FR2885711B1 - Procede et materiel modulaire et aleatoire pour la reduction polynomiale - Google Patents

Procede et materiel modulaire et aleatoire pour la reduction polynomiale

Info

Publication number
FR2885711B1
FR2885711B1 FR0504779A FR0504779A FR2885711B1 FR 2885711 B1 FR2885711 B1 FR 2885711B1 FR 0504779 A FR0504779 A FR 0504779A FR 0504779 A FR0504779 A FR 0504779A FR 2885711 B1 FR2885711 B1 FR 2885711B1
Authority
FR
France
Prior art keywords
modular
polynomial reduction
random equipment
random
equipment
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
FR0504779A
Other languages
English (en)
Other versions
FR2885711A1 (fr
Inventor
Vincent Dupaquis
Michel Douguet
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.)
Rambus Inc
Original Assignee
Atmel Corp
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 Atmel Corp filed Critical Atmel Corp
Priority to FR0504779A priority Critical patent/FR2885711B1/fr
Priority to US11/203,939 priority patent/US7805480B2/en
Priority to PCT/US2006/013795 priority patent/WO2006124160A2/fr
Priority to EP06749987.1A priority patent/EP1889398B1/fr
Priority to KR1020077029023A priority patent/KR101252318B1/ko
Priority to JP2008511127A priority patent/JP4875700B2/ja
Priority to CN2006800209415A priority patent/CN101194457B/zh
Priority to TW095116180A priority patent/TWI386818B/zh
Publication of FR2885711A1 publication Critical patent/FR2885711A1/fr
Application granted granted Critical
Publication of FR2885711B1 publication Critical patent/FR2885711B1/fr
Priority to US12/887,361 priority patent/US20110016167A1/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

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
    • G06F7/724—Finite field arithmetic
    • G06F7/726—Inversion; Reciprocal calculation; Division of elements of a finite field
    • 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
    • G06F7/724—Finite field arithmetic
    • 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

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)
  • Navigation (AREA)
FR0504779A 2005-05-12 2005-05-12 Procede et materiel modulaire et aleatoire pour la reduction polynomiale Expired - Fee Related FR2885711B1 (fr)

Priority Applications (9)

Application Number Priority Date Filing Date Title
FR0504779A FR2885711B1 (fr) 2005-05-12 2005-05-12 Procede et materiel modulaire et aleatoire pour la reduction polynomiale
US11/203,939 US7805480B2 (en) 2005-05-12 2005-08-15 Randomized modular polynomial reduction method and hardware therefor
EP06749987.1A EP1889398B1 (fr) 2005-05-12 2006-04-12 Méthode de réduction polynomiale modulaire randomisée et matériel destiné à la mise en oeuvre de ce procédé
KR1020077029023A KR101252318B1 (ko) 2005-05-12 2006-04-12 랜덤화된 모듈러 다항식 약분 방법 및 그 방법을 위한하드웨어
PCT/US2006/013795 WO2006124160A2 (fr) 2005-05-12 2006-04-12 Methode de reduction polynomiale modulaire randomisee et materiel destine a la mise en oeuvre de ce procede
JP2008511127A JP4875700B2 (ja) 2005-05-12 2006-04-12 ランダム化されたモジュラー多項式のリダクション方法およびそのためのハードウェア
CN2006800209415A CN101194457B (zh) 2005-05-12 2006-04-12 随机模数化多项式约简方法及其硬件
TW095116180A TWI386818B (zh) 2005-05-12 2006-05-08 密碼安全模多項式簡化方法及執行該方法之計算硬體
US12/887,361 US20110016167A1 (en) 2005-05-12 2010-09-21 Randomized modular polynomial reduction method and hardware therefor

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
FR0504779A FR2885711B1 (fr) 2005-05-12 2005-05-12 Procede et materiel modulaire et aleatoire pour la reduction polynomiale

Publications (2)

Publication Number Publication Date
FR2885711A1 FR2885711A1 (fr) 2006-11-17
FR2885711B1 true FR2885711B1 (fr) 2007-07-06

Family

ID=35431948

Family Applications (1)

Application Number Title Priority Date Filing Date
FR0504779A Expired - Fee Related FR2885711B1 (fr) 2005-05-12 2005-05-12 Procede et materiel modulaire et aleatoire pour la reduction polynomiale

Country Status (5)

Country Link
US (2) US7805480B2 (fr)
JP (1) JP4875700B2 (fr)
CN (1) CN101194457B (fr)
FR (1) FR2885711B1 (fr)
TW (1) TWI386818B (fr)

