FR2971600B1 - Dispositif et procede de calcul d'un resultat d'une multiplication scalaire - Google Patents

Dispositif et procede de calcul d'un resultat d'une multiplication scalaire Download PDF

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Publication number
FR2971600B1
FR2971600B1 FR1200280A FR1200280A FR2971600B1 FR 2971600 B1 FR2971600 B1 FR 2971600B1 FR 1200280 A FR1200280 A FR 1200280A FR 1200280 A FR1200280 A FR 1200280A FR 2971600 B1 FR2971600 B1 FR 2971600B1
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FR
France
Prior art keywords
calculating
result
scalar multiplication
scalar
multiplication
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
FR1200280A
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English (en)
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FR2971600A1 (fr
Inventor
Bernd Meyer
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.)
Infineon Technologies AG
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Infineon Technologies AG
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Filing date
Publication date
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Publication of FR2971600A1 publication Critical patent/FR2971600A1/fr
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Publication of FR2971600B1 publication Critical patent/FR2971600B1/fr
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

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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
    • G06F7/724—Finite field arithmetic
    • G06F7/725—Finite field arithmetic over elliptic curves
    • 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
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
    • 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
    • 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)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computing Systems (AREA)
  • Computational Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Complex Calculations (AREA)
  • Storage Device Security (AREA)
  • Executing Machine-Instructions (AREA)
FR1200280A 2011-02-11 2012-01-31 Dispositif et procede de calcul d'un resultat d'une multiplication scalaire Expired - Fee Related FR2971600B1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US13/025,221 US9400636B2 (en) 2011-02-11 2011-02-11 Apparatus and method for calculating a result in a scalar multiplication
US13025221 2011-02-11

Publications (2)

Publication Number Publication Date
FR2971600A1 FR2971600A1 (fr) 2012-08-17
FR2971600B1 true FR2971600B1 (fr) 2018-03-16

Family

ID=46579826

Family Applications (1)

Application Number Title Priority Date Filing Date
FR1200280A Expired - Fee Related FR2971600B1 (fr) 2011-02-11 2012-01-31 Dispositif et procede de calcul d'un resultat d'une multiplication scalaire

Country Status (4)

Country Link
US (1) US9400636B2 (fr)
CN (1) CN102638341B (fr)
DE (1) DE102012202015B4 (fr)
FR (1) FR2971600B1 (fr)

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* Cited by examiner, † Cited by third party
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US8542820B2 (en) * 2009-02-05 2013-09-24 Infineon Technologies Ag Apparatus for calculating a result of a scalar multiplication
US9400636B2 (en) * 2011-02-11 2016-07-26 Infineon Technologies Ag Apparatus and method for calculating a result in a scalar multiplication
FR3001315B1 (fr) * 2013-01-18 2016-05-06 Inside Secure Procede de cryptographie comprenant une operation de multiplication par un scalaire ou une exponentiation
FR3010210B1 (fr) * 2013-08-29 2017-01-13 Stmicroelectronics Rousset Protection d'un calcul contre des attaques par canaux caches
CN104601322A (zh) * 2013-10-31 2015-05-06 上海华虹集成电路有限责任公司 用于密码芯片中三元扩域的蒙哥马利阶梯算法
FR3016987B1 (fr) * 2014-01-29 2017-07-21 Morpho Echelle de montgomery desequilibree
US10268605B1 (en) * 2014-04-30 2019-04-23 Altera Corporation Hybrid architecture for signal processing and signal processing accelerator
CN106716344B (zh) 2014-10-03 2021-04-30 密码研究公司 用于密码运算的指数分裂
US9584320B1 (en) * 2014-12-23 2017-02-28 EMC IP Holding Company LLC Blinding function in elliptic curve cryptography
US9590805B1 (en) * 2014-12-23 2017-03-07 EMC IP Holding Company LLC Ladder-based cryptographic techniques using pre-computed points
CN105281889B (zh) * 2015-11-16 2019-02-01 中国电子科技集团公司第三十研究所 一种基于侧信道泄漏的算法还原方法和系统
US10275391B2 (en) * 2017-01-23 2019-04-30 International Business Machines Corporation Combining of several execution units to compute a single wide scalar result
EP3503459B1 (fr) * 2017-12-22 2021-04-21 Secure-IC SAS Dispositif et procédé pour protéger l'exécution d'une opération cryptographique
KR20200046481A (ko) 2018-10-24 2020-05-07 삼성전자주식회사 난수 생성기, 이를 포함하는 암호화 장치 및 이의 동작 방법
IT201900025567A1 (it) * 2019-12-24 2021-06-24 St Microelectronics Srl Procedimento per eseguire operazioni di crittografia in un dispositivo di elaborazione, corrispondenti dispositivo di elaborazione e prodotto informatico
IT202000000886A1 (it) 2020-01-17 2021-07-17 St Microelectronics Srl Procedimento per eseguire operazioni di crittografia su dati in un dispositivo di elaborazione, corrispondenti dispositivo di elaborazione e prodotto informatico
IT202000006475A1 (it) * 2020-03-27 2021-09-27 St Microelectronics Srl Procedimento per eseguire operazioni di crittografia su dati in un dispositivo di elaborazione, corrispondenti dispositivo di elaborazione e prodotto informatico
JP2022045614A (ja) * 2020-09-09 2022-03-22 キオクシア株式会社 演算装置
US20220368514A1 (en) * 2021-04-22 2022-11-17 Northeastern University Methods and Systems For Protecting Against Memory-Based Side-Channel Attacks
US12086246B2 (en) * 2022-07-01 2024-09-10 Nxp B.V. Method for protecting a machine learning model from a side channel attack
KR20240040437A (ko) * 2022-09-21 2024-03-28 주식회사 아이씨티케이 암호 연산 방법, 및 상기 방법을 수행하는 전자 장치
DE102022129607A1 (de) 2022-11-09 2024-05-16 Infineon Technologies Ag Schaltung für kombinierten schlüsselwertabhängigen austausch und randomisierung von zwei werten
DE102022129608A1 (de) 2022-11-09 2024-05-16 Infineon Technologies Ag Verfahren zum kombinierten schlüsselwertabhängigen austausch und zur randomisierung von zwei eingangswerten
DE102022129606A1 (de) 2022-11-09 2024-05-16 Infineon Technologies Ag Schaltung für kombinierten schlüsselwertabhängigen austausch und multiplikative randomisierung von zwei werten

