2007 Fiscal Year Final Research Report Summary
Development of a system for number theory by script language and related research on algorithmic number theory
| Project/Area Number |
16340011
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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 | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
NAKAMURA Ken Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Professor (80110849)
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| Co-Investigator(Kenkyū-buntansha) |
UCHIYAMA Shigenori Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Associate professor (40433172)
SUZUKI Toshio Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Associate professor (30235973)
TSUMURA Hirofumi Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Professor (20310419)
KIDA Masanari The Univ. of Electro-Communications, 大学院・理工学研究, Associate professor (20272057)
NAGAO Ko-ichi Kanto Gakuin University, 工学部, Professor (00308321)
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| Project Period (FY) |
2004 – 2007
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| Keywords | algorithmic number theory / cryptologic research / system for number theory / Python / NZMATH |
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| Research Abstract |
We started the development of a system for number theory by Python language and named it as NZMATH. Implemented packages are as follows : number theory, finite fields, combinatrics, several integer facorization algorithms, elliptic curves, structure computation of several finite commutative groups, quantum public key cryptosystem on imaginary quadratic fields, pairing on elliptic curves, structure of ring class groups of imaginary quadratic fields, successive division on some imaginary quadratic fields, cubic residues and related cubic roots in some imaginary quadratic fields, elliptic curve method for integer facorization. Number fields are going to be released soon in this April. Main web page is
http://tnt.math.metro-u.ac.jp/nzmath/
We also studied on algorithmic number theory and its application as in published papers and talks. In order to communicate the results, we mainly worked in the research group JANT in JSIAM. We organized 4 research meetings every year with about 50 participants. We published a special volume of JJAIM, an official journal of JSIAM, on algorithmic number theory. Main web page is
http://ntw.e-one.uec.ac.jp/jant/
For active interrelationship between algorithmic number theory and other areas on computer algebra, we organized the 6th and the 7th international Symposium on Algebra and Computation, AC2005 and AC2007, with more than 100 participants. Main web page is
http://tnt.math.metro-u.ac.jp/ac/
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Research Products
(199 results)
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[Journal Article] Efficient, Non-Optimistic Secure Circuit Evaluation Based on the EIGamal Encryption and Its Applications2007
Author(s)
Koji, Chida, Go, Yamamoto, Koutarou, Suzuki, Shigenori, Uchiyama, Noburou, Taniguchi, Osamu, Shionoiri, Atsushi, Kanai
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Journal Title
IEICE Trans. Fundamentals Vol.E90-A, No.1
Pages: 128-138
Description
「研究成果報告書概要(欧文)」より
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[Presentation] すぐ使える数論システム{\tt{NZMATH}}2007
Author(s)
市来 信吾, 小椋 直樹, 小泉 賢洋, 西本 啓一郎, 田中 覚, 松井 鉄史, 内山 成憲 and 中村 憲
Organizer
第七回代数学と計算研究集会
Place of Presentation
首都大学東京,講演
Year and Date
2007-12-06
Description
「研究成果報告書概要(和文)」より
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[Presentation] A-超幾何微分差分方程式2005
Author(s)
高山 信毅, 小原 功任
Organizer
(招待講演)微分方程式の総合的研究
Place of Presentation
東京大学
Year and Date
2005-12-16
Description
「研究成果報告書概要(和文)」より
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[Presentation] 暗号理論入門2004
Author(s)
内山 成憲
Organizer
拓殖大学情報工学科特別講義
Place of Presentation
拓殖大学情報工学科
Year and Date
2004-04-14
Description
「研究成果報告書概要(和文)」より
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[Book] 数論II2005
Author(s)
栗原 将人、黒川 信重、齋藤 毅と共著
Total Pages
620
Publisher
岩波書店
Description
「研究成果報告書概要(和文)」より
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