WO2003093969A3 - Berechnen eines ergebnisses einer modularen multiplikation - Google Patents

Berechnen eines ergebnisses einer modularen multiplikation Download PDF

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Publication number
WO2003093969A3
WO2003093969A3 PCT/EP2003/004426 EP0304426W WO03093969A3 WO 2003093969 A3 WO2003093969 A3 WO 2003093969A3 EP 0304426 W EP0304426 W EP 0304426W WO 03093969 A3 WO03093969 A3 WO 03093969A3
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WO
WIPO (PCT)
Prior art keywords
operands
length
mmd
bits
modulus
Prior art date
Application number
PCT/EP2003/004426
Other languages
English (en)
French (fr)
Other versions
WO2003093969A2 (de
Inventor
Wieland Fischer
Holger Sedlak
Jean-Pierre Seifert
Original Assignee
Infineon Technologies Ag
Wieland Fischer
Holger Sedlak
Jean-Pierre Seifert
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, Holger Sedlak, Jean-Pierre Seifert filed Critical Infineon Technologies Ag
Priority to AU2003233192A priority Critical patent/AU2003233192A1/en
Priority to DE50306309T priority patent/DE50306309D1/de
Priority to EP03727389A priority patent/EP1499954B1/de
Priority to CN03809672.2A priority patent/CN1650254B/zh
Publication of WO2003093969A2 publication Critical patent/WO2003093969A2/de
Publication of WO2003093969A3 publication Critical patent/WO2003093969A3/de
Priority to US10/977,561 priority patent/US7558817B2/en

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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
    • G06F7/722—Modular multiplication

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Executing Machine-Instructions (AREA)
  • Complex Calculations (AREA)
  • Advance Control (AREA)

Abstract

Zum Berechnen eines Ergebnisses einer modularen Multiplikation eines ersten Operanden (A) und eines zweiten Operanden (B) bezüglich eines Moduls (N), welche eine Länge von 2 n Bits haben, werden die Operanden und der Modul in Unteroperanden der halben Länge zerlegt und einer Steuerungseinrichtung (14) zugeführt, die eine MMD-Einrichtung zum Ausführen eines MultModDiv-Operation gemäß einer vorbestimmten Schrittsequenz mit entsprechenden Eingangsoperanden (12a, 12b) und MMD-Modulen (12c) ansteuert, um ganzzahlige Quotientenwerte (Q(i)) und Restwerte (R(i)) bezüglich des MMD-Moduls an einem Ausgang (12d) zu erhalten. Eine Zusammenfassungseinrichtung (16) ist wirksam, um ganzzahlige Quotientenwerte und Restwerte aus vorbestimmten Schritten der Schrittsequenz zusammenzufassen, um das Ergebnis zu erhalten. Durch Zerlegen einer modularen Multiplikation von Operanden z. B. der Länge von 2 n Bits in mehrere MMD-Operationen mit Operanden der Länge von n Bits, also der halben Länge, wird es ermöglicht, daß auf effiziente Art und Weise kryptographische Algorithmen mit langen Operanden auf einem für kürzere Operanden entwickelten Rechenwerk ausgeführt werden können, so daß zunehmende Sicherheitsanforderungen nach längeren Schlüsseln mit bestehenden Schaltungen effizient erfüllt werden.
PCT/EP2003/004426 2002-04-29 2003-04-28 Berechnen eines ergebnisses einer modularen multiplikation WO2003093969A2 (de)

Priority Applications (5)

Application Number Priority Date Filing Date Title
AU2003233192A AU2003233192A1 (en) 2002-04-29 2003-04-28 Device and method for calculating a result of a modular multiplication
DE50306309T DE50306309D1 (de) 2002-04-29 2003-04-28 Berechnung eines ergebnisses einer modularen multiplikation
EP03727389A EP1499954B1 (de) 2002-04-29 2003-04-28 Berechnung eines ergebnisses einer modularen multiplikation
CN03809672.2A CN1650254B (zh) 2002-04-29 2003-04-28 计算模数乘法之结果的装置及方法
US10/977,561 US7558817B2 (en) 2002-04-29 2004-10-28 Apparatus and method for calculating a result of a modular multiplication

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE2002119158 DE10219158B4 (de) 2002-04-29 2002-04-29 Vorrichtung und Verfahren zum Berechnen eines Ergebnisses einer modularen Multiplikation
DE10219158.1 2002-04-29

Related Child Applications (1)

Application Number Title Priority Date Filing Date
US10/977,561 Continuation US7558817B2 (en) 2002-04-29 2004-10-28 Apparatus and method for calculating a result of a modular multiplication

Publications (2)

Publication Number Publication Date
WO2003093969A2 WO2003093969A2 (de) 2003-11-13
WO2003093969A3 true WO2003093969A3 (de) 2004-10-14

Family

ID=29264903

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/EP2003/004426 WO2003093969A2 (de) 2002-04-29 2003-04-28 Berechnen eines ergebnisses einer modularen multiplikation

Country Status (6)

Country Link
EP (1) EP1499954B1 (de)
CN (1) CN1650254B (de)
AU (1) AU2003233192A1 (de)
DE (2) DE10219158B4 (de)
TW (1) TW200403584A (de)
WO (1) WO2003093969A2 (de)

