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

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.

Inspec keywords: recursive estimation; Gaussian processes; vectors; Toeplitz matrices; Hankel matrices

Other keywords: SMVP; subquadratic multiplier; Toeplitz matrix-vector product decomposition; n-way splitting methods; 2-way splitting methods; recursive formula; Hankel matrix; 3-way splitting methods; even-type Gaussian normal basis multiplication; symmetric matrix-vector product; TMVP block recombination

Subjects: Other topics in statistics; Statistics; Algebra, set theory, and graph theory; Probability theory, stochastic processes, and statistics; Algebra; Other topics in statistics; Algebra; Algebra

References

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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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http://iet.metastore.ingenta.com/content/journals/10.1049/el.2017.1719
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