Decomposition of symmetric matrix–vector product over <italic>GF</italic>(2^{<italic>m</italic>})

Abstract

Toeplitz matrix-vector product (TMVP) decomposition is an important approach for designing and implementing subquadratic multiplier. In this Letter, a symmetric matrix (SM), which is the sum of a symmetric TM and Hankel matrix, is proposed. Applying the symmetry property, 2-way, 3-way and <i>n</i>-way splitting methods of SMVP is presented. On the basis of 2-way splitting method, the recursive formula of SMVP is presented. Using the two cases <i>n</i> = 4 and 8, the SMVP decomposition approach has less space complexity than 2-way TMVP, TMVP block recombination and symmetric TMVP for even-type Gaussian normal basis multiplication.