ATE372541T1 - Verbessertes gerät und verfahren für modulare multiplikation und exponentation basierend auf montgomerymultiplikation - Google Patents

Verbessertes gerät und verfahren für modulare multiplikation und exponentation basierend auf montgomerymultiplikation

Info

Publication number
ATE372541T1
ATE372541T1 AT98910967T AT98910967T ATE372541T1 AT E372541 T1 ATE372541 T1 AT E372541T1 AT 98910967 T AT98910967 T AT 98910967T AT 98910967 T AT98910967 T AT 98910967T AT E372541 T1 ATE372541 T1 AT E372541T1
Authority
AT
Austria
Prior art keywords
multiplication
modular
exponentation
improved apparatus
montgomery
Prior art date
Application number
AT98910967T
Other languages
English (en)
Inventor
Isaac Hadad
Benjamin Arazi
Carmi Gressel
Itai Dror
Original Assignee
Milsys Ltd
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
Priority claimed from IL12077697A external-priority patent/IL120776A0/xx
Priority claimed from IL12131197A external-priority patent/IL121311A/xx
Application filed by Milsys Ltd filed Critical Milsys Ltd
Application granted granted Critical
Publication of ATE372541T1 publication Critical patent/ATE372541T1/de

Links

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
    • G06F7/728—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 using Montgomery reduction

Landscapes

  • 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)
  • Complex Calculations (AREA)
  • Error Detection And Correction (AREA)
  • Signal Processing For Digital Recording And Reproducing (AREA)
AT98910967T 1997-05-04 1998-03-29 Verbessertes gerät und verfahren für modulare multiplikation und exponentation basierend auf montgomerymultiplikation ATE372541T1 (de)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
IL12077697A IL120776A0 (en) 1997-05-04 1997-05-04 Apparatus and methods for modular multiplication and exponentiation based on montgomery multiplication
IL12131197A IL121311A (en) 1997-07-14 1997-07-14 Apparatus and method for modular multiplication and exponentiation based on montgomery multiplication

Publications (1)

Publication Number Publication Date
ATE372541T1 true ATE372541T1 (de) 2007-09-15

Family

ID=26323418

Family Applications (1)

Application Number Title Priority Date Filing Date
AT98910967T ATE372541T1 (de) 1997-05-04 1998-03-29 Verbessertes gerät und verfahren für modulare multiplikation und exponentation basierend auf montgomerymultiplikation

Country Status (9)

Country Link
US (1) US6185596B1 (de)
EP (1) EP1008026B1 (de)
JP (2) JP2001527673A (de)
KR (1) KR100684134B1 (de)
AT (1) ATE372541T1 (de)
AU (1) AU6516498A (de)
DE (1) DE69838390T2 (de)
ES (1) ES2293677T3 (de)
WO (1) WO1998050851A1 (de)

