Name
Title | ||
|---|---|---|
Novel bit-parallel multiplier for GF(2m) defined by all-one polynomial using generalized Karatsuba algorithm |
Abstract | ||
|---|---|---|
In this paper, a novel bit-parallel multiplier for finite field GF(2^m) defined by irreducible all-one polynomial (AOP) is proposed. We utilize a generalized Karatsuba algorithm (KA) to reduce the number of coefficient multiplications and the redundant representation to simplify polynomial modular reduction. Explicit formulae with respect to the space and time complexity of the proposed multiplier are given. By evaluating the asymptotic lower bound of the complexity, the selection of the generalized KA and decomposition of m are investigated to obtain the optimal result. Consequently, theoretical complexity analysis proved that our architecture requires even fewer logic gates than previous proposals, while it still maintains relatively low time delay. For a special class of GF(2^m) generated with AOPs, it even matches the best known multipliers found in the literatures. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.ipl.2013.10.009 | Inf. Process. Lett. |
Keywords | Field | DocType |
proposed multiplier,novel bit-parallel multiplier,known multiplier,irreducible all-one polynomial,theoretical complexity analysis,generalized ka,low time delay,generalized karatsuba algorithm,polynomial modular reduction,time complexity,cryptography | Discrete mathematics,Explicit formulae,Finite field,Primitive polynomial,Polynomial,Upper and lower bounds,Arithmetic,Multiplier (economics),All one polynomial,Mathematics,Karatsuba algorithm | Journal |
Volume | Issue | ISSN |
114 | 3 | 0020-0190 |
Citations | PageRank | References |
2 | 0.37 | 19 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiao-Ning Xie | 1 | 2 | 0.71 |
| Gong-Liang Chen | 2 | 160 | 13.54 |
| Yin Li | 3 | 11 | 2.95 |