ATE268022T1 - Gegen stromverbrauchsignaturanfall beständige kryptographie - Google Patents

Gegen stromverbrauchsignaturanfall beständige kryptographie

Info

Publication number
ATE268022T1
ATE268022T1 AT99971110T AT99971110T ATE268022T1 AT E268022 T1 ATE268022 T1 AT E268022T1 AT 99971110 T AT99971110 T AT 99971110T AT 99971110 T AT99971110 T AT 99971110T AT E268022 T1 ATE268022 T1 AT E268022T1
Authority
AT
Austria
Prior art keywords
point
points
computing
generate
power consumption
Prior art date
Application number
AT99971110T
Other languages
English (en)
Inventor
Scott A Vanstone
Robert P Gallant
Original Assignee
Certicom 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 Certicom Corp filed Critical Certicom Corp
Application granted granted Critical
Publication of ATE268022T1 publication Critical patent/ATE268022T1/de

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
    • G06F7/725—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

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Computing Systems (AREA)
  • Complex Calculations (AREA)
  • Emergency Protection Circuit Devices (AREA)
  • Executing Machine-Instructions (AREA)
  • Dc Digital Transmission (AREA)
  • Compositions Of Oxide Ceramics (AREA)
  • Control Of Electric Motors In General (AREA)
  • Control Of Eletrric Generators (AREA)
AT99971110T 1998-10-28 1999-10-05 Gegen stromverbrauchsignaturanfall beständige kryptographie ATE268022T1 (de)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CA002252078A CA2252078C (en) 1998-10-28 1998-10-28 Power signature attack resistant cryptographic system
PCT/CA1999/000919 WO2000025204A1 (en) 1998-10-28 1999-10-05 Power signature attack resistant cryptography

Publications (1)

Publication Number Publication Date
ATE268022T1 true ATE268022T1 (de) 2004-06-15

Family

ID=4162964

Family Applications (1)

Application Number Title Priority Date Filing Date
AT99971110T ATE268022T1 (de) 1998-10-28 1999-10-05 Gegen stromverbrauchsignaturanfall beständige kryptographie

Country Status (8)

Country Link
US (1) US6738478B1 (de)
EP (1) EP1044405B1 (de)
JP (1) JP4582912B2 (de)
AT (1) ATE268022T1 (de)
AU (1) AU5964299A (de)
CA (1) CA2252078C (de)
DE (1) DE69917592T2 (de)
WO (1) WO2000025204A1 (de)

