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WO2001052051A3 - Procede et dispositif pour realiser une inversion en particulier lors du cryptage au moyen de courbes elliptiques - Google Patents

Procede et dispositif pour realiser une inversion en particulier lors du cryptage au moyen de courbes elliptiques Download PDF

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Publication number
WO2001052051A3
WO2001052051A3 PCT/DE2001/000161 DE0100161W WO0152051A3 WO 2001052051 A3 WO2001052051 A3 WO 2001052051A3 DE 0100161 W DE0100161 W DE 0100161W WO 0152051 A3 WO0152051 A3 WO 0152051A3
Authority
WO
WIPO (PCT)
Prior art keywords
arithmetic unit
number field
operands
cryptography
long number
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.)
Ceased
Application number
PCT/DE2001/000161
Other languages
German (de)
English (en)
Other versions
WO2001052051A2 (fr
Inventor
Rainer Bluemel
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.)
CV CRYPTOVISION GmbH
Original Assignee
CV CRYPTOVISION GmbH
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 CV CRYPTOVISION GmbH filed Critical CV CRYPTOVISION GmbH
Priority to AU37218/01A priority Critical patent/AU3721801A/en
Priority to DE10190100T priority patent/DE10190100D2/de
Publication of WO2001052051A2 publication Critical patent/WO2001052051A2/fr
Publication of WO2001052051A3 publication Critical patent/WO2001052051A3/fr
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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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
    • G06F7/721—Modular inversion, reciprocal or quotient calculation
    • 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

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  • 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)

Abstract

L'objectif de l'invention est de permettre la mise en oeuvre efficace d'algorithmes standards pour la cryptographie sur des processeurs présentant des registres de nombres longs et une capacité de calcul limitée, ladite cryptographie étant fondée sur des courbes elliptiques. Le corps de nombres et la courbe elliptique peuvent être sélectionnés librement de telle sorte qu'ils doivent, de façon avantageuse, n'être enregistrés que lors de la personnalisation d'un support d'informations correspondant. Il est proposé, selon l'invention, d'utiliser l'algorithme euclidien élargi pour la détermination d'un inverse dans le corps de nombres premiers. Deux nombres sont stockés l'un derrière l'autre dans les registres de nombres longs du processeur correspondant. L'algorithme décrit permet l'obtention en une étape de calcul des résultats de deux opérateurs nécessaires, et donc d'accélérer le calcul. Une autre accélération est obtenue étant donné que, dans les processeurs habituellement utilisés, l'unité de calcul pour l'arithmétique à nombres longs est placée à l'extérieur et forme une unité de calcul avec un ensemble de registres séparé, l'enregistrement et la lecture des opérandes respectivement dans et à partir de l'unité séparée prenant du temps. Grâce au traitement simultané de deux opérandes, la moitié des cycles de charge peut être supprimée.
PCT/DE2001/000161 2000-01-16 2001-01-16 Procede et dispositif pour realiser une inversion en particulier lors du cryptage au moyen de courbes elliptiques Ceased WO2001052051A2 (fr)

Priority Applications (2)

Application Number Priority Date Filing Date Title
AU37218/01A AU3721801A (en) 2000-01-16 2001-01-16 Method and device for carrying out an inversion, especially during encoding by means of elliptic curves
DE10190100T DE10190100D2 (de) 2000-01-16 2001-01-16 Verfahren und Vorrichtungen zur Durchführung einer Inversion insbesondere bei der Verschlüsselung mittels elliptischer Kurven

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE10002901 2000-01-16
DE10002901.9 2000-01-16

Publications (2)

Publication Number Publication Date
WO2001052051A2 WO2001052051A2 (fr) 2001-07-19
WO2001052051A3 true WO2001052051A3 (fr) 2001-10-25

Family

ID=7628537

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/DE2001/000161 Ceased WO2001052051A2 (fr) 2000-01-16 2001-01-16 Procede et dispositif pour realiser une inversion en particulier lors du cryptage au moyen de courbes elliptiques

Country Status (3)

Country Link
AU (1) AU3721801A (fr)
DE (2) DE10190100D2 (fr)
WO (1) WO2001052051A2 (fr)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10220262A1 (de) 2002-05-06 2003-11-27 Giesecke & Devrient Gmbh Berechnung des modularen Inversen eines Wertes
WO2007045258A1 (fr) 2005-10-18 2007-04-26 Telecom Italia S.P.A. Méthode de multiplication scalaire au sein de groupes de courbes elliptiques sur des champs premiers pour systèmes de codage résistant aux attaques par canal latéral
ATE466329T1 (de) * 2005-10-28 2010-05-15 Telecom Italia Spa Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über binäre polynomische körper für nebenkanalattacken-beständige kryptosysteme

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1999004332A1 (fr) * 1997-07-14 1999-01-28 Cipherit Ltd. Calcul d'inverses multiplicateurs a champs composites a des fins de cryptographie de courbes elliptiques

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1999004332A1 (fr) * 1997-07-14 1999-01-28 Cipherit Ltd. Calcul d'inverses multiplicateurs a champs composites a des fins de cryptographie de courbes elliptiques

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
BRUCE SCHNEIER: "Applied Cryptography", 1996, JOHN WILEY & SONS, INC., UNITED STATES, XP002168658 *
DONALD E. KNUTH: "The Art of Computer Programming", 1998, ADDISON WESLEY, UNITED STATES, XP002168657 *
SEDLAK H ET AL: "EIN PUBLIC-KEY-CODE KRYPTOGRAPHIC-PROZESSOR A PUBLIC KEY CODE CRYPTOGRAPHY PROCESSOR", INFORMATIONSTECHNIK IT,DE,OLDENBOURG VERLAG. MUNCHEN, vol. 28, no. 3, 1986, pages 157 - 161, XP000615686 *

Also Published As

Publication number Publication date
AU3721801A (en) 2001-07-24
DE10101884A1 (de) 2001-10-25
WO2001052051A2 (fr) 2001-07-19
DE10190100D2 (de) 2002-06-06

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