CN101366232B - 同步标量乘法算法 - Google Patents

同步标量乘法算法 Download PDF

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Publication number
CN101366232B
CN101366232B CN200680045391.2A CN200680045391A CN101366232B CN 101366232 B CN101366232 B CN 101366232B CN 200680045391 A CN200680045391 A CN 200680045391A CN 101366232 B CN101366232 B CN 101366232B
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computing
scalar
bit
mentioned
next computing
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Chinese (zh)
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CN101366232A (zh
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艾德里安·安提帕
尤里·普易路夫
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Maliki Innovation Co ltd
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Certicom Corp
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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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/20—Manipulating the length of blocks of bits, e.g. padding or block truncation

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • Algebra (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Complex Calculations (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)
  • Executing Machine-Instructions (AREA)
  • Catalysts (AREA)
  • Exhaust Gas Treatment By Means Of Catalyst (AREA)
CN200680045391.2A 2005-11-03 2006-11-03 同步标量乘法算法 Active CN101366232B (zh)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
US73271505P 2005-11-03 2005-11-03
US60/732,715 2005-11-03
PCT/CA2006/001805 WO2007051305A1 (en) 2005-11-03 2006-11-03 Simultaneous scalar multiplication method

Publications (2)

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CN101366232A CN101366232A (zh) 2009-02-11
CN101366232B true CN101366232B (zh) 2012-05-16

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CN200680045391.2A Active CN101366232B (zh) 2005-11-03 2006-11-03 同步标量乘法算法

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US (3) US8045705B2 (enExample)
EP (3) EP2509253B1 (enExample)
JP (2) JP5073669B2 (enExample)
CN (1) CN101366232B (enExample)
AT (1) ATE507625T1 (enExample)
CA (1) CA2626847A1 (enExample)
DE (1) DE602006021601D1 (enExample)
WO (1) WO2007051305A1 (enExample)

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Publication number Priority date Publication date Assignee Title
EP1775880A1 (en) * 2005-10-11 2007-04-18 STMicroelectronics S.r.l. Method of processing information to be confidentially transmitted
US8422685B2 (en) * 2008-02-26 2013-04-16 King Fahd University Of Petroleum And Minerals Method for elliptic curve scalar multiplication
US8548160B2 (en) * 2010-01-13 2013-10-01 Microsoft Corporation Determination of pairings on a curve using aggregated inversions
US8755517B2 (en) * 2010-12-08 2014-06-17 Total Technology Solutions Co. Method for generic-point parallel elliptic curve scalar multiplication
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
KR101524661B1 (ko) * 2014-04-03 2015-06-03 고려대학교 산학협력단 재배치를 통한 트리플-베이스 체인 기반 타원곡선 스칼라 곱셈을 위한 연산 장치 및 방법
KR101983125B1 (ko) * 2014-05-08 2019-05-28 마이크로 모우션, 인코포레이티드 페일세이프 계산들을 수행하기 위한 방법
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
US9531531B2 (en) * 2015-05-06 2016-12-27 Qualcomm Incorporated Methods and devices for fixed execution flow multiplier recoding and scalar multiplication
EP3376705A1 (en) * 2017-03-17 2018-09-19 Koninklijke Philips N.V. Elliptic curve point multiplication device and method in a white-box context
CN109117677A (zh) * 2018-09-21 2019-01-01 阿里巴巴集团控股有限公司 一种用于椭圆曲线多倍点运算的电路
US11483152B2 (en) * 2020-12-30 2022-10-25 Pqsecure Technologies, Llc High-performance systems to validate isogeny-based cryptography keys

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1625104A (zh) * 2004-12-09 2005-06-08 中国电子科技集团公司第三十研究所 一种用于椭圆曲线密码算法芯片的倍点运算电路

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Publication number Priority date Publication date Assignee Title
CA2252078C (en) * 1998-10-28 2009-02-17 Certicom Corp. Power signature attack resistant cryptographic system
JP3820909B2 (ja) * 2001-04-24 2006-09-13 ソニー株式会社 楕円曲線暗号処理方法および楕円曲線暗号処理装置、並びにプログラム
JP2003131568A (ja) * 2001-10-26 2003-05-09 Hitachi Ltd 楕円曲線署名検証方法及び装置並びに記憶媒体
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
JP4203944B2 (ja) * 2002-01-28 2009-01-07 パナソニック株式会社 楕円曲線演算装置及び楕円曲線演算方法
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
JP3818193B2 (ja) 2002-03-27 2006-09-06 大阪瓦斯株式会社 カーボンナノチューブ含有炭素材料の製造方法
JP2004053814A (ja) * 2002-07-18 2004-02-19 Fujitsu Ltd 楕円曲線暗号装置及び楕円曲線暗号演算方法
AT412916B (de) 2002-07-19 2005-08-25 Avl List Gmbh Verfahren zur simulation des fahrverhaltens von fahrzeugen

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1625104A (zh) * 2004-12-09 2005-06-08 中国电子科技集团公司第三十研究所 一种用于椭圆曲线密码算法芯片的倍点运算电路

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Darrel Hankerson等.SOFTWARE IMPLEMENTATION OF ELLIPTIC CURVE CPYPTOGRAPHY OVER BINARY FIELDS.《Lecture Notes In COMPUTER SCIENCE》.2000,第1965卷1-24页. *
Toru Akishita.Fast Simultaneous Scalar Multiplication on Elliptic Curve with Montgomery Form.《Lecture Notes In Computer Science》.2001,第2259卷255-267. *

Also Published As

Publication number Publication date
EP2293491A1 (en) 2011-03-09
DE602006021601D1 (de) 2011-06-09
JP5073669B2 (ja) 2012-11-14
US20070098154A1 (en) 2007-05-03
CN101366232A (zh) 2009-02-11
US20130003964A1 (en) 2013-01-03
EP2509253B1 (en) 2014-06-18
EP1946480B1 (en) 2011-04-27
JP2009515206A (ja) 2009-04-09
EP1946480A4 (en) 2010-04-07
US8284930B2 (en) 2012-10-09
US8548163B2 (en) 2013-10-01
EP1946480A1 (en) 2008-07-23
US20110261956A1 (en) 2011-10-27
HK1155293A1 (en) 2012-05-11
ATE507625T1 (de) 2011-05-15
EP2509253A1 (en) 2012-10-10
JP2012185517A (ja) 2012-09-27
EP2293491B1 (en) 2012-08-22
CA2626847A1 (en) 2007-05-10
US8045705B2 (en) 2011-10-25
WO2007051305A1 (en) 2007-05-10

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