Based on Toeplitz matrix-vector products and coordinate transformation techniques, we present a new scheme for subquadratic space complexity parallel multiplication in GF(2n) using the shifted… (More)

A new nonpipelined bit-parallel-shifted polynomial basis multiplier for GF(2<sup>n</sup>) is presented. For some irreducible trinomials, the space complexity of the multiplier matches the best… (More)

Based on a recently proposed Toeplitz matrix-vector product approach, a subquadratic computational complexity scheme is presented for multiplications in binary extended finite fields using type I and… (More)

We describe how a simple way to split input operands allows fo r fast VLSI implementations of subquadraticGF (2)[x] Karatsuba-Ofman multipliers. The theoretical XOR gate del ay of the resulting… (More)

We show that multiplication complexities of n-term Karatsuba-Like formulae of GF (2)[x] (7 < n < 19) presented in the above paper can be further improved using the Chinese Remainder Theorem and the… (More)

Published in 1962 [1], Karatsuba-Ofman algorithm (KOA) was the first integer multiplication method broke the quadratic complexity barrier in positiona l number systems. Due to its simplicity, its… (More)

In this paper, two different normal basis multiplication algorithms for software implementation are proposed over GF(2). The first algorithm is suitable for high complexity normal bases and the… (More)

We show that the step “modulo the degree-n field generating irreducible polynomial” in the classical definition of the GF (2n) multiplication operation can be avoided. This leads to an alternative… (More)