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

Info

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
Authority
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.)
Filing date
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

Links

Classifications

    • 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

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)
  • Led Device Packages (AREA)
  • Fats And Perfumes (AREA)
  • Error Detection And Correction (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

Family

ID=35385314

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)

Families Citing this family (36)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8243920B2 (en) 2005-10-28 2012-08-14 Telecom Italia S.P.A. Method for scalar multiplication in elliptic curve groups over binary polynomial fields for side-channel attack-resistant cryptosystems
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
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
US8102998B2 (en) * 2007-05-02 2012-01-24 King Fahd University Of Petroleum And Minerals Method for elliptic curve scalar multiplication using parameterized projective coordinates
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
FR2926652B1 (fr) * 2008-01-23 2010-06-18 Inside Contactless Procede et dispositifs de contre-mesure pour cryptographie asymetrique a schema de signature
US8369517B2 (en) 2008-08-12 2013-02-05 Inside Secure Fast scalar multiplication for elliptic curve cryptosystems over prime fields
US8139765B2 (en) * 2008-12-29 2012-03-20 King Fahd University Of Petroleum & Minerals Elliptical polynomial-based message authentication code
FR2947647B1 (fr) * 2009-07-06 2011-08-26 Oberthur Technologies Procede de traitement de donnees et dispositif associe
US8351601B2 (en) * 2010-02-18 2013-01-08 King Fahd University Of Petroleum And Minerals Elliptic polynomial cryptography with secret key embedding
US8331558B2 (en) * 2010-02-18 2012-12-11 King Fahd University Of Petroleum And Minerals Method of cipher block chaining using elliptic curve cryptography
US8755517B2 (en) 2010-12-08 2014-06-17 Total Technology Solutions Co. Method for generic-point parallel elliptic curve scalar multiplication
ITMI20111992A1 (it) * 2011-11-03 2013-05-04 St Microelectronics Srl Metodo per crittografare un messaggio mediante calcolo di funzioni matematiche comprendenti moltiplicazioni modulari
EP2634993B1 (de) * 2012-03-01 2017-01-11 Certicom Corp. Vorrichtungen und Verfahren zum Verbinden von Client-Vorrichtungen mit einem Netzwerk
US9887833B2 (en) 2012-03-07 2018-02-06 The Trustees Of Columbia University In The City Of New York Systems and methods to counter side channel attacks
US8804952B2 (en) 2012-12-26 2014-08-12 Umm Al-Qura University System and method for securing scalar multiplication against differential power attacks
US8861721B2 (en) 2012-12-26 2014-10-14 Umm Al-Qura University System and method for securing scalar multiplication against simple 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
US9391773B2 (en) 2014-04-04 2016-07-12 Qualcomm Incorporated Elliptic curve point multiplication procedure resistant to side-channel information leakage
US9590805B1 (en) * 2014-12-23 2017-03-07 EMC IP Holding Company LLC Ladder-based cryptographic techniques using pre-computed points
FR3033965B1 (fr) * 2015-03-18 2018-12-07 Maxim Integrated Products, Inc. Systèmes et procédés de commande de dispositifs de cryptage sur courbe elliptique sécurisés
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
JP6746085B2 (ja) * 2017-03-09 2020-08-26 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
US11983280B2 (en) * 2019-01-07 2024-05-14 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

