DE60217131D1 - Universelles berechnungsverfahren für punkte auf einer elliptischen kurve - Google Patents

Universelles berechnungsverfahren für punkte auf einer elliptischen kurve

Info

Publication number
DE60217131D1
DE60217131D1 DE60217131T DE60217131T DE60217131D1 DE 60217131 D1 DE60217131 D1 DE 60217131D1 DE 60217131 T DE60217131 T DE 60217131T DE 60217131 T DE60217131 T DE 60217131T DE 60217131 D1 DE60217131 D1 DE 60217131D1
Authority
DE
Germany
Prior art keywords
points
calculation method
elliptic curve
universal calculation
universal
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 - Fee Related
Application number
DE60217131T
Other languages
English (en)
Other versions
DE60217131T2 (de
Inventor
Marc Joye
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.)
Gemplus SA
Original Assignee
Gemplus Card International SA
Gemplus SA
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 Gemplus Card International SA, Gemplus SA filed Critical Gemplus Card International SA
Application granted granted Critical
Publication of DE60217131D1 publication Critical patent/DE60217131D1/de
Publication of DE60217131T2 publication Critical patent/DE60217131T2/de
Anticipated expiration legal-status Critical
Expired - Fee Related 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2207/00—Indexing scheme relating to methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F2207/72—Indexing scheme relating to groups G06F7/72 - G06F7/729
    • G06F2207/7219—Countermeasures against side channel or fault attacks
    • G06F2207/7261—Uniform execution, e.g. avoiding jumps, or using formulae with the same power profile

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)
  • Complex Calculations (AREA)
  • Credit Cards Or The Like (AREA)
DE60217131T 2001-08-17 2002-07-31 Universelles berechnungsverfahren für punkte auf einer elliptischen kurve Expired - Fee Related DE60217131T2 (de)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
FR0110873 2001-08-17
FR0110873A FR2828779B1 (fr) 2001-08-17 2001-08-17 Procede de calcul universel applique a des points d'une courbe elliptique
PCT/FR2002/002769 WO2003017087A1 (fr) 2001-08-17 2002-07-31 Procede de calcul universel applique a des points d'une courbe elliptique

Publications (2)

Publication Number Publication Date
DE60217131D1 true DE60217131D1 (de) 2007-02-08
DE60217131T2 DE60217131T2 (de) 2007-09-27

Family

ID=8866574

Family Applications (1)

Application Number Title Priority Date Filing Date
DE60217131T Expired - Fee Related DE60217131T2 (de) 2001-08-17 2002-07-31 Universelles berechnungsverfahren für punkte auf einer elliptischen kurve

Country Status (7)

Country Link
US (1) US20040247114A1 (de)
EP (1) EP1421473B1 (de)
CN (1) CN1571952A (de)
DE (1) DE60217131T2 (de)
ES (1) ES2279887T3 (de)
FR (1) FR2828779B1 (de)
WO (1) WO2003017087A1 (de)