Families Citing this family (55)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6317769B1 (en) * 1996-09-18 2001-11-13 International Business Machines Corporation Apparatus for calculating of Bc (mod n) with repeatedly shifting a holding value
US7587044B2 (en) * 1998-01-02 2009-09-08 Cryptography Research, Inc. Differential power analysis method and apparatus
WO1999035782A1 (en) * 1998-01-02 1999-07-15 Cryptography Research, Inc. Leak-resistant cryptographic method and apparatus
IL139935A (en) 1998-06-03 2005-06-19 Cryptography Res Inc Des and other cryptographic processes with leak minimization for smartcards and other cryptosystems
CA2334597C (en) 1998-07-02 2007-09-04 Cryptography Research, Inc. Leak-resistant cryptographic indexed key update
IL128007A (en) * 1999-01-11 2003-02-12 Milsys Ltd Enhancements on compact logic devices and also for accelerating and securing computations in modular arithmetic especially for use in public key cryptographic co-processors designed for elliptic curve and rsa type computations
FR2791157A1 (fr) * 1999-03-17 2000-09-22 St Microelectronics Sa Dispositif et procede de mise en oeuvre d'une operation modulaire elementaire selon la methode de montgomery
FR2791156B1 (fr) 1999-03-17 2001-05-11 St Microelectronics Sa Dispositif et procede de mise en oeuvre d'une operation modulaire elementaire selon la methode de montgomery
FR2791155B1 (fr) * 1999-03-17 2001-05-11 St Microelectronics Sa Dispositif et procede de mise en oeuvre d'une operation modulaire elementaire selon la methode de montgomery
IL135247A0 (en) * 2000-03-23 2003-06-24 Cipherit Ltd Method and apparatus for the calculation of modular multiplicative inverses
US7240204B1 (en) * 2000-03-31 2007-07-03 State Of Oregon Acting By And Through The State Board Of Higher Education On Behalf Of Oregon State University Scalable and unified multiplication methods and apparatus
US6691143B2 (en) 2000-05-11 2004-02-10 Cyberguard Corporation Accelerated montgomery multiplication using plural multipliers
KR100848412B1 (ko) * 2000-05-15 2008-07-28 엠-시스템스 플래쉬 디스크 파이오니어스 리미티드 정수연산필드의 범위를 확장하는 장치 및 방법
FR2809894B1 (fr) * 2000-05-31 2002-10-25 France Telecom Procede de cryptographie, microcircuit pour carte a puce et cartes a puce incluant un tel microcircuit
IL140267A0 (en) 2000-12-13 2003-09-17 Milsys Ltd Dual processor trusted computing environment
US20020116429A1 (en) * 2000-12-19 2002-08-22 International Business Machines Corporation System and method for modular multiplication
US6963977B2 (en) * 2000-12-19 2005-11-08 International Business Machines Corporation Circuits and methods for modular exponentiation
US7607165B2 (en) * 2001-03-09 2009-10-20 The Athena Group, Inc. Method and apparatus for multiplication and/or modular reduction processing
FR2822260A1 (fr) * 2001-03-14 2002-09-20 Bull Sa Procedes et dispositifs pour accelerer le temps de calcul d'un produit de montgomery d'un multiplication et d'une exponentiation modulaire
JP3820909B2 (ja) * 2001-04-24 2006-09-13 ソニー株式会社 楕円曲線暗号処理方法および楕円曲線暗号処理装置、並びにプログラム
DE10127195A1 (de) * 2001-06-05 2002-12-19 Infineon Technologies Ag Prozessor mit interner Speicherkonfiguration
US6917956B2 (en) * 2001-08-14 2005-07-12 Sun Microsystems, Inc. Apparatus and method for efficient modular exponentiation
US20030072442A1 (en) * 2001-10-01 2003-04-17 Blakley George Robert Cisponentiation method, software, and device for exponentiation
US7376235B2 (en) * 2002-04-30 2008-05-20 Microsoft Corporation Methods and systems for frustrating statistical attacks by injecting pseudo data into a data system
US20040010470A1 (en) * 2002-07-09 2004-01-15 Mills Charles A. Anti-piracy system for software and digital entertainment
KR100458031B1 (ko) * 2003-03-14 2004-11-26 삼성전자주식회사 몽고메리 유형의 모듈라 곱셈 장치 및 방법
US7050475B2 (en) 2003-05-02 2006-05-23 Litelaser Llc Waveguide laser
CN1985458B (zh) * 2003-11-16 2013-05-08 桑迪斯克以色列有限公司 增强的自然蒙哥马利指数掩蔽和恢复的方法和装置
EP1692800B1 (de) 2003-11-16 2010-06-30 SanDisk IL Ltd Verbesserte natürliche montgomery-exponentenmaskierung
US7664810B2 (en) * 2004-05-14 2010-02-16 Via Technologies, Inc. Microprocessor apparatus and method for modular exponentiation
US7583717B2 (en) * 2004-08-30 2009-09-01 Videojet Technologies Inc Laser system
WO2006049634A1 (en) * 2004-10-27 2006-05-11 Litelaser L.L.C. Laser alignment system and method
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
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
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
JP4783382B2 (ja) 2006-01-13 2011-09-28 富士通株式会社 モンゴメリ法用乗算剰余計算装置
JP5027422B2 (ja) * 2006-02-09 2012-09-19 ルネサスエレクトロニクス株式会社 剰余演算処理装置
US7805479B2 (en) * 2006-03-28 2010-09-28 Michael Andrew Moshier Scalable, faster method and apparatus for montgomery multiplication
US8229109B2 (en) * 2006-06-27 2012-07-24 Intel Corporation Modular reduction using folding
US20080043406A1 (en) * 2006-08-16 2008-02-21 Secure Computing Corporation Portable computer security device that includes a clip
US7925011B2 (en) * 2006-12-14 2011-04-12 Intel Corporation Method for simultaneous modular exponentiations
US20080263115A1 (en) * 2007-04-17 2008-10-23 Horizon Semiconductors Ltd. Very long arithmetic logic unit for security processor
US8042025B2 (en) * 2007-12-18 2011-10-18 Intel Corporation Determining a message residue
US8402078B2 (en) * 2008-02-26 2013-03-19 International Business Machines Corporation Method, system and computer program product for determining required precision in fixed-point divide operations
US8626816B2 (en) * 2008-02-26 2014-01-07 International Business Machines Corporation Method, system and computer program product for detecting errors in fixed point division operation results
EP2334006B1 (de) * 2009-12-10 2016-03-23 Nxp B.V. Gegen Angriffe mit verborgenen Kanälen gesicherte modulare Potenzierung
FR2974201B1 (fr) 2011-04-18 2013-04-12 Inside Secure Circuit de multiplication de montgomery
FR2974202B1 (fr) 2011-04-18 2013-04-12 Inside Secure Procede de multiplication de montgomery
CN103699358B (zh) * 2013-12-05 2016-11-23 西安交通大学 一种适用于大数的快速模平方运算电路
US10025556B2 (en) * 2014-09-08 2018-07-17 Atmel Corporation Optimized multi-precision division
US11468797B2 (en) 2020-06-24 2022-10-11 Western Digital Technologies, Inc. Low complexity conversion to Montgomery domain
US11508263B2 (en) 2020-06-24 2022-11-22 Western Digital Technologies, Inc. Low complexity conversion to Montgomery domain
US11210067B1 (en) 2020-11-27 2021-12-28 Pqsecure Technologies, Llc Architecture for small and efficient modular multiplication using carry-save adders
TWI802095B (zh) 2021-11-22 2023-05-11 財團法人工業技術研究院 模數乘法電路與對應之計算模數乘法之方法