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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
US7308096B2 (en) * 2000-05-30 2007-12-11 Hitachi, Ltd. Elliptic scalar multiplication system
JP4067818B2 (ja) * 2001-12-10 2008-03-26 富士通株式会社 楕円曲線暗号装置、楕円曲線暗号プログラム及び楕円曲線暗号の演算方法
DE102005042339B4 (de) 2005-09-06 2007-08-16 Siemens Ag Verfahren zum sicheren Ver- oder Entschlüsseln einer Nachricht
KR100874909B1 (ko) * 2006-01-14 2008-12-19 삼성전자주식회사 Ｄｆａ에 대항하는 몽고메리 전력 래더 알고리즘을 사용하는 암호화 방법
JP4682852B2 (ja) 2006-01-16 2011-05-11 ソニー株式会社 暗号処理装置、および暗号処理方法、並びにコンピュータ・プログラム
KR100850202B1 (ko) * 2006-03-04 2008-08-04 삼성전자주식회사 Ｅｃｃ 패스트 몽고매리 전력 래더 알고리즘을 이용하여ｄｆａ 에 대응하는 암호화 방법
DE102006014353B4 (de) 2006-03-28 2007-11-22 Siemens Ag Verfahren zum sicheren Ermitteln von Daten
US8243919B2 (en) * 2007-03-07 2012-08-14 Research In Motion Limited Method and apparatus for performing elliptic curve scalar multiplication in a manner that counters power analysis attacks
WO2009055904A1 (fr) * 2007-10-30 2009-05-07 Certicom Corp. Détection d'erreur dans le cadre d'opérations d'exponentiation et de multiplication de points au moyen d'une échelle de montgomery
US8345864B1 (en) * 2008-12-12 2013-01-01 Emc Corporation Elliptic curve cryptography scalar multiplication with on demand acceleration table generation
FR2942560B1 (fr) 2009-02-24 2015-06-26 Oberthur Technologies Procede de traitement de donnees impliquant une exponentiation et un dispositif associe.
US8775813B2 (en) * 2010-02-26 2014-07-08 Certicom Corp. ElGamal signature schemes
KR101610917B1 (ko) * 2010-03-08 2016-04-11 삼성전자주식회사 암호 알고리즘의 복호 방법 및 그것을 포함하는 암호 시스템
US9400636B2 (en) * 2011-02-11 2016-07-26 Infineon Technologies Ag Apparatus and method for calculating a result in a scalar multiplication

Also Published As

Publication number Publication date
CN102638341A (zh) 2012-08-15
DE102012202015B4 (de) 2016-11-17
US20120207298A1 (en) 2012-08-16
FR2971600A1 (fr) 2012-08-17
CN102638341B (zh) 2016-08-03
US9400636B2 (en) 2016-07-26
DE102012202015A1 (de) 2012-08-16

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