Decomposition of symmetric matrix–vector product over GF(2 m )

Decomposition of symmetric matrix–vector product over GF(2 m )

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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 n-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 n = 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.


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      • 4. Pan, J.S., Meher, P.K., Lee, C.Y., et al: ‘Efficient subquadratic parallel multiplier based on modified SPB of GF(2m)’. IEEE Int. Symp. Circuits and Systems (ISCAS), Lisbon, Portugal, May 2015, pp. 14301433.
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