New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2n)

Authors:
Young In Cho;Nam Su Chang;Chang Han Kim;Young-Ho Park;Seokhie Hong
Affiliations:
Graduate School of Information Management and Security, Korea University, Seoul, Korea;Department of Information Security Systems, Sejong Cyber University, Seoul, Korea;Department of Information and Security, Semyung University, Jecheon, Korea;Department of Information Security Systems, Sejong Cyber University, Seoul, Korea;Graduate School of Information Management and Security, Korea University, Seoul, Korea
Venue:
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Year:
2012

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Abstract

Koç and Sunar proposed an architecture of the Mastrovito multiplier for the irreducible trinomial f(x) = xn + xk + 1, where k ≠ n/2 to reduce the time complexity. Also, many multipliers based on the Karatsuba-Ofman algorithm (KOA) was proposed that sacrificed time efficiency for lowspace complexity. In this paper, a new multiplication formula which is a variant of KOA presented. We also provide a straight forward architecture of a non-pipelined bit-parallel multiplier using the new formula. The proposed multiplier has lower space complexity than and comparable time complexity to previous Mastrovito multipliers' for all irreducible trinomials.