CA2155038A1 - Elliptic curve encryption systems - Google Patents

Elliptic curve encryption systems

Info

Publication number
CA2155038A1
CA2155038A1 CA 2155038 CA2155038A CA2155038A1 CA 2155038 A1 CA2155038 A1 CA 2155038A1 CA 2155038 CA2155038 CA 2155038 CA 2155038 A CA2155038 A CA 2155038A CA 2155038 A1 CA2155038 A1 CA 2155038A1
Authority
CA
Canada
Prior art keywords
coordinates
elliptic curve
key
curve
curve encryption
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.)
Granted
Application number
CA 2155038
Other languages
French (fr)
Other versions
CA2155038C (en
Inventor
Gordon B. Agnew
Ronald C. Mullin
Scott A. Vanstone
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
Priority to CA2640641A priority Critical patent/CA2640641C/en
Priority to CA 2155038 priority patent/CA2155038C/en
Publication of CA2155038A1 publication Critical patent/CA2155038A1/en
Application granted granted Critical
Publication of CA2155038C publication Critical patent/CA2155038C/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR 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)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Error Detection And Correction (AREA)
  • Complex Calculations (AREA)
  • Storage Device Security (AREA)

Abstract

An elliptic curve encryption system represents coordinates of a point on the curve as a vector of binary digits in a normal basis representation in F2m. A key is generated from multiple additions of one or more points in a finite field. Inverses of values are computed using a finite field multiplier and successive exponentiations. A key is represented as the coordinates of a point on the curve and key transfer may be accomplished with the transmission of only one coordinate and identifying information of the second. An encryption protocol using one of the coordinates and a further function of that coordinate is also described.
CA 2155038 1995-07-31 1995-07-31 Elliptic curve encryption systems Expired - Lifetime CA2155038C (en)

Priority Applications (2)

Application Number Priority Date Filing Date Title
CA2640641A CA2640641C (en) 1995-07-31 1995-07-31 Public key cryptography utilizing elliptic curves
CA 2155038 CA2155038C (en) 1995-07-31 1995-07-31 Elliptic curve encryption systems

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CA 2155038 CA2155038C (en) 1995-07-31 1995-07-31 Elliptic curve encryption systems

Related Child Applications (1)

Application Number Title Priority Date Filing Date
CA2640641A Division CA2640641C (en) 1995-07-31 1995-07-31 Public key cryptography utilizing elliptic curves

Publications (2)

Publication Number Publication Date
CA2155038A1 true CA2155038A1 (en) 1997-02-01
CA2155038C CA2155038C (en) 2008-12-09

Family

ID=4156325

Family Applications (2)

Application Number Title Priority Date Filing Date
CA2640641A Expired - Lifetime CA2640641C (en) 1995-07-31 1995-07-31 Public key cryptography utilizing elliptic curves
CA 2155038 Expired - Lifetime CA2155038C (en) 1995-07-31 1995-07-31 Elliptic curve encryption systems

Family Applications Before (1)

Application Number Title Priority Date Filing Date
CA2640641A Expired - Lifetime CA2640641C (en) 1995-07-31 1995-07-31 Public key cryptography utilizing elliptic curves

Country Status (1)

Country Link
CA (2) CA2640641C (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112805768A (en) * 2018-10-04 2021-05-14 日本电信电话株式会社 Secret sigmoid function calculation system, secret logistic regression calculation system, secret sigmoid function calculation device, secret logistic regression calculation device, secret sigmoid function calculation method, secret logistic regression calculation method, and program

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112805768A (en) * 2018-10-04 2021-05-14 日本电信电话株式会社 Secret sigmoid function calculation system, secret logistic regression calculation system, secret sigmoid function calculation device, secret logistic regression calculation device, secret sigmoid function calculation method, secret logistic regression calculation method, and program
CN112805768B (en) * 2018-10-04 2023-08-04 日本电信电话株式会社 Secret S-type function calculation system and method therefor, secret logistic regression calculation system and method therefor, secret S-type function calculation device, secret logistic regression calculation device, and program

Also Published As

Publication number Publication date
CA2640641C (en) 2010-12-21
CA2155038C (en) 2008-12-09
CA2640641A1 (en) 1997-02-01

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Legal Events

Date Code Title Description
EEER Examination request
MKEX Expiry

Effective date: 20150731