WO2003023605A3 - Vorrichtung und verfahren zum berechnen eines ergebnisses einer modularen exponentiation - Google Patents

Vorrichtung und verfahren zum berechnen eines ergebnisses einer modularen exponentiation Download PDF

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Publication number
WO2003023605A3
WO2003023605A3 PCT/EP2002/009405 EP0209405W WO03023605A3 WO 2003023605 A3 WO2003023605 A3 WO 2003023605A3 EP 0209405 W EP0209405 W EP 0209405W WO 03023605 A3 WO03023605 A3 WO 03023605A3
Authority
WO
WIPO (PCT)
Prior art keywords
result
rsa
calculating
auxiliary
modular exponentiation
Prior art date
Application number
PCT/EP2002/009405
Other languages
English (en)
French (fr)
Other versions
WO2003023605A2 (de
Inventor
Jean-Pierre Seifert
Joachim Velten
Original Assignee
Infineon Technologies Ag
Jean-Pierre Seifert
Joachim Velten
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 Infineon Technologies Ag, Jean-Pierre Seifert, Joachim Velten filed Critical Infineon Technologies Ag
Priority to EP02797920A priority Critical patent/EP1423786A2/de
Publication of WO2003023605A2 publication Critical patent/WO2003023605A2/de
Priority to US10/789,373 priority patent/US7248700B2/en
Publication of WO2003023605A3 publication Critical patent/WO2003023605A3/de

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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
    • G06F7/723—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
    • H04L9/002—Countermeasures against attacks on cryptographic mechanisms
    • H04L9/004—Countermeasures against attacks on cryptographic mechanisms for fault attacks
    • 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
    • G06F2207/7233—Masking, e.g. (A**e)+r mod n
    • G06F2207/7247—Modulo masking, e.g. A**e mod (n*r)
    • 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
    • G06F2207/7271—Fault verification, e.g. comparing two values which should be the same, unless a computational fault occurred

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • General Physics & Mathematics (AREA)
  • Physics & Mathematics (AREA)
  • Computing Systems (AREA)
  • Mathematical Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Storage Device Security (AREA)

Abstract

Bei einer Vorrichtung zum Berechnen eines Ergebnisses einer modularen Exponentiation wird der chinesische Restsatz (CRT) verwendet, bei dem unter Verwendung von zwei Hilfsexponenten und zwei Untermodulen zwei Hilfs-Exponentiationen berechnet werden. Um die Sicherheit der RSA-CRT-Berechnung gegenüber kryptographischen Attacken zu verbessern, wird eine Randomisierung der Hilfs-Exponenten und/oder eine Veränderung der Untermodule durchgeführt. Damit ist eine sichere RSA-Entschlüsselung bzw. RSA-Verschlüsselung mittels des rechenzeiteffizienten chinesischen Restsatzes gegeben.
PCT/EP2002/009405 2001-09-06 2002-08-22 Vorrichtung und verfahren zum berechnen eines ergebnisses einer modularen exponentiation WO2003023605A2 (de)

Priority Applications (2)

Application Number Priority Date Filing Date Title
EP02797920A EP1423786A2 (de) 2001-09-06 2002-08-22 Vorrichtung und verfahren zum berechnen eines ergebnisses einer modularen exponentiation
US10/789,373 US7248700B2 (en) 2001-09-06 2004-02-27 Device and method for calculating a result of a modular exponentiation

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE10143728.5 2001-09-06
DE10143728A DE10143728B4 (de) 2001-09-06 2001-09-06 Vorrichtung und Verfahren zum Berechnen eines Ergebnisses einer modularen Exponentiation

Related Child Applications (1)

Application Number Title Priority Date Filing Date
US10/789,373 Continuation US7248700B2 (en) 2001-09-06 2004-02-27 Device and method for calculating a result of a modular exponentiation

Publications (2)

Publication Number Publication Date
WO2003023605A2 WO2003023605A2 (de) 2003-03-20
WO2003023605A3 true WO2003023605A3 (de) 2004-04-01

Family

ID=7697946

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/EP2002/009405 WO2003023605A2 (de) 2001-09-06 2002-08-22 Vorrichtung und verfahren zum berechnen eines ergebnisses einer modularen exponentiation

Country Status (5)

Country Link
US (1) US7248700B2 (de)
EP (1) EP1423786A2 (de)
CN (1) CN1554047A (de)
DE (1) DE10143728B4 (de)
WO (1) WO2003023605A2 (de)

