| Paper Abstract and Keywords |
| Presentation |
2005-05-18 13:50
XTR over Characteristic 3
Masaaki Shirase, Yasushi Hibino (JAIST) |
| Abstract |
(in Japanese) |
(See Japanese page) |
| (in English) |
XTR represents elements in a cyclic subgroup $\langle h \rangle$ of a multiplicative group of a finite field ${\mathbb F}_{q^6}$ as those in ${\mathbb F}_{q^2}$ using the trace over ${\mathbb F}_{q^2}$, where
$h$ satisfies $h^{q^2-q+1}=1$. If we apply XTR to an ElGamal cryptosystem, then the calculation amount for encryption/decryption are reduced and the size of public key and the message length become a third of them. XTR has both efficiency and compactness. This paper shows that XTR becomes more compact representation when we use fields of characteristic 3. Let $q$ be $3^{2k-1}$, then $\sqrt{3q}$ is an integer and there exists $h \in {\mathbb F}_{q^6}$ such that $h^{q-\sqrt{3q}-1}=1$. Then we can represent elements in $\langle h \rangle$ as those in ${\mathbb F}_q$ using the trace over ${\mathbb F}_q$. Although this method requires only additional 25\% computational effort, it achieves as twice compactness as original XTR. This paper will also discuss that the selection of practical fields of characteristic 3. |
| Keyword |
(in Japanese) |
(See Japanese page) |
| (in English) |
XTR / characteristic 3 / algebraic torus / ElGamal cryptosystem / / / / |
| Reference Info. |
IEICE Tech. Rep., vol. 105, no. 51, ISEC2005-3, pp. 17-24, May 2005. |
| Paper # |
ISEC2005-3 |
| Date of Issue |
2005-05-11 (ISEC) |
| ISSN |
Print edition: ISSN 0913-5685 |
| Download PDF |
|
| Conference Information |
| Committee |
ISEC |
| Conference Date |
2005-05-18 - 2005-05-18 |
| Place (in Japanese) |
(See Japanese page) |
| Place (in English) |
Kikai-Shinko-Kaikan Bldg. |
| Topics (in Japanese) |
(See Japanese page) |
| Topics (in English) |
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| Paper Information |
| Registration To |
ISEC |
| Conference Code |
2005-05-ISEC |
| Language |
Japanese |
| Title (in Japanese) |
(See Japanese page) |
| Sub Title (in Japanese) |
(See Japanese page) |
| Title (in English) |
XTR over Characteristic 3 |
| Sub Title (in English) |
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| Keyword(1) |
XTR |
| Keyword(2) |
characteristic 3 |
| Keyword(3) |
algebraic torus |
| Keyword(4) |
ElGamal cryptosystem |
| Keyword(5) |
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| 1st Author's Name |
Masaaki Shirase |
| 1st Author's Affiliation |
Japan Adcanced Institute of
Science and Technology (JAIST) |
| 2nd Author's Name |
Yasushi Hibino |
| 2nd Author's Affiliation |
Japan Adcanced Institute of
Science and Technology (JAIST) |
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| Speaker |
Author-1 |
| Date Time |
2005-05-18 13:50:00 |
| Presentation Time |
25 minutes |
| Registration for |
ISEC |
| Paper # |
ISEC2005-3 |
| Volume (vol) |
vol.105 |
| Number (no) |
no.51 |
| Page |
pp.17-24 |
| #Pages |
8 |
| Date of Issue |
2005-05-11 (ISEC) |