상세정보
학술지
Efficient Bit-Parallel Multiplier for All Trinomials Based on n-Term Karatsuba Algorithm
- 저자
- 박선미, 장구영, 홍도원, 서창호
- 발행일
- 202009
- 출처
- IEEE Access, v.8, pp.173491-173507
- ISSN
- 2169-3536
- 출판사
- IEEE
- 협약과제
- 20ZR1300, 지능형 사이버 보안 및 신뢰 인프라 기술 연구, 김익균
- 초록
- 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 제안 키워드
- Bit-parallel multiplier, Extension field, Karatsuba algorithm, Space Complexity, Time Complexity, XOR gate