# New Efficient Algorithms for Multiplication Over Fields of Characteristic Three

2018-03-01
Cenk, Murat
Hasan, M. Anwar
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.
JOURNAL OF SIGNAL PROCESSING SYSTEMS FOR SIGNAL IMAGE AND VIDEO TECHNOLOGY

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Citation Formats
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.