In this paper, a generalized Montgomery multiplication algorithm in GF(2m) using the Toeplitz matrix-vector representation is presented. The hardware architectures derived from this algorithm provide low-complexity bit-parallel systolic multipliers with trinomials and pentanomials. The results reveal that our proposed multipliers reduce the space complexity of approximately 15% compared with an...

This work presents novel multipliers for Montgomery multiplication defined on binary fields GF(2). Different to state of the art Montgomery multipliers, this work uses a Linear Feedback Shift Register (LFSR) as the main building block. We studied different architectures for bit-serial and digit-serial Montgomery multipliers using the LFSR and the Montgomery factors x and x. The proposed multipl...

This work presents novel multipliers for Montgomery multiplication defined on binary fields GF(2). Different to state of the art Montgomery multipliers, this work uses a Linear Feedback Shift Register (LFSR) as the main building block. We studied different architectures for bit-serial and digit-serial Montgomery multipliers using the LFSR and the Montgomery factors x and xm−1. The proposed mult...

This paper proposes a DNA sticker algorithm for parallel reduction over finite field GF(2 n ). This algorithm is suitable for some specific finite fields defined with trinomials or pentanomials. We use one binary finite field GF(2 163 ) which is recommended by National Institute of Standards and Technology (NIST) to describe the details about our algorithm. The solution space of 2 325 cases cou...