WO2004070497A3 - Modulare exponentiation mit randomisierten exponenten - Google Patents

Modulare exponentiation mit randomisierten exponenten Download PDF

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Publication number
WO2004070497A3
WO2004070497A3 PCT/EP2004/000522 EP2004000522W WO2004070497A3 WO 2004070497 A3 WO2004070497 A3 WO 2004070497A3 EP 2004000522 W EP2004000522 W EP 2004000522W WO 2004070497 A3 WO2004070497 A3 WO 2004070497A3
Authority
WO
WIPO (PCT)
Prior art keywords
randomization
order
modular exponentiation
exponent
auxiliary number
Prior art date
Application number
PCT/EP2004/000522
Other languages
English (en)
French (fr)
Other versions
WO2004070497A2 (de
Inventor
Wieland Fischer
Original Assignee
Infineon Technologies Ag
Wieland Fischer
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, Wieland Fischer filed Critical Infineon Technologies Ag
Priority to EP04704224A priority Critical patent/EP1590731A2/de
Publication of WO2004070497A2 publication Critical patent/WO2004070497A2/de
Publication of WO2004070497A3 publication Critical patent/WO2004070497A3/de
Priority to US11/195,350 priority patent/US7908641B2/en

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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
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/065—Encryption by serially and continuously modifying data stream elements, e.g. stream cipher systems, RC4, SEAL or A5/3
    • H04L9/0656—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher
    • 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
    • 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
    • H04L9/003—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
    • H04L9/14—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using a plurality of keys or algorithms
    • 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
    • H04L2209/08—Randomization, e.g. dummy operations or using noise

Landscapes

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

Abstract

Zur Ermittlung eines Ergebnisses einer modularen Exponentiation wird zur Randomisierung des Exponenten eine Randomisierungs-Hilfszahl auf der Basis des Produkts aus dem öffentlichen Schlüssel und dem privaten Schlüssel weniger '1' eingesetzt. Diese Randomisierungs-Hilfszahl kann ohne spezielle Funktionalitäten aus dem privaten RSA-Datensatz abgeleitet werden. Somit kann eine aufwandsarme Exponenten-Randomisierung für jedes Sicherheitsprotokoll universell durchgeführt werden, um eine gegenüber Seitenkanal-Angriffen sichere digitale Signatur durchzuführen.
PCT/EP2004/000522 2003-02-04 2004-01-22 Modulare exponentiation mit randomisierten exponenten WO2004070497A2 (de)

Priority Applications (2)

Application Number Priority Date Filing Date Title
EP04704224A EP1590731A2 (de) 2003-02-04 2004-01-22 Modulare exponentiation mit randomisierten exponenten
US11/195,350 US7908641B2 (en) 2003-02-04 2005-08-01 Modular exponentiation with randomized exponent

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE10304451A DE10304451B3 (de) 2003-02-04 2003-02-04 Modulare Exponentiation mit randomisiertem Exponenten
DE10304451.5 2003-02-04

Related Child Applications (1)

Application Number Title Priority Date Filing Date
US11/195,350 Continuation US7908641B2 (en) 2003-02-04 2005-08-01 Modular exponentiation with randomized exponent

Publications (2)

Publication Number Publication Date
WO2004070497A2 WO2004070497A2 (de) 2004-08-19
WO2004070497A3 true WO2004070497A3 (de) 2005-01-06

Family

ID=32797314

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/EP2004/000522 WO2004070497A2 (de) 2003-02-04 2004-01-22 Modulare exponentiation mit randomisierten exponenten

Country Status (5)

Country Link
US (1) US7908641B2 (de)
EP (1) EP1590731A2 (de)
KR (1) KR100731387B1 (de)
DE (1) DE10304451B3 (de)
WO (1) WO2004070497A2 (de)