Families Citing this family (50)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE19963408A1 (de) * 1999-12-28 2001-08-30 Giesecke & Devrient Gmbh Tragbarer Datenträger mit Zugriffsschutz durch Schlüsselteilung
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
FR2825863B1 (fr) * 2001-06-07 2003-09-19 Gemplus Card Int Procede de securisation d'un calcul d'exponentiation dans un dispositif electronique
DE10151129B4 (de) * 2001-10-17 2004-07-29 Infineon Technologies Ag Verfahren und Vorrichtung zum Berechnen eines Ergebnisses einer Exponentiation in einer Kryptographieschaltung
DE10156708B4 (de) * 2001-11-19 2005-09-29 Infineon Technologies Ag Verfahren und Vorrichtung zum Multiplizieren und Verfahren und Vorrichtung zum Addieren auf einer elliptischen Kurve
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
US7555122B2 (en) 2002-12-04 2009-06-30 Wired Communications LLC Method for elliptic curve point multiplication
EP1548687B1 (de) 2002-12-18 2013-01-09 Fujitsu Limited Manipulationsbeständige verschlüsselung mit elliptischer kurve unter verwendung eines geheimschlüssels
US7646872B2 (en) * 2004-04-02 2010-01-12 Research In Motion Limited Systems and methods to securely generate shared keys
WO2006076804A1 (en) 2005-01-21 2006-07-27 Certicom Corp. Elliptic curve random number generation
WO2006118092A1 (ja) * 2005-04-27 2006-11-09 Matsushita Electric Industrial Co., Ltd. 情報セキュリティ装置及び楕円曲線演算装置
CA2542556C (en) 2005-06-03 2014-09-16 Tata Consultancy Services Limited An authentication system executing an elliptic curve digital signature cryptographic process
DE102005042339B4 (de) 2005-09-06 2007-08-16 Siemens Ag Verfahren zum sicheren Ver- oder Entschlüsseln einer Nachricht
WO2007045258A1 (en) 2005-10-18 2007-04-26 Telecom Italia S.P.A. A method for scalar multiplication in elliptic curve groups over prime fields for side-channel attack resistant cryptosystems
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
EP2293491B1 (de) * 2005-11-03 2012-08-22 Certicom Corp. Verfahren zur gleichzeigigen Skalarmultiplikation
FR2893796B1 (fr) * 2005-11-21 2008-01-04 Atmel Corp Procede de protection par chiffrement
US9313027B2 (en) 2005-12-29 2016-04-12 Proton World International N.V. Protection of a calculation performed by an integrated circuit
DE102006002891B4 (de) * 2006-01-20 2009-06-04 Siemens Ag Verfahren, Vorrichtung und System zum Verifizieren von auf einer elliptischen Kurve ermittelten Punkten
KR100850202B1 (ko) * 2006-03-04 2008-08-04 삼성전자주식회사 Ｅｃｃ 패스트 몽고매리 전력 래더 알고리즘을 이용하여ｄｆａ 에 대응하는 암호화 방법
WO2007104706A1 (fr) * 2006-03-16 2007-09-20 Gemplus Procede de securisation d'un calcul d'une exponentiation ou d'une multiplication par un scalaire dans un dispositif electronique
DE102006013515A1 (de) * 2006-03-23 2007-10-04 Siemens Ag Kryptographisches Verfahren mit elliptischen Kurven
EP1840732A1 (de) * 2006-03-31 2007-10-03 Axalto SA Schutz vor Seitenkanalangriffen
US8065531B2 (en) * 2006-04-06 2011-11-22 Nxp B.V. Decryption method
US7594104B2 (en) * 2006-06-09 2009-09-22 International Business Machines Corporation System and method for masking a hardware boot sequence
US20070288739A1 (en) * 2006-06-09 2007-12-13 Dale Jason N System and method for masking a boot sequence by running different code on each processor
US20070288761A1 (en) * 2006-06-09 2007-12-13 Dale Jason N System and method for booting a multiprocessor device based on selection of encryption keys to be provided to processors
US20070288740A1 (en) * 2006-06-09 2007-12-13 Dale Jason N System and method for secure boot across a plurality of processors
US7774616B2 (en) * 2006-06-09 2010-08-10 International Business Machines Corporation Masking a boot sequence by providing a dummy processor
US20070288738A1 (en) * 2006-06-09 2007-12-13 Dale Jason N System and method for selecting a random processor to boot on a multiprocessor system
US7856101B2 (en) * 2007-02-07 2010-12-21 King Fahd University Of Petroleum And Minerals Method for elliptic curve scalar multiplication
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
US8205097B2 (en) * 2007-07-05 2012-06-19 Nxp B.V. Microprocessor in a security-sensitive system
US7991162B2 (en) * 2007-09-14 2011-08-02 University Of Ottawa Accelerating scalar multiplication on elliptic curve cryptosystems over prime fields
EP2213037B1 (de) * 2007-10-30 2013-09-04 Certicom Corp. Fehlererkennung in potenzierungs- und kommamultiplikationsoperationen mithilfe einer montgomery-leiter
US8577028B2 (en) * 2009-02-27 2013-11-05 Certicom Corp. System and method for performing exponentiation in a cryptographic system
WO2012090284A1 (ja) * 2010-12-27 2012-07-05 三菱電機株式会社 演算装置、演算装置の楕円スカラー倍算方法、楕円スカラー倍算プログラム、演算装置の剰余演算方法、剰余演算プログラム、演算装置のゼロ判定方法およびゼロ判定プログラム
US8334705B1 (en) 2011-10-27 2012-12-18 Certicom Corp. Analog circuitry to conceal activity of logic circuitry
US8635467B2 (en) 2011-10-27 2014-01-21 Certicom Corp. Integrated circuit with logic circuitry and multiple concealing circuits
US9979543B2 (en) 2013-12-23 2018-05-22 Nxp B.V. Optimized hardware architecture and method for ECC point doubling using jacobian coordinates over short weierstrass curves
US9900154B2 (en) * 2013-12-23 2018-02-20 Nxp B.V. Optimized hardward architecture and method for ECC point addition using mixed affine-jacobian coordinates over short weierstrass curves
US9929862B2 (en) 2013-12-23 2018-03-27 Nxp B.V. Optimized hardware architecture and method for ECC point doubling using Jacobian coordinates over short Weierstrass curves
US9391773B2 (en) 2014-04-04 2016-07-12 Qualcomm Incorporated Elliptic curve point multiplication procedure resistant to side-channel information leakage
US9645794B2 (en) * 2014-09-23 2017-05-09 Texas Instruments Incorporated Homogeneous atomic pattern for double, add, and subtract operations for digital authentication using elliptic curve cryptography
US9590805B1 (en) * 2014-12-23 2017-03-07 EMC IP Holding Company LLC Ladder-based cryptographic techniques using pre-computed points
US9735953B2 (en) * 2015-03-06 2017-08-15 Qualcomm Incorporated Side channel analysis resistant architecture
US10491401B2 (en) 2017-02-21 2019-11-26 Google Llc Verification of code signature with flexible constraints
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

