Decomposition of symmetric matrix–vector product over GF(2m). Issue 24 (1st November 2017)

• Record Type: Journal Article
• Authors: Pan, Jeng‐Shyang; Yang, Chun‐Sheng; Lee, Chiou‐Yng
• Is Part Of: Electronics letters. Volume 53:Issue 24(2017)
• Page Start: 1568
• Page End: 1570
• Publication Date: 2017-11-01
• Subjects: vectors -- Hankel matrices -- Toeplitz matrices -- recursive estimation -- Gaussian processes; symmetric matrix‐vector product -- Toeplitz matrix‐vector product decomposition -- subquadratic multiplier -- SMVP -- Hankel matrix -- n‐way splitting methods -- 3‐way splitting methods -- 2‐way splitting methods -- recursive formula -- TMVP block recombination -- even‐type Gaussian normal basis multiplication; Electronics -- Periodicals; 621.381
• DOI: 10.1049/el.2017.1719
• Languages: English
• ISSNs: 0013-5194

Abstract

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 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.