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)


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.


Shifted polynomial basis multiplication binary extension fields digit-serial 


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© 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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