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Journal Article Efficient Bit-Parallel Multiplier for All Trinomials Based on n-Term Karatsuba Algorithm
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Authors
Sun-Mi Park, Ku-Young Chang, Dowon Hong, Changho Seo
Issue Date
2020-09
Citation
IEEE Access, v.8, pp.173491-173507
ISSN
2169-3536
Publisher
IEEE
Language
English
Type
Journal Article
DOI
https://dx.doi.org/10.1109/ACCESS.2020.3023804
Abstract
Recently, hybrid multiplication schemes over the binary extension field GF(2m) based on nterm Karatsuba algorithm (KA) have been proposed for irreducible trinomials. Their complexities depend on a decomposition of m and the choice of a generation polynomial. However, these multipliers have some limitations on a decomposition of m or generation polynomial xm + xk + 1 such that m ?돟 2k. In this paper, we loosen such limited conditions. We present a new hybrid bit-parallel multiplier based on n-term KA for any irreducible trinomial xm + xk + 1 (0 < k < m), where m is decomposed as m = nm0 + r with 0 < r < m0 and 1 < n. (Here, various values for n, m0 and r may be chosen.) To this end, we generalize the previously proposed multiplication scheme for xnm0+1 +xk +1 into xnm0+r +xk +1. We evaluate the explicit complexity of the proposed multiplier. Specific comparisons show that the proposed multiplier achieves the lowest space complexity with the same or lower time complexity among hybrid multipliers. Compared to the fastest multipliers, the time complexity of the proposed multiplier costs only TX higher while its space complexity is much lower (it has roughly 40% reduced space complexity), where TX is the delay of one 2-input XOR gate.
KSP Keywords
Bit-parallel multiplier, Extension field, Karatsuba algorithm, Space Complexity, Time Complexity, XOR gate
This work is distributed under the term of Creative Commons License (CCL)
(CC BY)
CC BY