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A Non-redundant and Efficient Architecture for Karatsuba-Ofman Algorithm

  • Nam Su Chang
  • Chang Han Kim
  • Young-Ho Park
  • Jongin Lim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3650)

Abstract

The divide-and-conquer method is efficiently used in parallel multiplier over finite field GF(2 n ). Leone proposed optimal stop condition for iteration of Karatsuba-Ofman algorithm (KOA). Multi-segment Karatsuba method (MSK) is proposed by Ernst et al. In this paper, we propose a Non-Redundant Karatsuba-Ofman algorithm (NRKOA) with removing redundancy operations, and design a parallel hardware architecture based on the proposed algorithm. Comparing with existing related Karatsuba architectures with the same time complexity, the proposed architecture reduces the area complexity. The proposed NRKOA multiplier has more efficient the space complexity than the previous KOA multipliers, where n is a prime. Furthermore, the space complexity of the proposed multiplier is reduced by 43% in the best case.

Keywords

Polynomial Multiplication Karatsuba-Ofman Algorithm Non-Redundant Karatsuba-Ofman Algorithm Hardware Architecture 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Nam Su Chang
    • 1
  • Chang Han Kim
    • 2
  • Young-Ho Park
    • 3
  • Jongin Lim
    • 1
  1. 1.Center for Information and Security Technologies(CIST)Korea UniversitySeoulKorea
  2. 2.Dept. of Information and SecuritySemyung UniversityJecheonKorea
  3. 3.Dept. of Information SecuritySejong Cyber UnivSeoulKorea

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