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FR2862454A1 (fr) * 2003-11-18 2005-05-20 Atmel Corp Methode de reduction modulaire aleatoire et equipement associe
FR2885711B1 (fr) * 2005-05-12 2007-07-06 Atmel Corp Procede et materiel modulaire et aleatoire pour la reduction polynomiale
US7961877B2 (en) * 2006-12-14 2011-06-14 Intel Corporation Factoring based modular exponentiation
US8144864B2 (en) * 2007-12-28 2012-03-27 Intel Corporation Method for speeding up the computations for characteristic 2 elliptic curve cryptographic systems
TWI406548B (zh) * 2010-10-27 2013-08-21 Univ Southern Taiwan 橢圓曲線加密運算電路
US9471308B2 (en) 2013-01-23 2016-10-18 International Business Machines Corporation Vector floating point test data class immediate instruction
US9715385B2 (en) 2013-01-23 2017-07-25 International Business Machines Corporation Vector exception code
US9513906B2 (en) 2013-01-23 2016-12-06 International Business Machines Corporation Vector checksum instruction
US9804840B2 (en) 2013-01-23 2017-10-31 International Business Machines Corporation Vector Galois Field Multiply Sum and Accumulate instruction
US9778932B2 (en) 2013-01-23 2017-10-03 International Business Machines Corporation Vector generate mask instruction
US9823924B2 (en) 2013-01-23 2017-11-21 International Business Machines Corporation Vector element rotate and insert under mask instruction
CN103699357B (zh) * 2013-12-05 2016-11-23 西安交通大学 一种用于模乘和模平方的快速模约简算法电路
US9425961B2 (en) * 2014-03-24 2016-08-23 Stmicroelectronics S.R.L. Method for performing an encryption of an AES type, and corresponding system and computer program product
IL239880B (en) * 2015-07-09 2018-08-30 Kaluzhny Uri Simplified montgomery multiplication
CN106254059B (zh) * 2016-07-26 2020-03-20 华为技术有限公司 一种运算方法和安全芯片
JP6602276B2 (ja) * 2016-08-29 2019-11-06 キヤノン株式会社 情報処理装置、情報処理装置の制御方法及びプログラム
US10833868B2 (en) * 2017-12-06 2020-11-10 Intel Corporation Direct anonymous attestation-based apparatus and method
US10218494B1 (en) * 2018-02-23 2019-02-26 ISARA Corporation Performing block form reductions modulo non-Mersenne primes in cryptographic protocols
DE102018113475A1 (de) * 2018-06-06 2019-12-12 Infineon Technologies Ag Rechenwerk zum rechnen mit maskierten daten
WO2020145503A1 (fr) * 2019-01-10 2020-07-16 Crypto Lab Inc. Appareil de traitement de messages approximativement chiffrés et procédés associés
CN112506470B (zh) * 2020-12-21 2024-07-02 深圳比特微电子科技有限公司 芯片和计算系统
KR20220105495A (ko) * 2021-01-20 2022-07-27 삼성전자주식회사 부채널 공격에 내성이 있는 모듈라 곱셈을 위한 장치 및 방법
US11502819B2 (en) * 2021-01-21 2022-11-15 Nxp B.V. Efficient masked polynomial comparison
CN113253972A (zh) * 2021-05-13 2021-08-13 南京航空航天大学 一种lac中稀疏多项式乘法加速器的fpga实现方法

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US5144574A (en) * 1989-01-30 1992-09-01 Nippon Telegraph And Telephone Corporation Modular multiplication method and the system for processing data
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EP0611506B1 (fr) * 1991-11-05 1997-04-09 THOMSON multimedia Procede, appareil emetteur et appareil recepteur destines a l'exploitation modulo
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FR2856537B1 (fr) 2003-06-18 2005-11-04 Gemplus Card Int Procede de contre-mesure par masquage de l'accumulateur dans un composant electronique mettant en oeuvre un algorithme de cryptographie a cle publique
FR2862454A1 (fr) * 2003-11-18 2005-05-20 Atmel Corp Methode de reduction modulaire aleatoire et equipement associe
EP1889398B1 (fr) 2005-05-12 2016-01-13 Inside Secure Méthode de réduction polynomiale modulaire randomisée et matériel destiné à la mise en oeuvre de ce procédé
FR2885711B1 (fr) * 2005-05-12 2007-07-06 Atmel Corp Procede et materiel modulaire et aleatoire pour la reduction polynomiale
US8024391B2 (en) * 2006-11-06 2011-09-20 Atmel Rousset S.A.S. Modular multiplication method with precomputation using one known operand

Also Published As

Publication number Publication date
CN101194457A (zh) 2008-06-04
JP4875700B2 (ja) 2012-02-15
TW200703037A (en) 2007-01-16
FR2885711A1 (fr) 2006-11-17
US20100023572A1 (en) 2010-01-28
US7805480B2 (en) 2010-09-28
CN101194457B (zh) 2011-06-01
US20110016167A1 (en) 2011-01-20
TWI386818B (zh) 2013-02-21
JP2008541166A (ja) 2008-11-20

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Legal Events

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Owner name: INSIDE SECURE, FR

Effective date: 20121115

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Effective date: 20191119

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Effective date: 20200402

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RG Lien (pledge) cancelled

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