2001 Fiscal Year Final Research Report Summary
Research on public-key cryptosystems from hyperelliptic-curves
| Project/Area Number |
11558033
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 展開研究 |
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| Research Field |
計算機科学
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| Research Institution | Kyushu University |
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Principal Investigator |
SAKURAI Kouichi Kyushu Univ., Dept. Computer Science, Associate Prof., システム情報科学研究院, 助教授 (60264066)
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| Co-Investigator(Kenkyū-buntansha) |
ASAHIRO Yuichi Kyushu Univ., Dept. Computer Science, Assistant, 大学院・システム情報科学研究院, 助手 (40304761)
SUZUKI Masakazu Kyushu Univ., Dept. Mathematics, Prof., 大学院・数理学研究院, 教授 (20112302)
SHIZUYA Hiroki TOHOKU Univ., Information Synergy Center, Prof., 情報シナジーセンター, 教授 (50196383)
SAKAI Yasuyuki Mitsubishi Electronic Co., Information Systems Lab., Research Engineer, 情報総合研究所, 主任研究員
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| Project Period (FY) |
1999 – 2001
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| Keywords | cryptography / information security / hyperelliptic curve / public-key encryption / algorithm / cryptanalysis / elliptic curve / fast computation |
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| Research Abstract |
We have designed hyperelliptic curve cryptosystems with considering security and efficiency.
We have implemented our designed hyperelliptic curve cryptosystems both over software and over hardware, and confirm their practical performance.
We consider the performance of hyperelliptic curve cryptosystems over GF(p) vs. over GF(2^n).
We analyze the complexity of the group law of Jacobians and make comparison of their performance between over over GF(p) vs. over GF(2^n). with considering the effectiveness of the word size (32-bit or 64-bit) of the applied CPU (Alpha and Pentium) on the arithmetic on the definition field.
We also develop efficient algorithms for the jacobian of the hyperelliptic curve defined by the equation $y^2 = x^p-x+1$ over a finite field GF(p^n) of odd characteristic p. We first determine the zeta function of the curve which yields the order of the jacobian. And we investigate the Frobenius operator and use it to show that, for field extensions GF(p^n) of degree n prime to p, the jacobian has a cyclic group structure. We furthermore propose a method for faster scalar multiplication in the jacobian by using efficient operators other than the Frobenius that have smaller eigenvalues.
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