| Presentation | 2007-03-09 A Combined Circuit for Multiplication and Inversion in GF(2^m) Based on the Extended Euclid's Algorithm Katsuki KOBAYASHI, Naofumi TAKAGI, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | A combined circuit for multiplication and inversion in GF(2^m) is proposed. In contrast with previously proposed combined circuits, the proposed circuit does not depend on the irreducible polynomial that defined the field nor need to reverse the order of the coefficients of inputs and putput 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) |
| Keyword(in English) | Galois field / GF(2^m) / multiplication / inversion / extended Euclid's algorithm |
| Paper # | VLD2006-142,ICD2006-233 |
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| Conference Information | |
| Committee | VLD |
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| Conference Date | 2007/3/2(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | VLSI Design Technologies (VLD) |
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| Language | JPN |
| 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) | GF(2^m) |
| Keyword(3) | multiplication |
| Keyword(4) | inversion |
| Keyword(5) | extended Euclid's algorithm |
| 1st Author's Name | Katsuki KOBAYASHI |
| 1st Author's Affiliation | Department of Information Engineering, Graduate School of Information Science, Nagoya University() |
| 2nd Author's Name | Naofumi TAKAGI |
| 2nd Author's Affiliation | Department of Information Engineering, Graduate School of Information Science, Nagoya University |
| Date | 2007-03-09 |
| Paper # | VLD2006-142,ICD2006-233 |
| Volume (vol) | vol.106 |
| Number (no) | 549 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |