Name
Title | ||
|---|---|---|
Finding a Basis Conversion Matrix Using a Polynomial Basis Derived by a Small Multiplicative Cyclic Group |
Abstract | ||
|---|---|---|
Several methods for finding a basis conversion matrix between two different bases in an extension field ${\\BBF _{p^{m}}}$ have been proposed. Among them, the one based on Gauss period normal basis (GNB) is on average the most efficient. However, since it needs to construct a certain tower field ${\\BBF _{(p^{m})^{n}}}$, some inefficient cases in which the towering degree $n$ becomes large have been reported. This paper first determines that such inefficient cases are caused by the GNB condition. In order to overcome this inefficiency, we propose a method that does not use any GNB in the target extension field ${\\BBF _{p^{m}}}$, but instead uses a certain polynomial basis in ${\\BBF _{p^{m}}}$ derived by a certain small cyclic group in ${\\BBF _{(p^{m})^{n}}}$. This causes relaxation of the condition for the towering degree $n$. In addition, our experimental results show that the proposed method substantially accelerates the computation time for finding a basis conversion matrix. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/TIT.2012.2191477 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
gaussian process,public key cryptography,polynomials,matrix multiplication,generators,normal basis,cyclic group,vectors,manganese,extension field,cryptography,gaussian processes | Polynomial basis,Discrete mathematics,Cyclic group,Multiplicative function,Polynomial,Matrix (mathematics),Normal basis,Gaussian process,Matrix multiplication,Mathematics | Journal |
Volume | Issue | ISSN |
58 | 7 | 0018-9448 |
Citations | PageRank | References |
1 | 0.34 | 12 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yasuyuki Nogami | 1 | 146 | 52.44 |
| Hidehiro Kato | 2 | 20 | 3.30 |
| Kenta Nekado | 3 | 44 | 4.07 |
| Satoshi Uehara | 4 | 9 | 1.47 |
| Yoshitaka Morikawa | 5 | 100 | 14.92 |