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Digit-Serial Structures for the Shifted Polynomial Basis Multiplication over Binary Extension Fields

  • Arash Hariri
  • Arash Reyhani-Masoleh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5130)

Abstract

Finite field multiplication is one of the most important operations in the finite field arithmetic. Recently, a variation of the polynomial basis, which is known as the shifted polynomial basis, has been introduced. Current research shows that this new basis provides better performance in designing bit-parallel and subquadratic space complexity multipliers over binary extension fields. In this paper, we study digit-serial multiplication algorithms using the shifted polynomial basis. They include a Most Significant Digit (MSD)-first digit-serial multiplication algorithm and a hybrid digit-serial multiplication algorithm, which includes parallel computations. Then, we explain the hardware architectures of the proposed algorithms and compare them to their existing counterparts. We show that our MSD-first digit-serial shifted polynomial basis multiplier has the same complexity of the Least Significant Digit (LSD)-first polynomial basis multiplier. Also, we present the results for the hybrid digit-serial multiplier which offers almost the half of the latency of the best known digit-serial polynomial basis multipliers.

Keywords

Shifted polynomial basis multiplication binary extension fields digit-serial 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Arash Hariri
    • 1
  • Arash Reyhani-Masoleh
    • 1
  1. 1.Department of Electrical and Computer EngineeringThe University of Western OntarioLondonCanada

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