JP4598269B2 - 楕円曲線上の高速有限体演算 - Google Patents

楕円曲線上の高速有限体演算 Download PDF

Info

Publication number
JP4598269B2
JP4598269B2 JP2000538291A JP2000538291A JP4598269B2 JP 4598269 B2 JP4598269 B2 JP 4598269B2 JP 2000538291 A JP2000538291 A JP 2000538291A JP 2000538291 A JP2000538291 A JP 2000538291A JP 4598269 B2 JP4598269 B2 JP 4598269B2
Authority
JP
Japan
Prior art keywords
coordinate
point
affine
elliptic curve
value
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
Application number
JP2000538291A
Other languages
English (en)
Japanese (ja)
Other versions
JP2002508523A (ja
JP2002508523A5 (https=
Inventor
ヴァンストーン，スコット，エー．
ミューリン，ロナルド，シー．
アンティパ，エイドリアン
ギャラント，ロバート
Original Assignee
サーティコム コーポレーション
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by サーティコム コーポレーション filed Critical サーティコム コーポレーション
Publication of JP2002508523A publication Critical patent/JP2002508523A/ja
Publication of JP2002508523A5 publication Critical patent/JP2002508523A5/ja
Application granted granted Critical
Publication of JP4598269B2 publication Critical patent/JP4598269B2/ja
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
    • G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
    • G06F7/724—Finite field arithmetic
    • G06F7/725—Finite field arithmetic over elliptic curves

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Complex Calculations (AREA)
JP2000538291A 1998-03-25 1999-03-25 楕円曲線上の高速有限体演算 Expired - Lifetime JP4598269B2 (ja)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
US4751898A 1998-03-25 1998-03-25
US09/047,518 1998-03-25
PCT/CA1999/000254 WO1999049386A1 (en) 1998-03-25 1999-03-25 Accelerated finite field operations on an elliptic curve

Publications (3)

Publication Number Publication Date
JP2002508523A JP2002508523A (ja) 2002-03-19
JP2002508523A5 JP2002508523A5 (https=) 2006-06-15
JP4598269B2 true JP4598269B2 (ja) 2010-12-15

Family

ID=21949428

Family Applications (1)

Application Number Title Priority Date Filing Date
JP2000538291A Expired - Lifetime JP4598269B2 (ja) 1998-03-25 1999-03-25 楕円曲線上の高速有限体演算

Country Status (6)

Country Link
EP (1) EP1066558B1 (https=)
JP (1) JP4598269B2 (https=)
AU (1) AU2917699A (https=)
CA (1) CA2324621C (https=)
DE (1) DE69905145T2 (https=)
WO (1) WO1999049386A1 (https=)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2243761C (en) * 1998-07-21 2009-10-06 Certicom Corp. Timing attack resistant cryptographic system
DE10156708B4 (de) * 2001-11-19 2005-09-29 Infineon Technologies Ag Verfahren und Vorrichtung zum Multiplizieren und Verfahren und Vorrichtung zum Addieren auf einer elliptischen Kurve
JP4067818B2 (ja) 2001-12-10 2008-03-26 富士通株式会社 楕円曲線暗号装置、楕円曲線暗号プログラム及び楕円曲線暗号の演算方法
DE10161138B4 (de) * 2001-12-12 2008-02-14 Siemens Ag Verfahren und Vorrichtung zum Ermitteln einer elliptischen Kurve, Verfahren und Vorrichtung zum Multiplizieren eines Punktes mit einem Skalar
DE10161137B4 (de) * 2001-12-12 2008-02-14 Siemens Ag Verfahren und System zum kryptographischen Bearbeiten von Daten

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1996004602A1 (en) * 1994-07-29 1996-02-15 Certicom Corp. Elliptic curve encryption systems
EP0874307B2 (en) * 1997-03-25 2016-12-28 Certicom Corp. Accelerated finite field operations on an elliptic curve

Also Published As

Publication number Publication date
JP2002508523A (ja) 2002-03-19
CA2324621C (en) 2009-07-07
AU2917699A (en) 1999-10-18
EP1066558A1 (en) 2001-01-10
EP1066558B1 (en) 2003-01-29
DE69905145T2 (de) 2003-06-05
WO1999049386A1 (en) 1999-09-30
DE69905145D1 (de) 2003-03-06
CA2324621A1 (en) 1999-09-30

