WO2004017193A3 - Procede de calcul universel applique a des points d'une courbe elliptique - Google Patents

Procede de calcul universel applique a des points d'une courbe elliptique Download PDF

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Publication number
WO2004017193A3
WO2004017193A3 PCT/FR2003/002462 FR0302462W WO2004017193A3 WO 2004017193 A3 WO2004017193 A3 WO 2004017193A3 FR 0302462 W FR0302462 W FR 0302462W WO 2004017193 A3 WO2004017193 A3 WO 2004017193A3
Authority
WO
WIPO (PCT)
Prior art keywords
points
elliptic curve
universal
universal calculation
concerns
Prior art date
Application number
PCT/FR2003/002462
Other languages
English (en)
Other versions
WO2004017193A2 (fr
Inventor
Olivier Billet
Marc Joye
Original Assignee
Gemplus Card Int
Olivier Billet
Marc Joye
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 Int, Olivier Billet, Marc Joye filed Critical Gemplus Card Int
Priority to US10/523,840 priority Critical patent/US20060056619A1/en
Priority to EP03753669A priority patent/EP1530753A2/fr
Priority to JP2004528585A priority patent/JP2005535927A/ja
Priority to AU2003271831A priority patent/AU2003271831A1/en
Publication of WO2004017193A2 publication Critical patent/WO2004017193A2/fr
Publication of WO2004017193A3 publication Critical patent/WO2004017193A3/fr

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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/002—Countermeasures against attacks on cryptographic mechanisms
    • H04L9/003—Countermeasures against attacks on cryptographic mechanisms for power analysis, e.g. differential power analysis [DPA] or simple power analysis [SPA]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computer Security & Cryptography (AREA)
  • Computational Mathematics (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Complex Calculations (AREA)
  • Cash Registers Or Receiving Machines (AREA)

Abstract

L'invention concerne un procédé de calcul universel sur des points d'une courbe elliptique. Selon l'invention, la courbe elliptique est définie par une équation quartique et des moyens de calcul programmés identiques sont utilisés pour réaliser une opération d'addition de points, une opération de doublement de points, et une opération d'addition d'un point neutre, les moyens de calcul comprenant notamment une unité centrale (2) associée à une mémoire (4, 6, 8). L'invention concerne également un procédé cryptographique utilisant un tel procédé universel. L'invention concerne encore un composant pour mettre en uvre le procédé de calcul universel et / ou le procédé cryptographique. Exemple d'application: cartes à puce.
PCT/FR2003/002462 2002-08-09 2003-08-05 Procede de calcul universel applique a des points d'une courbe elliptique WO2004017193A2 (fr)

Priority Applications (4)

Application Number Priority Date Filing Date Title
US10/523,840 US20060056619A1 (en) 2002-08-09 2003-08-05 Method for universal calculation applied to points of an elliptic curve
EP03753669A EP1530753A2 (fr) 2002-08-09 2003-08-05 Procede de calcul universel applique a des points d'une courbe elliptique
JP2004528585A JP2005535927A (ja) 2002-08-09 2003-08-05 四次方程式により定義される楕円曲線上の点に適用される汎用計算方法、および関連暗号化方法および電子構成要素
AU2003271831A AU2003271831A1 (en) 2002-08-09 2003-08-05 Method for universal calculation applied to points of an elliptic curve

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
FR0210193A FR2843506B1 (fr) 2002-08-09 2002-08-09 Procede de calcul universel applique a des points d'une courbe elliptique definie par une quartique, procede cryptographique et composant electronique associes
FR02/10193 2002-08-09

Publications (2)

Publication Number Publication Date
WO2004017193A2 WO2004017193A2 (fr) 2004-02-26
WO2004017193A3 true WO2004017193A3 (fr) 2004-05-06

Family

ID=30471060

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/FR2003/002462 WO2004017193A2 (fr) 2002-08-09 2003-08-05 Procede de calcul universel applique a des points d'une courbe elliptique

Country Status (6)

