Studies on security and efficiency of elliptic curve cryptosystems 楕円曲線暗号の安全性と効率に関する研究
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著者
書誌事項
- タイトル
-
Studies on security and efficiency of elliptic curve cryptosystems
- タイトル別名
-
楕円曲線暗号の安全性と効率に関する研究
- 著者名
-
宮地, 充子
- 著者別名
-
ミヤジ, アツコ
- 学位授与大学
-
大阪大学
- 取得学位
-
博士 (理学)
- 学位授与番号
-
乙第7368号
- 学位授与年月日
-
1997-12-16
注記・抄録
博士論文
目次
- Abstract/p1 (3コマ目)
- Contents/p5 (5コマ目)
- 1 Introduction/p1 (7コマ目)
- 1.1 Elliptic curve cryptosystems/p1 (7コマ目)
- 1.2 Overview of the Thesis/p4 (9コマ目)
- 2 Background/p7 (10コマ目)
- 2.1 Complexity Theory/p8 (11コマ目)
- 2.2 Public key cryptosystems/p9 (11コマ目)
- 2.3 Elliptic Curve cryptosystems/p12 (13コマ目)
- 2.4 Known attacks against DLP and EDLP/p16 (15コマ目)
- 3 The extension of MOV-reduction/p19 (16コマ目)
- 3.1 Motivation/p19 (16コマ目)
- 3.2 Reducing EDLP to DLP in a finite field/p20 (17コマ目)
- 3.3 Inapplicable case/p21 (17コマ目)
- 3.4 Constructing elliptic curves/p23 (18コマ目)
- 3.5 Summary/p26 (20コマ目)
- 4 Elliptic curves with a small basepoint/p27 (20コマ目)
- 4.1 Motivation/p27 (20コマ目)
- 4.2 Addition formula of Elliptic curve/p27 (20コマ目)
- 4.3 Schnorr signature on elliptic curves/p29 (21コマ目)
- 4.4 Essence of construction of elliptic curves/p33 (23コマ目)
- 4.5 Example of elliptic curves with a small basepoint/p34 (24コマ目)
- 4.6 Summary/p43 (28コマ目)
- 5 Elliptic curves over a optimal field [数式]/p45 (29コマ目)
- 5.1 Motivation/p45 (29コマ目)
- 5.2 Fundamental operations/p45 (29コマ目)
- 5.3 Optimal definition field [数式]/p46 (30コマ目)
- 5.4 Elliptic curves over a optimal field [数式]/p47 (30コマ目)
- 5.5 Summary/p50 (32コマ目)
- 6 Isogenous elliptic curve cryptosystems/p51 (32コマ目)
- 6.1 Motivation/p51 (32コマ目)
- 6.2 Different Elliptic Curve Cryptosystems/p52 (33コマ目)
- 6.3 Isogenous Elliptic Curve/p53 (33コマ目)
- 6.4 Example of isogenous elliptic curve/p57 (35コマ目)
- 6.5 Summary/p58 (36コマ目)
- 7 Security of ECElG,ECDSA and ECMR/p59 (36コマ目)
- 7.1 Motivation/p59 (36コマ目)
- 7.2 ElGamal,DSA and message recovery signature/p60 (37コマ目)
- 7.3 Strongly equivalent classes/p62 (38コマ目)
- 7.4 Aspect of elliptic curve signature schemes/p65 (39コマ目)
- 7.5 Bleichenbacher-attack over elliptic curves/p70 (42コマ目)
- 7.6 Summary/p73 (43コマ目)
- 8 Conclusion/p75 (44コマ目)
- 8.1 Summary/p75 (44コマ目)
- 8.2 Further research/p77 (45コマ目)
- 8.3 Recent tendency of standardization and implementations/p77 (45コマ目)
