JP4582912B2 - 耐パワーシグニチャーアタック暗号法 - Google Patents

耐パワーシグニチャーアタック暗号法 Download PDF

Info

Publication number
JP4582912B2
JP4582912B2 JP2000578723A JP2000578723A JP4582912B2 JP 4582912 B2 JP4582912 B2 JP 4582912B2 JP 2000578723 A JP2000578723 A JP 2000578723A JP 2000578723 A JP2000578723 A JP 2000578723A JP 4582912 B2 JP4582912 B2 JP 4582912B2
Authority
JP
Japan
Prior art keywords
point
power signature
processor
bits
representation
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 - Lifetime
Application number
JP2000578723A
Other languages
English (en)
Japanese (ja)
Other versions
JP2002528771A5 (enExample
JP2002528771A (ja
Inventor
ヴァンストーン，スコット，エー．
ギャラント，ロバート，ピー．
Original Assignee
サーティコム コーポレーション
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 サーティコム コーポレーション filed Critical サーティコム コーポレーション
Publication of JP2002528771A publication Critical patent/JP2002528771A/ja
Publication of JP2002528771A5 publication Critical patent/JP2002528771A5/ja
Application granted granted Critical
Publication of JP4582912B2 publication Critical patent/JP4582912B2/ja
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

Images

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
    • G06F2207/7261—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)
  • Compositions Of Oxide Ceramics (AREA)
  • Executing Machine-Instructions (AREA)
  • Control Of Electric Motors In General (AREA)
  • Control Of Eletrric Generators (AREA)
  • Dc Digital Transmission (AREA)
JP2000578723A 1998-10-28 1999-10-05 耐パワーシグニチャーアタック暗号法 Expired - Lifetime JP4582912B2 (ja)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
CA2,252,078 1998-10-28
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 (3)

Publication Number Publication Date
JP2002528771A JP2002528771A (ja) 2002-09-03
JP2002528771A5 JP2002528771A5 (enExample) 2006-11-24
JP4582912B2 true JP4582912B2 (ja) 2010-11-17

Family

ID=4162964

Family Applications (1)

Application Number Title Priority Date Filing Date
JP2000578723A Expired - Lifetime JP4582912B2 (ja) 1998-10-28 1999-10-05 耐パワーシグニチャーアタック暗号法

Country Status (8)

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

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 (en) * 2002-12-18 2013-01-09 Fujitsu Limited Tamper-resistant elliptical curve encryption using secret key
US7646872B2 (en) 2004-04-02 2010-01-12 Research In Motion Limited Systems and methods to securely generate shared keys
JP5147412B2 (ja) 2005-01-21 2013-02-20 サーティコム コーポレーション 楕円曲線乱数生成
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
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
CA2626847A1 (en) 2005-11-03 2007-05-10 Certicom Corporation Simultaneous scalar multiplication method
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 (en) * 2006-03-31 2007-10-03 Axalto SA Protection against side channel attacks
US8065531B2 (en) * 2006-04-06 2011-11-22 Nxp B.V. Decryption method
US7774616B2 (en) * 2006-06-09 2010-08-10 International Business Machines Corporation Masking a boot sequence by providing a dummy processor
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
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
US7594104B2 (en) * 2006-06-09 2009-09-22 International Business Machines Corporation System and method for masking a hardware boot sequence
US20070288740A1 (en) * 2006-06-09 2007-12-13 Dale Jason N System and method for secure boot across a plurality of processors
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
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
US8442216B2 (en) * 2007-10-30 2013-05-14 Certicom Corp. Fault detection in exponentiation and point multiplication operations using a montgomery ladder
WO2010096902A1 (en) * 2009-02-27 2010-09-02 Certicom Corp. System and method for performing exponentiation in a cryptographic system
EP2660796B1 (en) * 2010-12-27 2018-10-31 Mitsubishi Electric Corporation Arithmetical device, arithmetical device elliptical scalar multiplication method and elliptical scalar multiplication program, arithmetical device multiplicative operation method and multiplicative operation program, as well as arithmetical device zero determination method and zero determination program
US8635467B2 (en) 2011-10-27 2014-01-21 Certicom Corp. Integrated circuit with logic circuitry and multiple concealing circuits
US8334705B1 (en) 2011-10-27 2012-12-18 Certicom Corp. Analog circuitry to conceal activity of logic circuitry
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
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
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
US6263081B1 (en) * 1997-07-17 2001-07-17 Matsushita Electric Industrial Co., Ltd. Elliptic curve calculation apparatus capable of calculating multiples at high speed
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
EP1323027A1 (en) * 2000-08-29 2003-07-02 NTRU Cryptosystems, Inc. Speed enhanced cryptographic method and apparatus
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
EP1044405B1 (en) 2004-05-26
CA2252078A1 (en) 2000-04-28
AU5964299A (en) 2000-05-15
CA2252078C (en) 2009-02-17
EP1044405A1 (en) 2000-10-18
JP2002528771A (ja) 2002-09-03
DE69917592T2 (de) 2005-06-02
DE69917592D1 (de) 2004-07-01
US6738478B1 (en) 2004-05-18
WO2000025204A1 (en) 2000-05-04
ATE268022T1 (de) 2004-06-15