Country Link
US (1) US20060056619A1 (fr)
EP (1) EP1530753A2 (fr)
JP (1) JP2005535927A (fr)
AU (1) AU2003271831A1 (fr)
FR (1) FR2843506B1 (fr)
WO (1) WO2004017193A2 (fr)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100530372B1 (ko) * 2003-12-20 2005-11-22 삼성전자주식회사 사이드채널 공격을 방지할 수 있는 타원곡선 암호화 방법
US7991162B2 (en) * 2007-09-14 2011-08-02 University Of Ottawa Accelerating scalar multiplication on elliptic curve cryptosystems over prime fields
KR101549291B1 (ko) * 2012-10-25 2015-09-02 엘지디스플레이 주식회사 표시장치
US11146397B2 (en) * 2017-10-31 2021-10-12 Micro Focus Llc Encoding abelian variety-based ciphertext with metadata
CN108875416B (zh) * 2018-06-22 2020-05-19 北京智芯微电子科技有限公司 椭圆曲线多倍点运算方法和装置

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6778666B1 (en) * 1999-03-15 2004-08-17 Lg Electronics Inc. Cryptographic method using construction of elliptic curve cryptosystem
FR2828779B1 (fr) * 2001-08-17 2004-01-16 Gemplus Card Int Procede de calcul universel applique a des points d'une courbe elliptique

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
BRIER E ET AL: "WEIERSTRASS ELLIPTIC CURVES AND SIDE-CHANNEL ATTACKS", 5TH INTERNATIONAL WORKSHOP ON PRACTICE AND THEORY IN PUBLIC KEY CRYPTOSYSTEMS, PKC 2002, PARIS, FRANCE. LNCS 2274, February 2002 (2002-02-01), Springer-Verlag, Berlin (DE), pages 335 - 345, XP001068195, Retrieved from the Internet <URL:http://link.springer.de/link/service/series/0558/tocs/t2274.htm> [retrieved on 20020205] *
CHUDNOVSKY D V ET AL: "SEQUENCES OF NUMBERS GENERATED BY ADDITION IN FORMAL GROUPS AND NEWPRIMALITY AND FACTORIZATION TESTS", ADVANCES IN APPLIED MATHEMATICS, ACADEMIC PRESS, SAN DIEGO, CA, US, vol. 7, 1986, pages 385 - 434, XP008000716, ISSN: 0196-8858 *
JOYE M ET AL: "HESSIAN ELLIPTIC CURVES AND SIDE-CHANNEL ATTACKS", CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS CHES 2001. THIRD INTERNATIONAL WORKSHOP, PARIS, FRANCE, MAY 14-16, 2001, PROCEEDINGS. LNCS 2162, vol. 2162, 14 May 2001 (2001-05-14), pages 402 - 410, XP008002643, ISBN: 3-540-42521-7 *
KHELDOUNI A ET AL: "Elliptic cohomology operation defined by Hecke operator T2", COMPTES RENDUS DES SEANCES DE L'ACADEMIE DES SCIENCES. SERIE I: MATHEMATIQUES, EDITIONS SCIENTIFIQUES & MEDICALES ELSEVIER, FR, vol. 324, no. 2, January 1997 (1997-01-01), pages 215 - 220, XP004269356, ISSN: 0764-4442 *
P. BARRETO ET AL.: "Constructing Elliptic Curves with Prescribed Embedding Degrees", SECURITY IN COMMUNICATION NETWORKS. THIRD INTERNATIONAL CONFERENCE, SCN 2002, AMALFI, ITALY, SEPTEMBER 11-13, 2002. REVISED PAPERS. LNCS 2576, 2003, Springer Verlag, Berlin (DE), pages 257 - 267, XP002241906, Retrieved from the Internet <URL:http://link.springer.de/link/service/series/0558/papers/2576/25760257.pdf> [retrieved on 20030314] *

Also Published As

Publication number Publication date
AU2003271831A8 (en) 2004-03-03
FR2843506B1 (fr) 2004-10-29
AU2003271831A1 (en) 2004-03-03
FR2843506A1 (fr) 2004-02-13
EP1530753A2 (fr) 2005-05-18
WO2004017193A2 (fr) 2004-02-26
JP2005535927A (ja) 2005-11-24
US20060056619A1 (en) 2006-03-16

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