CA2324621C - Accelerated finite field operations on an elliptic curve - Google Patents

Accelerated finite field operations on an elliptic curve Download PDF

Info

Publication number
CA2324621C
CA2324621C CA002324621A CA2324621A CA2324621C CA 2324621 C CA2324621 C CA 2324621C CA 002324621 A CA002324621 A CA 002324621A CA 2324621 A CA2324621 A CA 2324621A CA 2324621 C CA2324621 C CA 2324621C
Authority
CA
Canada
Prior art keywords
coordinate
affine
elliptic curve
point
coordinates
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
CA002324621A
Other languages
English (en)
French (fr)
Other versions
CA2324621A1 (en
Inventor
Scott A. Vanstone
Ronald C. Mullin
Adrian Antipa
Robert P. Gallant
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Certicom Corp
Original Assignee
Certicom Corp
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 Certicom Corp filed Critical Certicom Corp
Publication of CA2324621A1 publication Critical patent/CA2324621A1/en
Application granted granted Critical
Publication of CA2324621C publication Critical patent/CA2324621C/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

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)
CA002324621A 1998-03-25 1999-03-25 Accelerated finite field operations on an elliptic curve Expired - Lifetime CA2324621C (en)

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 (2)

Publication Number Publication Date
CA2324621A1 CA2324621A1 (en) 1999-09-30
CA2324621C true CA2324621C (en) 2009-07-07

Family

ID=21949428

Family Applications (1)

Application Number Title Priority Date Filing Date
CA002324621A Expired - Lifetime CA2324621C (en) 1998-03-25 1999-03-25 Accelerated finite field operations on an elliptic curve

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
AU2917699A (en) 1999-10-18
EP1066558A1 (en) 2001-01-10
JP4598269B2 (ja) 2010-12-15
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
CA2233120C (en) Accelerated finite field operations on an elliptic curve
EP0804758B1 (en) Elliptic curve encryption systems
AU677269B2 (en) A cryptographic method
Naehrig et al. New software speed records for cryptographic pairings
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
EP1445891A1 (en) Elliptic curve scalar multiple calculation method and device, and storage medium
US20020052906A1 (en) Method for efficient modular division over prime integer fields
CA2324621C (en) Accelerated finite field operations on an elliptic curve
Meshram et al. New efficient QERPKC based on partial discrete logarithm problem
US6826586B2 (en) Method for efficient computation of point doubling operation of elliptic curve point scalar multiplication over finite fields F(2m)
US20160149703A1 (en) Method for efficient postcomputation-based generic-point parallel scalar multiplication
Ebeid et al. Securing the elliptic curve montgomery ladder against fault attacks
US20070121935A1 (en) Method for countermeasuring in an electronic component
CA2129203C (en) Public key cryptography utilizing elliptic curves
CA2155038C (en) Elliptic curve encryption systems
JPH0798563A (ja) 楕円曲線による署名、認証及び秘密通信方式
Han et al. Side channel cryptanalysis on XTR public key cryptosystem
Lee et al. Improved scalar multiplication on elliptic curves defined over F2mn
Moldovyan et al. Vector Finite Groups as Primitives for Fast Digital Signature Algorithms
Huang et al. FleS: A Compact and Parameter-Flexible Supersingular Isogeny Based Public Key Encryption Scheme
CA2711188C (en) Public key cryptography utilizing elliptic curves
Msurert New Public-Key Schemes Based on Elliptic Curves over the Ring Z
Zhu Efficient algorithms for implementing the elliptic curve cryptosystems

Legal Events

Date Code Title Description
EEER Examination request
MKEX Expiry

Effective date: 20190325