| Paper Abstract and Keywords |
| Presentation |
2007-03-09 09:20
A Combined Circuit for Multiplication and Inversion in GF(2^m) Based on the Extended Euclid's Algorithm
Katsuki Kobayashi, Naofumi Takagi (Nagoya Univ.) |
| Abstract |
(in Japanese) |
(See Japanese page) |
| (in English) |
A combined circuit for multiplication and inversion in
$\mathrm{GF}(2^m)$ is proposed.
In contrast with previously proposed combined circuits,
the proposed circuit does not depend on the irreducible polynomial
that defines the field
nor need to reverse the order of the coefficients of inputs and
output polynomials.
In the proposed combined circuit,
multiplication is based on MSB-first algorithm
and inversion is based on the extended Euclid's algorithm.
To share almost all hardware components of the circuit
for multiplication and inversion,
we combine these algorithms
by focusing similarity between those.
Since the degrees of reduction polynomials in
multiplication and inversion needs to be identical,
we modify the reduction polynomial of multiplication
to satisfy the condition.
Additionally, we adjust other variables to this modification.
The area of the proposed circuit has been estimated by
logic synthesis.
The area of the proposed circuit is about $40\%$ smaller
than the total area of ordinary multiplication circuit
and inversion circuit. |
| Keyword |
(in Japanese) |
(See Japanese page) |
| (in English) |
Galois field / multiplication / inversion / extended Euclid's algorithm / / / / |
| Reference Info. |
IEICE Tech. Rep., vol. 106, no. 549, VLD2006-142, pp. 13-18, March 2007. |
| Paper # |
VLD2006-142 |
| Date of Issue |
2007-03-02 (VLD, ICD) |
| ISSN |
Print edition: ISSN 0913-5685 |
| Download PDF |
|
| Conference Information |
| Committee |
ICD VLD |
| Conference Date |
2007-03-07 - 2007-03-09 |
| Place (in Japanese) |
(See Japanese page) |
| Place (in English) |
Mielparque Okinawa |
| Topics (in Japanese) |
(See Japanese page) |
| Topics (in English) |
System-on-silicon design techniques and related VLSs |
| Paper Information |
| Registration To |
VLD |
| Conference Code |
2007-03-ICD-VLD |
| Language |
Japanese |
| Title (in Japanese) |
(See Japanese page) |
| Sub Title (in Japanese) |
(See Japanese page) |
| Title (in English) |
A Combined Circuit for Multiplication and Inversion in GF(2^m) Based on the Extended Euclid's Algorithm |
| Sub Title (in English) |
|
| Keyword(1) |
Galois field |
| Keyword(2) |
multiplication |
| Keyword(3) |
inversion |
| Keyword(4) |
extended Euclid's algorithm |
| Keyword(5) |
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| Keyword(6) |
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| Keyword(7) |
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| 1st Author's Name |
Katsuki Kobayashi |
| 1st Author's Affiliation |
Nagoya University (Nagoya Univ.) |
| 2nd Author's Name |
Naofumi Takagi |
| 2nd Author's Affiliation |
Nagoya University (Nagoya Univ.) |
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| Speaker |
Author-1 |
| Date Time |
2007-03-09 09:20:00 |
| Presentation Time |
20 minutes |
| Registration for |
VLD |
| Paper # |
VLD2006-142, ICD2006-233 |
| Volume (vol) |
vol.106 |
| Number (no) |
no.549(VLD), no.552(ICD) |
| Page |
pp.13-18 |
| #Pages |
6 |
| Date of Issue |
2007-03-02 (VLD, ICD) |