Families Citing this family (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10219161A1 (de) 2002-04-29 2003-11-20 Infineon Technologies Ag Vorrichtung und Verfahren zum Umrechnen eines Terms
FR2859030B1 (fr) * 2003-08-21 2005-11-04 Gemplus Card Int Procede de realisation d'une multiplication modulaire et procede de realisation d'une multiplication euclidienne sur des nombres de 2n bits
DE102004016412A1 (de) * 2004-03-30 2005-10-27 Cv Cryptovision Gmbh Vorrichtung und Verfahren zur effizienten und sicheren modularen Multiplikation zweier Langzahlen
KR100652376B1 (ko) * 2004-07-29 2006-12-01 삼성전자주식회사 분리 연산 가능한 구조를 가지는 모듈러 곱셈기와 이를포함하는 암호화 시스템
DE102006025569A1 (de) 2005-10-28 2007-05-03 Infineon Technologies Ag Vorrichtung und Verfahren zum Berechnen einer Multiplikations-Additions-Operation und zum Berechnen eines Ergebnisses einer modularen Multiplikation
DE102006025713B9 (de) 2005-10-28 2013-10-17 Infineon Technologies Ag Kryptographie-Vorrichtung und Kryptographie-Verfahren zum Berechnen eines Ergebnisses einer modularen Multiplikation
DE102006025673B9 (de) 2005-10-28 2010-12-16 Infineon Technologies Ag Rechenwerk zum Reduzieren einer Eingabe-Zahl bezüglich eines Moduls
DE102006025677B4 (de) 2005-10-28 2020-03-12 Infineon Technologies Ag Vorrichtung und Verfahren zum Berechnen eines Ergebnisses einer Summe mit einem Rechenwerk mit begrenzter Wortlänge
CN104104504B (zh) * 2014-07-22 2017-05-10 大唐微电子技术有限公司 一种rsa解密的方法及装置
IL239880B (en) * 2015-07-09 2018-08-30 Kaluzhny Uri Simplified montgomery multiplication
IL244842A0 (en) * 2016-03-30 2016-07-31 Winbond Electronics Corp Efficient non-modular multiplexing is protected against side-channel attacks
CN110088727A (zh) * 2016-12-12 2019-08-02 皇家飞利浦有限公司 被布置为计算整数的乘积的电子计算设备
TWI784406B (zh) * 2020-06-04 2022-11-21 熵碼科技股份有限公司 採用迭代計算的模數運算電路
US20220121424A1 (en) * 2020-10-21 2022-04-21 PUFsecurity Corporation Device and Method of Handling a Modular Multiplication

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2002033885A1 (en) * 2000-10-17 2002-04-25 Novacatus Invest Ab Modular multiplication for rsa and other assymetric encryption/decryption

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3631992A1 (de) * 1986-03-05 1987-11-05 Holger Sedlak Kryptographie-verfahren und kryptographie-prozessor zur durchfuehrung des verfahrens
CA2008774C (en) * 1989-01-30 1999-10-05 Hikaru Morita Modular multiplication method and the system for processing data
US6366940B1 (en) * 1998-03-02 2002-04-02 Matsushita Electric Industrial Co., Ltd. High-speed modular multiplication apparatus achieved in small circuit

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2002033885A1 (en) * 2000-10-17 2002-04-25 Novacatus Invest Ab Modular multiplication for rsa and other assymetric encryption/decryption

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
DUGDALE M: "RESIDUE MULTIPLIERS USING FACTORED DECOMPOSITION", IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: ANALOG AND DIGITAL SIGNAL PROCESSING, IEEE INC. NEW YORK, US, vol. 41, no. 9, 1 September 1994 (1994-09-01), pages 623 - 627, XP000468163, ISSN: 1057-7130 *
FISCHER W ET AL: "INCREASING THE BITLENGTH OF A CRYPTO-COPROCESSOR", CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS. INTERNATIONAL WORKSHOP, XX, XX, 13 August 2002 (2002-08-13), pages 71 - 81, XP001160522 *
PAILLIER P: "Low-cost double-size modular exponentiation or how to stretch your cryptoprocessor", PUBLIC KEY CRYPTOGRAPHY. SECOND INTERNATIONAL WORKSHOP ON PRACTICE AND THEORY IN PUBLIC KEY CRYPTOGRAPHY, PKC'99. PROCEEDINGS, PUBLIC KEY CRYPTOGRAPHY. SECOND INTERNATIONAL WORKSHOP ON PRACTICE AND THEORY IN PUBLIC KEY CRYPTOGRAPHY, PKC'99. PROCEEDIN, 1999, Berlin, Germany, Springer-Verlag, Germany, pages 223 - 234, XP002274671, ISBN: 3-540-65644-8 *

Also Published As

Publication number Publication date
TW200403584A (en) 2004-03-01
EP1499954B1 (de) 2007-01-17
DE10219158B4 (de) 2004-12-09
AU2003233192A1 (en) 2003-11-17
DE50306309D1 (de) 2007-03-08
AU2003233192A8 (en) 2003-11-17
WO2003093969A2 (de) 2003-11-13
EP1499954A2 (de) 2005-01-26
CN1650254B (zh) 2011-01-26
DE10219158A1 (de) 2003-11-20
CN1650254A (zh) 2005-08-03

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