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New Efficient Algorithms for Multiplication Over Fields of Characteristic Three
Date
2018-03-01
Author
Cenk, Murat
Hasan, M. Anwar
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In this paper, we first present an enhancement of the well-known Karatsuba 2-way and 3-way algorithms for characteristic three fields, denoted by where nae1. We then derive a 3-way polynomial multiplication algorithm with five 1/3 sized multiplications that use interpolation in . Following the computation of the arithmetic and delay complexity of the proposed algorithm, we provide the results of our hardware implementation of polynomial multiplications over and . The final proposal is a new 3-way polynomial multiplication algorithm over that uses three polynomial multiplications of 1/3 of the original size over and one polynomial multiplication of 1/3 of the original size over . We show that this algorithm represents about 15% reduction of the complexity over previous algorithms for the polynomial multiplications whose sizes are of practical interest.
Subject Keywords
Polynomial Multiplication
,
Elliptic curves
,
Characteristic three fields
URI
https://hdl.handle.net/11511/30457
Journal
JOURNAL OF SIGNAL PROCESSING SYSTEMS FOR SIGNAL IMAGE AND VIDEO TECHNOLOGY
DOI
https://doi.org/10.1007/s11265-017-1234-x
Collections
Graduate School of Applied Mathematics, Article
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M. Cenk and M. A. Hasan, “New Efficient Algorithms for Multiplication Over Fields of Characteristic Three,”
JOURNAL OF SIGNAL PROCESSING SYSTEMS FOR SIGNAL IMAGE AND VIDEO TECHNOLOGY
, pp. 285–294, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30457.