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Fast Bit-Parallel Polynomial Basis Multiplier for GF(2m) Defined by Pentanomials Using Weakly Dual Basis
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- Authors
- Sun-Mi PARK, Ku-Young CHANG, Dowon HONG, Changho SEO
- Issue Date
- 2013-01
- Citation
- IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, v.E96.A, no.1, pp.322-331
- ISSN
- 1745-1337
- Publisher
- 일본, 전자정보통신학회 (IEICE)
- Language
- English
- Type
- Journal Article
- Abstract
- In this paper, we derive a fast polynomial basis multiplier for GF(2m) defined by pentanomials xm+xk3+xk2+xk1+1 with 1 ≤ k1 < k2 < k3 ≤ m/2 using the presented method by Park and Chang. The proposed multiplier has the time delay TA+(2+⌈log2(m-1)⌉)TX or TA+(3+⌈log2(m-1)⌉)TX which is the lowest one compared with known multipliers for pentanomials except for special types, where TA and TX denote the delays of one AND gate and one XOR gate, respectively. On the other hand, its space complexity is very slightly greater than the best known results.
- KSP Keywords
- AND gate, Polynomial basis, Space Complexity, Time Delay, Weakly dual basis, XOR gate, bit-parallel