A non-redundant and efficient architecture for karatsuba-ofman algorithm

Authors:
Nam Su Chang;Chang Han Kim;Young-Ho Park;Jongin Lim
Affiliations:
Center for Information and Security Technologies(CIST), Korea University, Seoul, Korea;Dept. of Information and Security, Semyung University, Jecheon, Korea;Dept. of Information Security, Sejong Cyber Univ, Seoul, Korea;Center for Information and Security Technologies(CIST), Korea University, Seoul, Korea
Venue:
ISC'05 Proceedings of the 8th international conference on Information Security
Year:
2005

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Abstract

The divide-and-conquer method is efficiently used in parallel multiplier over finite field GF(2n). 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.