Family Cites Families (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3621218A (en) * 1967-09-29 1971-11-16 Hitachi Ltd High-speed divider utilizing carry save additions
US4110832A (en) * 1977-04-28 1978-08-29 International Business Machines Corporation Carry save adder
US4514592A (en) 1981-07-27 1985-04-30 Nippon Telegraph & Telephone Public Corporation Cryptosystem
US4538238A (en) * 1983-01-18 1985-08-27 Honeywell Information Systems Inc. Method and apparatus for calculating the residue of a signed binary number
KR19990024971A (ko) * 1997-09-09 1999-04-06 정선종 모듈러 승산장치
US5073870A (en) * 1989-01-30 1991-12-17 Nippon Telegraph And Telephone Corporation Modular multiplication method and the system for processing data
JP2710412B2 (ja) * 1989-06-20 1998-02-10 日本電気株式会社 乗除算回路
US5185714A (en) * 1989-09-19 1993-02-09 Canon Kabushiki Kaisha Arithmetic operation processing apparatus
US5101431A (en) 1990-12-14 1992-03-31 Bell Communications Research, Inc. Systolic array for modular multiplication
US5321752A (en) * 1991-09-05 1994-06-14 Canon Kabushiki Kaisha Method of and apparatus for encryption and decryption of communication data
IL101623A (en) 1992-04-16 1997-06-10 Fortress U & T 2000 Ltd Digital signature device
US5513133A (en) * 1992-11-30 1996-04-30 Fortress U&T Ltd. Compact microelectronic device for performing modular multiplication and exponentiation over large numbers
US5349551A (en) * 1993-07-30 1994-09-20 The United States Of America As Represented By The Director Of National Security Agency Device for and method of preforming an N-bit modular multiplication in approximately N/2 steps
GB2332542B (en) * 1997-12-20 2002-08-07 Motorola Ltd Data processing system for performing multiplication and multiplication method