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Publication number Priority date Publication date Assignee Title
EP1939838A1 (de) * 2005-10-19 2008-07-02 Matsushita Electric Industrial Co., Ltd. Informations-sicherheitseinrichtung, informations-sicherheitsverfahren, computerprogramm, computerlesbares aufzeichnungsmedium und integrierte schaltung
EP1840732A1 (de) * 2006-03-31 2007-10-03 Axalto SA Schutz vor Seitenkanalangriffen
US8670557B2 (en) * 2007-09-10 2014-03-11 Spansion Llc Cryptographic system with modular randomization of exponentiation
KR100953716B1 (ko) * 2008-02-28 2010-04-19 고려대학교 산학협력단 Ｃｒｔ-ｒｓａ 기반의 비트 연산을 이용한 디지털 서명방법, 그 장치 및 이를 기록한 기록 매체
EP2669789A3 (de) * 2008-05-07 2014-06-25 Irdeto Corporate B.V. Verschattung von Exponenten
KR101334040B1 (ko) * 2010-01-20 2013-11-28 한국전자통신연구원 대칭키 암호화 시스템의 마스킹 연산 방법 및 장치
DE102010039273B4 (de) * 2010-08-12 2014-12-04 Infineon Technologies Ag Kryptographie-Prozessor, Chipkarte und Verfahren zur Berechnung eines Ergebnisses einer Exponentiation
KR101344402B1 (ko) * 2010-08-12 2013-12-26 한국전자통신연구원 Ｒｓａ 서명 방법 및 장치
FR3010210B1 (fr) * 2013-08-29 2017-01-13 Stmicroelectronics Rousset Protection d'un calcul contre des attaques par canaux caches
WO2015088525A1 (en) * 2013-12-12 2015-06-18 Empire Technology Development, Llc Randomization of processor subunit timing to enhance security
US9444623B2 (en) * 2013-12-20 2016-09-13 Cryptography Research, Inc. Modular exponentiation optimization for cryptographic systems
KR101604009B1 (ko) 2014-05-12 2016-03-17 주식회사 키페어 공인인증을 위한 보안 토큰 및 그 구동 방법
US10181944B2 (en) 2015-06-16 2019-01-15 The Athena Group, Inc. Minimizing information leakage during modular exponentiation and elliptic curve point multiplication
US10367637B2 (en) * 2016-07-22 2019-07-30 Qualcomm Incorporated Modular exponentiation with transparent side channel attack countermeasures
US11902420B2 (en) * 2021-11-23 2024-02-13 Theon Technology Llc Partial cryptographic key transport using one-time pad encryption

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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
DE19828936A1 (de) * 1998-05-29 1999-12-02 Siemens Ag Verfahren und Vorrichtung zum Verarbeiten von Daten
DE10042234A1 (de) * 2000-08-28 2002-03-14 Infineon Technologies Ag Verfahren und Vorrichtung zum Durchführen einer modularen Exponentiation in einem kryptographischen Prozessor
EP1239365A2 (de) * 2001-03-06 2002-09-11 Hitachi, Ltd. Betrugssicheres Verarbeitungsverfahren

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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
DE19828936A1 (de) * 1998-05-29 1999-12-02 Siemens Ag Verfahren und Vorrichtung zum Verarbeiten von Daten
DE10042234A1 (de) * 2000-08-28 2002-03-14 Infineon Technologies Ag Verfahren und Vorrichtung zum Durchführen einer modularen Exponentiation in einem kryptographischen Prozessor
EP1239365A2 (de) * 2001-03-06 2002-09-11 Hitachi, Ltd. Betrugssicheres Verarbeitungsverfahren

Also Published As

Publication number Publication date
US7908641B2 (en) 2011-03-15
KR100731387B1 (ko) 2007-06-21
KR20050106416A (ko) 2005-11-09
DE10304451B3 (de) 2004-09-02
EP1590731A2 (de) 2005-11-02
US20070064930A1 (en) 2007-03-22
WO2004070497A2 (de) 2004-08-19

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