Families Citing this family (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2843506B1 (fr) * 2002-08-09 2004-10-29 Gemplus Card Int Procede de calcul universel applique a des points d'une courbe elliptique definie par une quartique, procede cryptographique et composant electronique associes
US7961874B2 (en) * 2004-03-03 2011-06-14 King Fahd University Of Petroleum & Minerals XZ-elliptic curve cryptography with secret key embedding
US7379546B2 (en) * 2004-03-03 2008-05-27 King Fahd University Of Petroleum And Minerals Method for XZ-elliptic curve cryptography
US7961873B2 (en) * 2004-03-03 2011-06-14 King Fahd University Of Petroleum And Minerals Password protocols using XZ-elliptic curve cryptography
WO2007045258A1 (en) 2005-10-18 2007-04-26 Telecom Italia S.P.A. A method for scalar multiplication in elliptic curve groups over prime fields for side-channel attack resistant cryptosystems
DE602005020991D1 (de) * 2005-10-28 2010-06-10 Telecom Italia Spa Verfahren zur skalarmultiplikation in gruppen ellir nebenkanalattacken-beständige kryptosysteme
US8102998B2 (en) * 2007-05-02 2012-01-24 King Fahd University Of Petroleum And Minerals Method for elliptic curve scalar multiplication using parameterized projective coordinates
US8369517B2 (en) * 2008-08-12 2013-02-05 Inside Secure Fast scalar multiplication for elliptic curve cryptosystems over prime fields
US8509426B1 (en) 2010-12-01 2013-08-13 King Fahd University Of Petroleum And Minerals XZ-elliptic curve cryptography system and method
US8699701B2 (en) 2010-12-01 2014-04-15 King Fahd University Method of performing XZ-elliptic curve cryptography for use with network security protocols
US8861721B2 (en) * 2012-12-26 2014-10-14 Umm Al-Qura University System and method for securing scalar multiplication against simple power attacks
US8804952B2 (en) 2012-12-26 2014-08-12 Umm Al-Qura University System and method for securing scalar multiplication against differential power attacks
US11146397B2 (en) * 2017-10-31 2021-10-12 Micro Focus Llc Encoding abelian variety-based ciphertext with metadata
CN112099760B (zh) * 2020-08-24 2022-11-11 清华大学 国密sm2算法中点加与倍点的单乘法器无缝调度方法

Family Cites Families (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
ATE128297T1 (de) * 1991-03-14 1995-10-15 Omnisec Ag Verschlüsselungssystem mit öffentlichem schlüssel unter verwendung elliptischer kurven über ringe.
US5272755A (en) * 1991-06-28 1993-12-21 Matsushita Electric Industrial Co., Ltd. Public key cryptosystem with an elliptic curve
US6038581A (en) * 1997-01-29 2000-03-14 Nippon Telegraph And Telephone Corporation Scheme for arithmetic operations in finite field and group operations over elliptic curves realizing improved computational speed
JPH11242434A (ja) * 1998-02-26 1999-09-07 Hitachi Ltd 楕円曲線暗号実行方法及び暗号処理システム
JP3796993B2 (ja) * 1998-12-22 2006-07-12 株式会社日立製作所 楕円曲線暗号実行方法及び装置並びに記録媒体
US6611597B1 (en) * 1999-01-25 2003-08-26 Matsushita Electric Industrial Co., Ltd. Method and device for constructing elliptic curves
FR2791497B1 (fr) * 1999-03-26 2001-05-18 Gemplus Card Int Procedes de contre-mesure dans un composant electronique mettant en oeuvre un algorithme de crytographie a cle publique de type courbe elliptique
JP3821631B2 (ja) * 2000-05-30 2006-09-13 株式会社日立製作所 楕円曲線暗号におけるスカラー倍計算方法及び装置、並びに記憶媒体
US6826586B2 (en) * 2000-12-15 2004-11-30 Sun Microsystems, Inc. Method for efficient computation of point doubling operation of elliptic curve point scalar multiplication over finite fields F(2m)
KR100817048B1 (ko) * 2005-03-05 2008-03-26 삼성전자주식회사 여러 가지 포인트 표현을 기반으로 한 ｅｃｃ에서 ｄｆａ대책을 위한 암호화 방법 및 장치

Also Published As

Publication number Publication date
FR2828779B1 (fr) 2004-01-16
EP1421473A1 (de) 2004-05-26
FR2828779A1 (fr) 2003-02-21
DE60217131T2 (de) 2007-09-27
EP1421473B1 (de) 2006-12-27
CN1571952A (zh) 2005-01-26
WO2003017087A1 (fr) 2003-02-27
ES2279887T3 (es) 2007-09-01
US20040247114A1 (en) 2004-12-09

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Legal Events

Date Code Title Description
8364 No opposition during term of opposition
8339 Ceased/non-payment of the annual fee