DE602005020991D1 - Verfahren zur skalarmultiplikation in gruppen ellir nebenkanalattacken-beständige kryptosysteme - Google Patents

Verfahren zur skalarmultiplikation in gruppen ellir nebenkanalattacken-beständige kryptosysteme

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Publication number
DE602005020991D1
DE602005020991D1 DE602005020991T DE602005020991T DE602005020991D1 DE 602005020991 D1 DE602005020991 D1 DE 602005020991D1 DE 602005020991 T DE602005020991 T DE 602005020991T DE 602005020991 T DE602005020991 T DE 602005020991T DE 602005020991 D1 DE602005020991 D1 DE 602005020991D1
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elliptic curve
point
coordinates
field operations
points
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Jovan Golic
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Telecom Italia SpA
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Telecom Italia SpA
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    • 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
    • G06F7/725—Finite field arithmetic over 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
    • G06F2207/7261—Uniform execution, e.g. avoiding jumps, or using formulae with the same power profile

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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)
  • Complex Calculations (AREA)
  • Mushroom Cultivation (AREA)
  • Air Bags (AREA)
  • Filters For Electric Vacuum Cleaners (AREA)
DE602005020991T 2005-10-28 2005-10-28 Verfahren zur skalarmultiplikation in gruppen ellir nebenkanalattacken-beständige kryptosysteme Active DE602005020991D1 (de)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/EP2005/011567 WO2007048430A1 (en) 2005-10-28 2005-10-28 A method for scalar multiplication in elliptic curve groups over binary polynomial fields for side-channel attack-resistant cryptosystems

Publications (1)

Publication Number Publication Date
DE602005020991D1 true DE602005020991D1 (de) 2010-06-10

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ID=35566210

Family Applications (1)

Application Number Title Priority Date Filing Date
DE602005020991T Active DE602005020991D1 (de) 2005-10-28 2005-10-28 Verfahren zur skalarmultiplikation in gruppen ellir nebenkanalattacken-beständige kryptosysteme

Country Status (5)

Country Link
US (1) US8243920B2 (de)
EP (1) EP1946204B1 (de)
AT (1) ATE466329T1 (de)
DE (1) DE602005020991D1 (de)
WO (1) WO2007048430A1 (de)

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DE602005020702D1 (de) 2005-10-18 2010-05-27 Telecom Italia Spa Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über primkörpern für nebenkanal-attacken-beständige kryptosysteme
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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
US8781111B2 (en) * 2007-07-05 2014-07-15 Broadcom Corporation System and methods for side-channel attack prevention
US7991162B2 (en) 2007-09-14 2011-08-02 University Of Ottawa Accelerating scalar multiplication on elliptic curve cryptosystems over prime fields
US8707042B2 (en) * 2008-08-28 2014-04-22 Red Hat, Inc. Sharing keys between cooperating parties
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JP5776927B2 (ja) * 2011-03-28 2015-09-09 ソニー株式会社 情報処理装置及び方法、並びにプログラム
KR20140046568A (ko) * 2012-10-05 2014-04-21 한국전자통신연구원 단순 전력 파형 분석 및 오류 주입 분석을 방지하는 타원곡선 암호화 방법 및 그 시스템
US8861721B2 (en) * 2012-12-26 2014-10-14 Umm Al-Qura University System and method for securing scalar multiplication against simple power attacks
US8804952B2 (en) 2012-12-26 2014-08-12 Umm Al-Qura University System and method for securing scalar multiplication against differential power attacks
US20140334621A1 (en) * 2013-05-13 2014-11-13 Universidad De Santiago De Chile Method for Complete Atomic Blocks for Elliptic Curves in Jacobian Coordinates over Prime Fields Countermeasure for Simple-Side Channel Attacks and C-Safe-Fault Attacks for Left-to-Right Algorithms
FR3024808B1 (fr) * 2014-08-05 2016-07-29 Inside Secure Procede de cryptographie sur courbe elliptique comprenant une detection d’erreur
WO2016053792A1 (en) 2014-10-03 2016-04-07 Cryptography Research, Inc. Exponent splitting for cryptographic operations
CN105656629B (zh) * 2014-11-25 2018-12-11 上海华虹集成电路有限责任公司 芯片中安全的非相邻表示型实现方法
US9590805B1 (en) * 2014-12-23 2017-03-07 EMC IP Holding Company LLC Ladder-based cryptographic techniques using pre-computed points
CN106357378B (zh) * 2016-08-22 2019-04-05 上海交通大学 用于sm2签名的密钥检测方法及其系统
WO2018145189A1 (en) * 2017-02-13 2018-08-16 Infosec Global Inc. Countermeasures and optimizations in elliptic curve cryptographic schemes
CN107040364B (zh) * 2017-03-29 2020-05-08 北京华大信安科技有限公司 一种防止功耗攻击的电路
US10637656B2 (en) * 2017-11-28 2020-04-28 Blackberry Limited Method and system for key agreement utilizing semigroups
CN108875416B (zh) * 2018-06-22 2020-05-19 北京智芯微电子科技有限公司 椭圆曲线多倍点运算方法和装置

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US6748410B1 (en) * 1997-05-04 2004-06-08 M-Systems Flash Disk Pioneers, Ltd. Apparatus and method for modular multiplication and exponentiation based on montgomery multiplication
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JP4284320B2 (ja) * 2003-08-06 2009-06-24 富士通株式会社 楕円曲線暗号装置，楕円曲線暗号方法および楕円曲線暗号プログラム
KR100530372B1 (ko) * 2003-12-20 2005-11-22 삼성전자주식회사 사이드채널 공격을 방지할 수 있는 타원곡선 암호화 방법
JP4599859B2 (ja) * 2004-03-12 2010-12-15 ソニー株式会社 暗号処理演算方法、および暗号処理装置、並びにコンピュータ・プログラム
US7602907B2 (en) * 2005-07-01 2009-10-13 Microsoft Corporation Elliptic curve point multiplication
DE602005020702D1 (de) 2005-10-18 2010-05-27 Telecom Italia Spa Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über primkörpern für nebenkanal-attacken-beständige kryptosysteme
US7864951B2 (en) * 2006-07-10 2011-01-04 King Fahd University Of Petroleum And Minerals Scalar multiplication method with inherent countermeasures

Also Published As

Publication number Publication date
EP1946204A1 (de) 2008-07-23
WO2007048430A1 (en) 2007-05-03
ATE466329T1 (de) 2010-05-15
EP1946204B1 (de) 2010-04-28
US8243920B2 (en) 2012-08-14
US20090052657A1 (en) 2009-02-26

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