Also Published As

Publication number Publication date
KR100684134B1 (ko) 2007-02-16
EP1008026B1 (de) 2007-09-05
EP1008026A4 (de) 2000-06-14
DE69838390T2 (de) 2008-05-29
ES2293677T3 (es) 2008-03-16
WO1998050851A1 (en) 1998-11-12
AU6516498A (en) 1998-11-27
KR20010012222A (ko) 2001-02-15
US6185596B1 (en) 2001-02-06
JP2009230153A (ja) 2009-10-08
DE69838390D1 (de) 2007-10-18
JP2001527673A (ja) 2001-12-25
EP1008026A1 (de) 2000-06-14

Similar Documents

Publication Publication Date Title
ATE372541T1 (de) Verbessertes gerät und verfahren für modulare multiplikation und exponentation basierend auf montgomerymultiplikation
DE69716331D1 (de) Schaltung für Modulo-Multiplikations- und Exponentiationsarithmetik
DE69329929T2 (de) Mikroelektronische Kompaktanlage zum Ausführen modulärer Multiplizierung und Potenzierung mit grossen Operanden
DE69325105T2 (de) Datenmultiplexer für mehrwegempfänger
ATE305154T1 (de) Verfahren und vorrichtung zum bereitstellen von rechnerdiensten
WO2001097007A3 (en) Math coprocessor
KR890003321B1 (en) Anti recovery divider
GB2334358A (en) Multiplier for performing 3D graphics interpolations
NO980873L (no) Apparat for utf÷relse av multiplisÚr/addÚroperasjoner pÕ pakkede data
Garcia et al. Algebraic function fields over finite fields with many rational places
EP0377994A3 (de) Gerät zum Ausführen arithmetischer Gleitkommaoperationen
Walter Space/Time trade-offs for higher radix modular multiplication using repeated addition
ATE305683T1 (de) Verfahren zur sicheren verteilung von software
DE69716428T2 (de) Verfahren und apparat zum mehrmaligen ausführen einer operation in antwort auf eine einzige instruktion
EP0180340A2 (de) Verfahren und Gerät zur Summierung von Produkten von Zahlpaaren
TWI263936B (en) Device and method for calculating modular multiplication, and computer product
SE431690B (sv) Forfarande for forskjutning av en urladdningspunkt i en vexelstromsgasurladdningspanel
DE3485774D1 (de) Multiplikationswerk und verfahren zu dessen betrieb.
WO2002048901A3 (de) Verfahren und schaltungsanordnung zur durchführung einer fast fourier transformation sowie anwendung derselben
Bajguz et al. On generalisation of lucas symmetric functions and tchebycheff polynomials
DE69227744T2 (de) Teilmultiplikatorselektor für Multiplikationsschaltung
Archambeau et al. Built-in test compiler in an ASIC environment
SU1522194A1 (ru) Устройство дл умножени
Ries Splittable Jacobi Varieties
Chuang et al. The automatic element routine generator: An automatic programming tool for functional simulator design

Legal Events

Date Code Title Description
RER Ceased as to paragraph 5 lit. 3 law introducing patent treaties