Similar Documents

Publication Publication Date Title
US6782100B1 (en) Accelerated finite field operations on an elliptic curve
US7961873B2 (en) Password protocols using XZ-elliptic curve cryptography
US7961874B2 (en) XZ-elliptic curve cryptography with secret key embedding
EP0503119B1 (en) Public key cryptographic system using elliptic curves over rings
US6618483B1 (en) Elliptic curve encryption systems
JP4662577B2 (ja) 楕円曲線上での暗号操作の速度を高める方法
EP0874307B2 (en) Accelerated finite field operations on an elliptic curve
US8184803B2 (en) Hash functions using elliptic curve cryptography
US7688973B2 (en) Encryption apparatus, decryption apparatus, key generation apparatus, program, and method
EP0936776A2 (en) A network system using a threshold secret sharing method
US6111952A (en) Asymmetrical cryptographic communication method and portable object therefore
EP2742644A1 (en) Encryption and decryption method
EP0952697B1 (en) Elliptic curve encryption method and system
JP4875686B2 (ja) 楕円曲線上の有限体演算の加速方法
JP2003098962A (ja) 楕円曲線スカラー倍計算方法及び装置並びに記録媒体
US6772184B2 (en) Method for efficient modular division over prime integer fields
US7912216B2 (en) Elliptic curve cryptosystem optimization using two phase key generation
Paar et al. The RSA cryptosystem
JP4598269B2 (ja) 楕円曲線上の高速有限体演算
JP2003255831A (ja) 楕円曲線スカラー倍計算方法及び装置
JP4690819B2 (ja) 楕円曲線暗号におけるスカラー倍計算方法およびスカラー倍計算装置
WO2004070681A2 (ja) 楕円曲線スカラー倍計算方法および装置
JPH0695590A (ja) 電子署名システム及び電子署名方法
Wade The Iso-RSA Cryptographic Scheme
CA2649680A1 (en) Method and apparatus for finite field basis conversion

Legal Events

Date Code Title Description
A521 Request for written amendment filed

Free format text: JAPANESE INTERMEDIATE CODE: A523

Effective date: 20060324

A621 Written request for application examination

Free format text: JAPANESE INTERMEDIATE CODE: A621

Effective date: 20060324

A131 Notification of reasons for refusal

Free format text: JAPANESE INTERMEDIATE CODE: A131

Effective date: 20090721

A601 Written request for extension of time

Free format text: JAPANESE INTERMEDIATE CODE: A601

Effective date: 20091019

RD02 Notification of acceptance of power of attorney

Free format text: JAPANESE INTERMEDIATE CODE: A7422

Effective date: 20091019

A602 Written permission of extension of time

Free format text: JAPANESE INTERMEDIATE CODE: A602

Effective date: 20091112

A601 Written request for extension of time

Free format text: JAPANESE INTERMEDIATE CODE: A601

Effective date: 20091119

A602 Written permission of extension of time

Free format text: JAPANESE INTERMEDIATE CODE: A602

Effective date: 20091127

A521 Request for written amendment filed

Free format text: JAPANESE INTERMEDIATE CODE: A523

Effective date: 20091218

RD04 Notification of resignation of power of attorney

Free format text: JAPANESE INTERMEDIATE CODE: A7424

Effective date: 20100514

TRDD Decision of grant or rejection written
A01 Written decision to grant a patent or to grant a registration (utility model)

Free format text: JAPANESE INTERMEDIATE CODE: A01

Effective date: 20100826

A01 Written decision to grant a patent or to grant a registration (utility model)

Free format text: JAPANESE INTERMEDIATE CODE: A01

A61 First payment of annual fees (during grant procedure)

Free format text: JAPANESE INTERMEDIATE CODE: A61

Effective date: 20100924

R150 Certificate of patent or registration of utility model

Free format text: JAPANESE INTERMEDIATE CODE: R150

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20131001

Year of fee payment: 3

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

EXPY Cancellation because of completion of term