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Subquadratic Space Complexity Multiplier Using Even Type GNB Based on Efficient Toeplitz Matrix-Vector Product
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- Authors
- Sun-Mi Park, Ku-Young Chang, Dowon Hong, Changho Seo
- Issue Date
- 2018-12
- Citation
- IEEE Transactions on Computers, v.67, no.12, pp.1794-1805
- ISSN
- 0018-9340
- Publisher
- IEEE
- Language
- English
- Type
- Journal Article
- 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(2m) 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.
- KSP Keywords
- Field multiplication, Gaussian normal basis, Space Complexity, Three-way, Toeplitz matrix-vector product, Type 2, matrix formation, two-way