ATE464599T1 - Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über primkörpern für nebenkanal-attacken-beständige kryptosysteme - Google Patents

Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über primkörpern für nebenkanal-attacken-beständige kryptosysteme

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Publication number
ATE464599T1
ATE464599T1 AT05797792T AT05797792T ATE464599T1 AT E464599 T1 ATE464599 T1 AT E464599T1 AT 05797792 T AT05797792 T AT 05797792T AT 05797792 T AT05797792 T AT 05797792T AT E464599 T1 ATE464599 T1 AT E464599T1
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AT
Austria
Prior art keywords
elliptic curve
field
point
coordinates
multiplication
Prior art date
Application number
AT05797792T
Other languages
English (en)
Inventor
Jovan Golic
Original Assignee
Telecom Italia Spa
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.)
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Publication date
Application filed by Telecom Italia Spa filed Critical Telecom Italia Spa
Application granted granted Critical
Publication of ATE464599T1 publication Critical patent/ATE464599T1/de

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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; 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 OR CALCULATING; 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
    • G06F2207/7257—Random modification not requiring correction
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; 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
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; 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
    • G06F7/721—Modular inversion, reciprocal or quotient calculation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; 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

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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)
  • Fats And Perfumes (AREA)
  • Error Detection And Correction (AREA)
  • Led Device Packages (AREA)
AT05797792T 2005-10-18 2005-10-18 Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über primkörpern für nebenkanal-attacken-beständige kryptosysteme ATE464599T1 (de)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/EP2005/011208 WO2007045258A1 (en) 2005-10-18 2005-10-18 A method for scalar multiplication in elliptic curve groups over prime fields for side-channel attack resistant cryptosystems

Publications (1)

Publication Number Publication Date
ATE464599T1 true ATE464599T1 (de) 2010-04-15

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Family Applications (1)

Application Number Title Priority Date Filing Date
AT05797792T ATE464599T1 (de) 2005-10-18 2005-10-18 Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über primkörpern für nebenkanal-attacken-beständige kryptosysteme

Country Status (5)

Country Link
US (1) US8913739B2 (de)
EP (1) EP1946205B1 (de)
AT (1) ATE464599T1 (de)
DE (1) DE602005020702D1 (de)
WO (1) WO2007045258A1 (de)

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WO2013172913A2 (en) 2012-03-07 2013-11-21 The Trustees Of Columbia University In The City Of New York Systems and methods to counter side channels attacks
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
US20150092940A1 (en) * 2013-10-02 2015-04-02 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 Right-to-Left Algorithms
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US9590805B1 (en) * 2014-12-23 2017-03-07 EMC IP Holding Company LLC Ladder-based cryptographic techniques using pre-computed points
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WO2018145190A1 (en) * 2017-02-13 2018-08-16 Infosec Global Inc. Elliptic curve cryptography scheme with simple side-channel attack countermeasure
WO2018148819A1 (en) * 2017-02-15 2018-08-23 Infosec Global Inc. Cryptographic scheme with fault injection attack countermeasure
WO2018163342A1 (ja) * 2017-03-09 2018-09-13 日本電気株式会社 異常検知装置、異常検知方法および異常検知プログラム
CN108809622B (zh) * 2018-06-15 2021-10-26 上海科技大学 一种抗功耗侧信道攻击对策验证方法
WO2020146285A1 (en) * 2019-01-07 2020-07-16 Cryptography Research, Inc. Protection of cryptographic operations by intermediate randomization
CN112068801B (zh) * 2019-06-11 2022-09-09 云南大学 一种乘法群上的最优带符号二进制快速计算方法及模幂运算
CN111339546B (zh) * 2020-03-20 2023-12-01 苏州链原信息科技有限公司 用于生成数据标签的方法、电子设备及计算机存储介质
CN113783702B (zh) * 2021-09-28 2024-11-19 南京宁麒智能计算芯片研究院有限公司 一种椭圆曲线数字签名与验签的硬件实现方法和系统
CN114527956B (zh) * 2022-01-25 2024-05-10 北京航空航天大学 抗spa攻击的sm2算法中非定点标量乘法的计算方法
CN116647318A (zh) * 2022-02-16 2023-08-25 瑞昱半导体股份有限公司 防御密码系统时间攻击的方法及密码系统处理电路
CN115001691A (zh) * 2022-03-08 2022-09-02 北京大学 一种素数域下点乘运算的硬件快速实现方法
CN115361128B (zh) * 2022-08-25 2025-12-16 大唐微电子技术有限公司 一种sm2/nist算法实现方法和装置
DE102022129608A1 (de) * 2022-11-09 2024-05-16 Infineon Technologies Ag Verfahren zum kombinierten schlüsselwertabhängigen austausch und zur randomisierung von zwei eingangswerten
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ATE466329T1 (de) 2005-10-28 2010-05-15 Telecom Italia Spa Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über binäre polynomische körper für nebenkanalattacken-beständige kryptosysteme

Also Published As

Publication number Publication date
DE602005020702D1 (de) 2010-05-27
EP1946205B1 (de) 2010-04-14
WO2007045258A1 (en) 2007-04-26
EP1946205A1 (de) 2008-07-23
US8913739B2 (en) 2014-12-16
US20090214025A1 (en) 2009-08-27

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