1. Subquadratic Space Complexity Multiplier Using Even Type GNB Based on Efficient Toeplitz Matrix-Vector Product
- Author
-
Dowon Hong, Sun-Mi Park, Changho Seo, and Ku-Young Chang
- Subjects
020206 networking & telecommunications ,Field (mathematics) ,02 engineering and technology ,Toeplitz matrix ,020202 computer hardware & architecture ,Theoretical Computer Science ,Matrix decomposition ,symbols.namesake ,Matrix (mathematics) ,Computational Theory and Mathematics ,Hardware and Architecture ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Symmetric matrix ,Multiplier (economics) ,Multiplication ,Arithmetic ,Gaussian process ,Software ,Mathematics - Abstract
Multiplication schemes based on Toeplitz matrix-vector product (TMVP) have been proposed by many researchers. TMVP can be computed using the recursive two-way and three-way split methods, which are composed of four blocks. Among them, we improve the space complexity of the component matrix formation (CMF) block. This result derives the improvements of multiplication schemes based on TMVP. Also, we present a subquadratic space complexity $GF(2^m)$ multiplier with even type Gaussian normal basis (GNB). In order to design the multiplier, we formulate field multiplication as a sum of two TMVPs and efficiently compute the sum. As a result, for type 2 and 4 GNBs, the proposed multipliers outperform other similar schemes. The proposed type 6 GNB is the first subquadrtic space complexity multiplier with its explicit complexity formula.
- Published
- 2018