FR2828608B1 - Procede securise de realisation d'une operation d'exponentiation modulaire - Google Patents

Procede securise de realisation d'une operation d'exponentiation modulaire

Info

Publication number
FR2828608B1
FR2828608B1 FR0110671A FR0110671A FR2828608B1 FR 2828608 B1 FR2828608 B1 FR 2828608B1 FR 0110671 A FR0110671 A FR 0110671A FR 0110671 A FR0110671 A FR 0110671A FR 2828608 B1 FR2828608 B1 FR 2828608B1
Authority
FR
France
Prior art keywords
modular exponentiation
secure process
exponentiation operation
parameter
modulo
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
FR0110671A
Other languages
English (en)
Other versions
FR2828608A1 (fr
Inventor
Marc Joye
Karine Villegas
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
Priority to FR0110671A priority Critical patent/FR2828608B1/fr
Priority to PCT/FR2002/002771 priority patent/WO2003014916A1/fr
Priority to CN02820000.4A priority patent/CN1568457A/zh
Priority to US10/486,340 priority patent/US20040184604A1/en
Priority to EP02772476A priority patent/EP1419434A1/fr
Publication of FR2828608A1 publication Critical patent/FR2828608A1/fr
Application granted granted Critical
Publication of FR2828608B1 publication Critical patent/FR2828608B1/fr
Anticipated expiration legal-status Critical
Expired - Fee Related legal-status Critical Current

Links

Classifications

    • 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
    • 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
    • G06F7/723—Modular exponentiation
    • 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
    • H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
    • H04L9/302—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters involving the integer factorization problem, e.g. RSA or quadratic sieve [QS] schemes
    • 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
    • G06F2207/7223—Randomisation as countermeasure against side channel attacks
    • G06F2207/7233—Masking, e.g. (A**e)+r mod n
    • G06F2207/7242—Exponent masking, i.e. key masking, e.g. A**(e+r) mod n; (k+r).P
    • 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
    • G06F2207/7223—Randomisation as countermeasure against side channel attacks
    • G06F2207/7257—Random modification not requiring correction
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/04—Masking or blinding

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Computer Security & Cryptography (AREA)
  • Computing Systems (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Storage Device Security (AREA)
FR0110671A 2001-08-10 2001-08-10 Procede securise de realisation d'une operation d'exponentiation modulaire Expired - Fee Related FR2828608B1 (fr)

Priority Applications (5)

Application Number Priority Date Filing Date Title
FR0110671A FR2828608B1 (fr) 2001-08-10 2001-08-10 Procede securise de realisation d'une operation d'exponentiation modulaire
PCT/FR2002/002771 WO2003014916A1 (fr) 2001-08-10 2002-07-31 Procede securise de realisation d'une operation d'exponentiation modulaire
CN02820000.4A CN1568457A (zh) 2001-08-10 2002-07-31 一种安全的模数取幂运算方法
US10/486,340 US20040184604A1 (en) 2001-08-10 2002-07-31 Secure method for performing a modular exponentiation operation
EP02772476A EP1419434A1 (fr) 2001-08-10 2002-07-31 Procede securise de realisation d'une operation d'exponentiation modulaire

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
FR0110671A FR2828608B1 (fr) 2001-08-10 2001-08-10 Procede securise de realisation d'une operation d'exponentiation modulaire

Publications (2)

Publication Number Publication Date
FR2828608A1 FR2828608A1 (fr) 2003-02-14
FR2828608B1 true FR2828608B1 (fr) 2004-03-05

Family

ID=8866432

Family Applications (1)

Application Number Title Priority Date Filing Date
FR0110671A Expired - Fee Related FR2828608B1 (fr) 2001-08-10 2001-08-10 Procede securise de realisation d'une operation d'exponentiation modulaire

Country Status (5)

Country Link
US (1) US20040184604A1 (fr)
EP (1) EP1419434A1 (fr)
CN (1) CN1568457A (fr)
FR (1) FR2828608B1 (fr)
WO (1) WO2003014916A1 (fr)

Families Citing this family (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2847402B1 (fr) * 2002-11-15 2005-02-18 Gemplus Card Int Procede de division entiere securise contre les attaques a canaux caches
TW586086B (en) * 2002-12-27 2004-05-01 Ind Tech Res Inst Method and apparatus for protecting public key schemes from timing, power and fault attacks
DE10341096A1 (de) 2003-09-05 2005-03-31 Giesecke & Devrient Gmbh Übergang zwischen maskierten Repräsentationen eines Wertes bei kryptographischen Berechnungen
WO2005048008A2 (fr) 2003-11-16 2005-05-26 M-Systems Flash Disk Pioneers Ltd. Masquage naturel d'exposant amélioré effectué avec l'arithmétique de montgomery
KR100652377B1 (ko) * 2004-08-06 2007-02-28 삼성전자주식회사 모듈라 지수승 알고리즘, 기록매체 및 시스템
DE102004061312B4 (de) * 2004-12-20 2007-10-25 Infineon Technologies Ag Vorrichtung und Verfahren zum Detektieren eines potentiellen Angriffs auf eine kryptographische Berechnung
FR2884004B1 (fr) 2005-03-30 2007-06-29 Oberthur Card Syst Sa Procede de traitement de donnees impliquant une exponentiation modulaire et un dispositif associe
WO2007020566A1 (fr) * 2005-08-19 2007-02-22 Nxp B.V. Montage de circuit et procede associe pour l'application d'une operation non dans un calcul cryptographique
US8265265B2 (en) * 2005-08-19 2012-09-11 Nxp B.V. Circuit arrangement and method for RSA key generation
US8280041B2 (en) * 2007-03-12 2012-10-02 Inside Secure Chinese remainder theorem-based computation method for cryptosystems
KR101383690B1 (ko) * 2008-12-10 2014-04-09 한국전자통신연구원 안전한 멀티캐스트 통신을 위한 그룹키 관리방법

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5991415A (en) * 1997-05-12 1999-11-23 Yeda Research And Development Co. Ltd. At The Weizmann Institute Of Science Method and apparatus for protecting public key schemes from timing and fault attacks
DE19963408A1 (de) * 1999-12-28 2001-08-30 Giesecke & Devrient Gmbh Tragbarer Datenträger mit Zugriffsschutz durch Schlüsselteilung

Also Published As

Publication number Publication date
US20040184604A1 (en) 2004-09-23
FR2828608A1 (fr) 2003-02-14
EP1419434A1 (fr) 2004-05-19
CN1568457A (zh) 2005-01-19
WO2003014916A1 (fr) 2003-02-20

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Legal Events

Date Code Title Description
ST Notification of lapse

Effective date: 20100430