Family Cites Families (24)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE69534603T2 (de) 1994-07-29 2006-08-03 Certicom Corp., Mississauga Verschlüsselungssystem für elliptische kurve
US6782100B1 (en) * 1997-01-29 2004-08-24 Certicom Corp. Accelerated finite field operations on an elliptic curve
US5854759A (en) * 1997-05-05 1998-12-29 Rsa Data Security, Inc. Methods and apparatus for efficient finite field basis conversion
US6252959B1 (en) 1997-05-21 2001-06-26 Worcester Polytechnic Institute Method and system for point multiplication in elliptic curve cryptosystem
IL121297A0 (en) 1997-07-14 1998-02-22 L P K Information Integrity Lt A method and apparatus for the efficient execution of elliptic curve cryptographic operations
US6466668B1 (en) 1998-01-28 2002-10-15 Hitachi, Ltd. IC card equipped with elliptical curve encryption processing facility
CN1235446A (zh) 1998-03-05 1999-11-17 松下电器产业株式会社 椭圆曲线变换装置、利用装置和利用系统
CA2252078C (en) 1998-10-28 2009-02-17 Certicom Corp. Power signature attack resistant cryptographic system
JP3796993B2 (ja) * 1998-12-22 2006-07-12 株式会社日立製作所 楕円曲線暗号実行方法及び装置並びに記録媒体
AU762650B2 (en) 1999-09-29 2003-07-03 Hitachi Limited Device, program or system for processing secret information
AU3721801A (en) 2000-01-16 2001-07-24 Cv Cryptovision Gmbh Method and device for carrying out an inversion, especially during encoding by means of elliptic curves
KR100848412B1 (ko) * 2000-05-15 2008-07-28 엠-시스템스 플래쉬 디스크 파이오니어스 리미티드 정수연산필드의 범위를 확장하는 장치 및 방법
JP3821631B2 (ja) 2000-05-30 2006-09-13 株式会社日立製作所 楕円曲線暗号におけるスカラー倍計算方法及び装置、並びに記憶媒体
FR2809893B1 (fr) * 2000-06-02 2002-11-15 Gemplus Card Int Procede de contre-mesure dans un composant electronique mettant en oeuvre un algorithme de cryptographie a cle publique sur courbe elliptique
JP3794266B2 (ja) * 2000-11-08 2006-07-05 株式会社日立製作所 楕円曲線スカラー倍計算方法及び装置並びに記憶媒体
US6826586B2 (en) * 2000-12-15 2004-11-30 Sun Microsystems, Inc. Method for efficient computation of point doubling operation of elliptic curve point scalar multiplication over finite fields F(2m)
FR2824210B1 (fr) 2001-04-27 2003-05-30 Gemplus Card Int Procede de contre-mesure dans un composant electronique mettant en oeuvre un algorithme cryptographique du type a cle publique sur une courbe elliptique
FR2828779B1 (fr) 2001-08-17 2004-01-16 Gemplus Card Int Procede de calcul universel applique a des points d'une courbe elliptique
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
JP4034585B2 (ja) 2002-01-28 2008-01-16 松下電器産業株式会社 楕円曲線演算装置及び楕円曲線演算方法
FR2838210B1 (fr) 2002-04-03 2005-11-04 Gemplus Card Int Procede cryptographique protege contre les attaques de type a canal cache
US7257709B2 (en) * 2002-09-03 2007-08-14 Certicom Corp. Method and apparatus for performing validation of elliptic curve public keys
US20070053506A1 (en) * 2004-09-15 2007-03-08 Katsuyuki Takashima Elliptic curve encryption processor, processing method of the processor using elliptic curves, and program for causing a computer to execute point scalar multiplication on elliptic curves
US8243920B2 (en) 2005-10-28 2012-08-14 Telecom Italia S.P.A. Method for scalar multiplication in elliptic curve groups over binary polynomial fields for side-channel attack-resistant cryptosystems

Also Published As

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

Similar Documents

Publication Publication Date Title
ATE464599T1 (de) Verfahren zur skalarmultiplikation in gruppen elliptischer kurven über primkörpern für nebenkanal-attacken-beständige kryptosysteme
DE602005020991D1 (de) Verfahren zur skalarmultiplikation in gruppen ellir nebenkanalattacken-beständige kryptosysteme
Joye et al. Hessian elliptic curves and side-channel attacks
Mamiya et al. Efficient countermeasures against RPA, DPA, and SPA
Bernstein et al. Analysis and optimization of elliptic-curve single-scalar multiplication
KR20090006465A (ko) 타원 곡선 암호 시스템에 대한 부채널 공격에 대응하는방법
ATE527594T1 (de) Verfahren und vorrichtung zur erzeugung eines öffentlichen schlüssel gegen leistungsanalyseangriffe
ATE534950T1 (de) Schaltungen und verfahren zur durchführung von potenzierung und invertierung finiter feldelemente
JP5403630B2 (ja) スカラ倍算器及びスカラ倍算プログラム
CN104506316A (zh) 一种基于sm2基点的点乘运算方法
Guyot et al. Explicit algorithm for the arithmetic on the hyperelliptic Jacobians of genus 3
US20120039462A1 (en) Rsa signature method and apparatus
CN102104482A (zh) 椭圆曲线密码体制中无穷远点在仿射坐标系下的表示方法
DE502006007709D1 (de) Verfahren, vorrichtung und system zum verifizieren von auf einer elliptischen kurve ermittelten punkten
CN104901792A (zh) 密码处理椭圆曲线数据的方法、电子设备及计算机程序
WO2008127444A3 (en) Fast rsa signature verification
EP2085877A1 (de) Vorrichtung und Computerprogrammprodukt zur Berechnung von Punktadditionen auf elliptischen Kurven
RU2012101253A (ru) Криптография на эллиптической кривой
Pote et al. Arithmetic of Koblitz Curve Secp256k1 Used in Bitcoin Cryptocurrency Based on One Variable Polynomial Division
Ghosh et al. Security of prime field pairing cryptoprocessor against differential power attack
Adachi et al. Combination of mixed coordinates strategy and direct computations for efficient scalar multiplications
Kopřiva et al. Parallel computations based on automatic transformation of ordinary differential equations
Gsenger et al. Improving the Efficiency of Elliptic Curve Scalar Multiplication Using Binary Huff Curves
Sung et al. A Public-key Cryptography Processor supporting P-224 ECC and 2048-bit RSA
Mishra et al. A metric on the set of elliptic curves over Fp

Legal Events

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