Families Citing this family (21)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2830146B1 (fr) * 2001-09-24 2003-10-31 Gemplus Card Int Procede de mise en oeuvre, dans un composant electronique, d'un algorithme de cryptographie et composant correspondant
DE10222212A1 (de) 2002-05-16 2003-12-04 Giesecke & Devrient Gmbh Ausspähungsgeschützte modulare Inversion
WO2004032411A1 (de) * 2002-09-11 2004-04-15 Giesecke & Devrient Gmbh Geschützte kryptographische berechnung
DE10304451B3 (de) * 2003-02-04 2004-09-02 Infineon Technologies Ag Modulare Exponentiation mit randomisiertem Exponenten
FR2858496B1 (fr) 2003-07-31 2005-09-30 Gemplus Card Int Procede pour la mise en oeuvre securisee d'un algorithme de cryptographie de type rsa et composant correspondant
JP4626148B2 (ja) * 2004-01-07 2011-02-02 株式会社日立製作所 復号または署名作成におけるべき乗剰余算の計算方法
US7426749B2 (en) * 2004-01-20 2008-09-16 International Business Machines Corporation Distributed computation in untrusted computing environments using distractive computational units
FR2880148A1 (fr) * 2004-12-23 2006-06-30 Gemplus Sa Procede d'exponentiation securisee et compacte pour la cryptographie
FR2887351A1 (fr) * 2005-06-16 2006-12-22 St Microelectronics Sa Protection d'un calcul d'exponentiation modulaire effectue par un circuit integre
FR2888690A1 (fr) * 2005-07-13 2007-01-19 Gemplus Sa Procede cryptographique pour la mise en oeuvre securisee d'une exponentiation et composant associe
US9313027B2 (en) * 2005-12-29 2016-04-12 Proton World International N.V. Protection of a calculation performed by an integrated circuit
US8150029B2 (en) * 2005-12-29 2012-04-03 Proton World International N.V. Detection of a disturbance in a calculation performed by an integrated circuit
FR2898199A1 (fr) * 2006-03-02 2007-09-07 Gemplus Sa Procede de securisation de l'execution d'une suite d'etapes logiquement enchainees
US20080104402A1 (en) * 2006-09-28 2008-05-01 Shay Gueron Countermeasure against fault-based attack on RSA signature verification
US8280041B2 (en) * 2007-03-12 2012-10-02 Inside Secure Chinese remainder theorem-based computation method for cryptosystems
EP1998491A1 (de) * 2007-05-31 2008-12-03 Thomson Licensing Verfahren zur Berechnung von komprimierten RSA-Moduli
FR2919739B1 (fr) * 2007-08-03 2009-12-04 Oberthur Card Syst Sa Procede de traitement de donnees protege contre les attaques par generation de fautes et dispositif associe
CN100576226C (zh) * 2008-07-10 2009-12-30 浙江工业大学 基于中国剩余定理的数据库加密方法
FR2977952A1 (fr) * 2011-07-13 2013-01-18 St Microelectronics Rousset Protection d'un calcul d'exponentiation modulaire par multiplication par une quantite aleatoire
CN103580869B (zh) * 2013-11-06 2016-09-21 北京华大信安科技有限公司 一种crt-rsa签名方法及装置
FR3112003B1 (fr) * 2020-06-26 2023-03-03 Idemia France Procede de traitement cryptographique, dispositif electronique et programme d'ordinateur associes

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2318892A (en) * 1996-10-31 1998-05-06 Motorola Ltd Co-processor for performing modular multiplication
WO1998052319A1 (en) * 1997-05-12 1998-11-19 Yeda Research And Development Co. Ltd. Improved method and apparatus for protecting public key schemes from timing and fault attacks
WO1999035782A1 (en) * 1998-01-02 1999-07-15 Cryptography Research, Inc. Leak-resistant cryptographic method and apparatus

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA1318027C (en) * 1987-10-12 1993-05-18 Jun Takayama Method and apparatus for encoding and decoding data in residue number system
US6282290B1 (en) * 1997-03-28 2001-08-28 Mykotronx, Inc. High speed modular exponentiator
DE19811833A1 (de) * 1998-03-18 1999-09-30 Siemens Ag Schlüsselaustauschprotokoll
JP3551853B2 (ja) * 1999-08-27 2004-08-11 日本電気株式会社 αＹａ＋βＸｂ＋１＝０という形の定義方程式をもつ代数曲線暗号における安全なパラメータの生成装置、生成方法、および記録媒体

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2318892A (en) * 1996-10-31 1998-05-06 Motorola Ltd Co-processor for performing modular multiplication
WO1998052319A1 (en) * 1997-05-12 1998-11-19 Yeda Research And Development Co. Ltd. Improved method and apparatus for protecting public key schemes from timing and fault attacks
WO1999035782A1 (en) * 1998-01-02 1999-07-15 Cryptography Research, Inc. Leak-resistant cryptographic method and apparatus

Also Published As

Publication number Publication date
EP1423786A2 (de) 2004-06-02
US7248700B2 (en) 2007-07-24
DE10143728A1 (de) 2003-04-03
US20040215685A1 (en) 2004-10-28
WO2003023605A2 (de) 2003-03-20
DE10143728B4 (de) 2004-09-02
CN1554047A (zh) 2004-12-08

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