Project/Area Number  10680349 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
計算機科学

Research Institution  Nagoya University 
Principal Investigator 
TAKAGI Naofumi Nagoya University, Graduate School of Engineering, Professor, 工学研究科, 教授 (10171422)

CoInvestigator(Kenkyūbuntansha) 
TAKAGI Kazuyoshi Nagoya University, Graduate School of Engineering, Assistant Professor, 工学研究科, 講師 (70273844)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥3,100,000 (Direct Cost : ¥3,100,000)
Fiscal Year 2000 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1999 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1998 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  arithmetic circuit / hardware algorithm / VLSI / Euclidean norm computation / cube rooting / powering / division in GF (2^m) / modular division / 算術演算 / ハート・ウェアアルゴリズム / ユークリッドノルム計算 / 立方根計算 / べき乗算 / GF(2^m)上の除算 / 剰余除算 / ハードウェアアルゴリズム / ノルム計算 / コンピュータグラフィクス / 符号化 / 復号 / 三角関数計算 / 加算 / 加算木 / 乗算 
Research Abstract 
1. We have developed a hardware algorithm for computing the Euclidean norm of a 3D vector which often appears in 3D computer graphics, and designed and implemented an LSI based on it. 2. We have developed a hardware algorithm for cube rooting which appears in computer graphics, and designed and implemented an LSI based on it. 3. We have developed a hardware algorithm for generating powers of an operand, such as recirocal, square root, reciprocal square root, reciprocal square, and so on, using a multiplier with operand modifier. 4. We have developed a hardware algorithm for addition under the assumption of lefttorigh input arrival, which is optimal in theory and very efficient in practice. 5. We have developed a hardware algorithms for modular division with very large modulus which is required in cryptosystems. It is based on the binay GCD algorithm. 6. We have developed a hardware algorithms for division in GF (2^m) which is required in coding and cryptosystems, and designed and implemented an LSI based on it. We have also developed a fast algorithms for multiplicative inversion in GF (2^m) based Fermar's theorem. 7. We have developed a fast addition algorithm on an elliptic curve over GF (2^n) using the projective coordinates which is required in publickey cryptosystems. 8. We have shown that the VLSI layout problem of a bit slice of an adder tree can be treated as the minimum cut linear arrangement problem of its corresponding pq dag, and proposed two algorithms for minimum cut linear arrangement of pq dags.
