Date
2022-01-01
Author
Yeniaras, Esra
Cenk, Murat
Metadata
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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Efficient computation of polynomial multiplication over characteristic three fields is required for post-quantum cryptographic applications which gain importance upon the recent advances in quantum computers. In this paper, we propose three new polynomial multiplication algorithms over F-3 and show that they are more efficient than the current state-of-the-art algorithms. We first examine through the well-known multiplication algorithms in F-3[x] including the Karatsuba 2-way and 3-way split formulas along with the latest enhancements. Then, we propose a new 4-way split polynomial multiplication algorithm and an improved version of it which are both derived by using interpolation in F-9, the finite field with nine elements. Moreover, we propose a 5-way split multiplication algorithm and then compare the efficiencies of these algorithms altogether. Even though there exist 4-way or 5-way split multiplication algorithms in characteristic two (binary) fields, there has not been any such algorithms developed for characteristic three fields before this paper. We apply the proposed algorithms to the NTRU Prime protocol, a post-quantum key encapsulation mechanism, submitted to the MST PQC Competition by Bernstein et al., performing polynomial multiplication over characteristic three fields in its decapsulation phase. We observe that the new hybrid algorithms provide a 12.9% reduction in the arithmetic complexity. Furthermore, we implement these new hybrid methods on Intel (R) Core (TM) i7-9750H architecture using C and obtain a 37.3% reduction in the implementation cycle count.
Subject Keywords
Characteristic three fields
,
Karatsuba
,
Key encapsulation
,
Lattice-based cryptography
,
NTRU Prime
,
Polynomial multiplication
,
Post-quantum cryptography
,
DISCRETE LOGARITHMS
,
ALGORITHMS
,
FORMULAS
,
FIELDS
URI
https://hdl.handle.net/11511/95275
Journal
JOURNAL OF CRYPTOGRAPHIC ENGINEERING
DOI
https://doi.org/10.1007/s13389-021-00282-7
Collections
Graduate School of Applied Mathematics, Article
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NEW EFFICIENT CHARACTERISTIC THREE POLYNOMIAL MULTIPLICATION ALGORITHMS AND THEIR APPLICATIONS TO NTRU PRIME
Yeniaras, Esra; Cenk, Murat; Department of Cryptography (2022-1-21)
Some of the post-quantum cryptographic protocols require polynomial multiplication in characteristic three fields, thus the efficiency of such multiplication algorithms gain more importance recently. In this thesis, we propose four new polynomial multiplication algorithms in characteristic three fields and we show that they are more efficient than the current state-of-the-art methods. We first analyze the well-known algorithms such as the schoolbook method, Karatsuba 2-way and 3-way split methods, Bernstein...
Improved Polynomial Multiplication Algorithms over Characteristic Three Fields and Applications to NTRU Prime
Yeniaras, Esra; Cenk, Murat (2022-01-01)
© 2022, Springer Nature Switzerland AG.This paper introduces a new polynomial multiplication algorithm which decreases the arithmetic complexity and another modified algorithm that speeds up the implementation run-time over the characteristic three fields. We first introduce a new polynomial multiplication algorithm using a 4-way split approach and observe that its asymptotic arithmetic complexity is better than Bernstein’s 3-way method for characteristic three fields. We then define an unbalanced split ver...
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E. Yeniaras and M. Cenk, “Faster characteristic three polynomial multiplication and its application to NTRU Prime decapsulation,”
JOURNAL OF CRYPTOGRAPHIC ENGINEERING
, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/95275.