Family Cites Families (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH10222065A (ja) * 1997-02-03 1998-08-21 Nippon Telegr & Teleph Corp <Ntt> 冪乗剰余演算方法及び装置
US6252959B1 (en) * 1997-05-21 2001-06-26 Worcester Polytechnic Institute Method and system for point multiplication in elliptic curve cryptosystem
EP1710951A3 (de) * 1997-07-17 2006-10-25 Matsushita Electric Industrial Co., Ltd. Vorrichtung zur Berechnung einer elliptischen Kurve welche vielfache mit hoher Geschwindigkeit berechnen kann
CA2243761C (en) * 1998-07-21 2009-10-06 Certicom Corp. Timing attack resistant cryptographic system
US20020057796A1 (en) * 1998-12-24 2002-05-16 Lambert Robert J. Method for accelerating cryptographic operations on elliptic curves
JP2004507789A (ja) * 2000-08-29 2004-03-11 エヌティーアールユー・クリプトシステムズ・インコーポレーテッド 高速強化暗号の方法および装置
US7215780B2 (en) * 2001-12-31 2007-05-08 Certicom Corp. Method and apparatus for elliptic curve scalar multiplication

Also Published As

Publication number Publication date
CA2252078A1 (en) 2000-04-28
AU5964299A (en) 2000-05-15
WO2000025204A1 (en) 2000-05-04
DE69917592D1 (de) 2004-07-01
CA2252078C (en) 2009-02-17
EP1044405A1 (de) 2000-10-18
JP4582912B2 (ja) 2010-11-17
JP2002528771A (ja) 2002-09-03
US6738478B1 (en) 2004-05-18
EP1044405B1 (de) 2004-05-26
DE69917592T2 (de) 2005-06-02

Similar Documents

Publication Publication Date Title
ATE268022T1 (de) Gegen stromverbrauchsignaturanfall beständige kryptographie
CN101366232B (zh) 同步标量乘法算法
US6212279B1 (en) Method of elliptic curve cryptographic key exchange using reduced base tau expansion in non-adjacent form
US6243467B1 (en) Method of elliptic curve cryptographic digital signature generation and verification using reduced base tau expansion in non-adjacent form
ATE418099T1 (de) Gesicherte moduläre potenzierung mit leckminimierung für chipkarten und andere kryptosysteme
ATE374478T1 (de) System und verfahren für das erneuern von schlüsseln, welche in public-key kryptographie genutzt werden
GB2318709A (en) Private key with random and sequential components
WO1995005712A3 (en) Secret key exchange
US7062043B1 (en) Method of elliptic curve digital signature using coefficient splitting
Park et al. Parallel implementations of SIMON and SPECK
Pettit Efficient threshold-optimal ECDSA
CA2259738A1 (en) A resilient cryptographic scheme
US7024559B1 (en) Method of elliptic curve digital signature using expansion in joint sparse form
Longa et al. Novel precomputation schemes for elliptic curve cryptosystems
Han et al. Fast algorithms for elliptic curve cryptosystems over binary finite field
Klisowski et al. The implementation of cubic public keys based on a new family of algebraic graphs
WO2004104918A3 (en) Dna based number system and arithmetic
Li et al. A novel algorithm for scalar multiplication in ECDSA
US7505585B2 (en) Method of generating cryptographic key using elliptic curve and expansion in joint sparse form and using same
Lee et al. Analysis of Gong et al.'s CCA2-secure homomorphic encryption
Kashyap et al. A Cryptosystem Based on DLP gamma= alphaabetab mod p.
Barham et al. New second preimage attacks on dithered hash functions with low memory complexity
Teske Computing discrete logarithms in arithmetic progressions
Chen et al. A new elliptic curve undeniable signature scheme
WO2023052603A1 (en) Digital signatures with re-randomized presignatures

Legal Events

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