Similar Documents

Publication Publication Date Title
JP4582912B2 (ja) 耐パワーシグニチャーアタック暗号法
Yen et al. Power analysis by exploiting chosen message and internal collisions–vulnerability of checking mechanism for RSA-decryption
US8913739B2 (en) Method for scalar multiplication in elliptic curve groups over prime fields for side-channel attack resistant cryptosystems
US6876745B1 (en) Method and apparatus for elliptic curve cryptography and recording medium therefore
De Win et al. A fast software implementation for arithmetic operations in GF (2n)
US7536011B2 (en) Tamper-proof elliptic encryption with private key
Ciet et al. Elliptic curve cryptosystems in the presence of permanent and transient faults
US7864951B2 (en) Scalar multiplication method with inherent countermeasures
US8243920B2 (en) Method for scalar multiplication in elliptic curve groups over binary polynomial fields for side-channel attack-resistant cryptosystems
US20110016167A1 (en) Randomized modular polynomial reduction method and hardware therefor
Trichina et al. Implementation of elliptic curve cryptography with built-in counter measures against side channel attacks
Möller Parallelizable elliptic curve point multiplication method with resistance against side-channel attacks
US7809133B2 (en) Randomized modular reduction method and hardware therefor
US8014520B2 (en) Exponentiation ladder for cryptography
Mohamed et al. Improved fixed-base comb method for fast scalar multiplication
US20090136025A1 (en) Method for scalarly multiplying points on an elliptic curve
Hodjat et al. A scalable and high performance elliptic curve processor with resistance to timing attacks
Sakai et al. Simple power analysis on fast modular reduction with generalized mersenne prime for elliptic curve cryptosystems
Takemura et al. ECC Atomic Block with NAF against Strong Side-Channel Attacks on Binary Curves
US7480380B2 (en) Method for efficient generation of modulo inverse for public key cryptosystems
Mahboob et al. Lookup table based multiplication technique for GF (2 m) with cryptographic significance
Sakai et al. A new attack with side channel leakage during exponent recoding computations
Sakai et al. Simple power analysis on fast modular reduction with NIST recommended elliptic curves
Katagi et al. Some improved algorithms for hyperelliptic curve cryptosystems using degenerate divisors
Amin et al. Elliptic curve cryptoprocessor with hierarchical security

Legal Events

Date Code Title Description
A521 Request for written amendment filed

Free format text: JAPANESE INTERMEDIATE CODE: A523

Effective date: 20061002

A621 Written request for application examination

Free format text: JAPANESE INTERMEDIATE CODE: A621

Effective date: 20061002

RD02 Notification of acceptance of power of attorney

Free format text: JAPANESE INTERMEDIATE CODE: A7422

Effective date: 20100121

A131 Notification of reasons for refusal

Free format text: JAPANESE INTERMEDIATE CODE: A131

Effective date: 20100205

A601 Written request for extension of time

Free format text: JAPANESE INTERMEDIATE CODE: A601

Effective date: 20100430

A602 Written permission of extension of time

Free format text: JAPANESE INTERMEDIATE CODE: A602

Effective date: 20100512

RD04 Notification of resignation of power of attorney

Free format text: JAPANESE INTERMEDIATE CODE: A7424

Effective date: 20100514

A601 Written request for extension of time

Free format text: JAPANESE INTERMEDIATE CODE: A601

Effective date: 20100607

A602 Written permission of extension of time

Free format text: JAPANESE INTERMEDIATE CODE: A602

Effective date: 20100614

A521 Request for written amendment filed

Free format text: JAPANESE INTERMEDIATE CODE: A523

Effective date: 20100705

TRDD Decision of grant or rejection written
A01 Written decision to grant a patent or to grant a registration (utility model)

Free format text: JAPANESE INTERMEDIATE CODE: A01

Effective date: 20100804

A01 Written decision to grant a patent or to grant a registration (utility model)

Free format text: JAPANESE INTERMEDIATE CODE: A01

A61 First payment of annual fees (during grant procedure)

Free format text: JAPANESE INTERMEDIATE CODE: A61

Effective date: 20100831

R150 Certificate of patent or registration of utility model

Free format text: JAPANESE INTERMEDIATE CODE: R150

Ref document number: 4582912

Country of ref document: JP

Free format text: JAPANESE INTERMEDIATE CODE: R150

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20130910

Year of fee payment: 3

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

EXPY Cancellation because of completion of term