CA2587474C - New trapdoor one-way function on elliptic curves and their applications to shorter signatures and asymmetric encryption - Google Patents

New trapdoor one-way function on elliptic curves and their applications to shorter signatures and asymmetric encryption Download PDF

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Publication number
CA2587474C
CA2587474C CA2587474A CA2587474A CA2587474C CA 2587474 C CA2587474 C CA 2587474C CA 2587474 A CA2587474 A CA 2587474A CA 2587474 A CA2587474 A CA 2587474A CA 2587474 C CA2587474 C CA 2587474C
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CA
Canada
Prior art keywords
key operation
endomorphism
cryptographic
message
private key
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
CA2587474A
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English (en)
French (fr)
Other versions
CA2587474A1 (en
Inventor
Daniel R.L. Brown
Robert P. Gallant
Marinus Struik
Scott A. Vanstone
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BlackBerry Ltd
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Certicom Corp
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Publication of CA2587474A1 publication Critical patent/CA2587474A1/en
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Publication of CA2587474C publication Critical patent/CA2587474C/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

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Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/08—Network architectures or network communication protocols for network security for authentication of entities
    • H04L63/0823—Network architectures or network communication protocols for network security for authentication of entities using certificates
    • 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
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/60—Protecting data
    • G06F21/64—Protecting data integrity, e.g. using checksums, certificates or signatures
    • 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
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
    • H04L9/3252—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using DSA or related signature schemes, e.g. elliptic based signatures, ElGamal or Schnorr schemes

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Theoretical Computer Science (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Physics & Mathematics (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Algebra (AREA)
  • General Health & Medical Sciences (AREA)
  • Bioethics (AREA)
  • Health & Medical Sciences (AREA)
  • Software Systems (AREA)
  • Complex Calculations (AREA)
  • Storage Device Security (AREA)
  • Devices For Executing Special Programs (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Remote Monitoring And Control Of Power-Distribution Networks (AREA)
  • Facsimile Transmission Control (AREA)
CA2587474A 2004-11-11 2005-11-14 New trapdoor one-way function on elliptic curves and their applications to shorter signatures and asymmetric encryption Expired - Lifetime CA2587474C (en)

Applications Claiming Priority (5)

Application Number Priority Date Filing Date Title
IBPCT/IB2004/003700 2004-11-11
IB2004003700 2004-11-11
US62688404P 2004-11-12 2004-11-12
US60/626,884 2004-11-12
PCT/CA2005/001720 WO2006050605A1 (en) 2004-11-11 2005-11-14 New trapdoor one-way function on elliptic curves and their applications to shorter signatures and asymmetric encryption

Publications (2)

Publication Number Publication Date
CA2587474A1 CA2587474A1 (en) 2006-05-18
CA2587474C true CA2587474C (en) 2016-08-09

Family

ID=36336180

Family Applications (1)

Application Number Title Priority Date Filing Date
CA2587474A Expired - Lifetime CA2587474C (en) 2004-11-11 2005-11-14 New trapdoor one-way function on elliptic curves and their applications to shorter signatures and asymmetric encryption

Country Status (7)

Country Link
US (3) US7844051B2 (enExample)
EP (1) EP1815636B1 (enExample)
JP (2) JP4842276B2 (enExample)
CN (1) CN101099329B (enExample)
AT (1) ATE546909T1 (enExample)
CA (1) CA2587474C (enExample)
WO (1) WO2006050605A1 (enExample)

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GB2406484B (en) 2003-08-19 2007-01-31 Certicom Corp Method and apparatus for synchronizing an adaptable security level in an electronic communication
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JP4842276B2 (ja) * 2004-11-11 2011-12-21 サーティコム コーポレーション 楕円曲線上の新しいトラップドア１方向性関数と、その、より短い署名及び非対称暗号化への応用
DE102005045733A1 (de) * 2005-09-23 2007-04-05 Nec Europe Ltd. Verfahren zum Übermitteln von Nachrichten
EP1775880A1 (en) * 2005-10-11 2007-04-18 STMicroelectronics S.r.l. Method of processing information to be confidentially transmitted
JP4911736B2 (ja) 2006-04-13 2012-04-04 サーティコム コーポレーション 電子通信において適合可能なセキュリティレベルを提供する方法と装置
US7885406B2 (en) * 2006-10-10 2011-02-08 Microsoft Corporation Computing endomorphism rings of Abelian surfaces over finite fields
US9059838B2 (en) * 2007-03-30 2015-06-16 Verizon Patent And Licensing Inc. Encryption algorithm with randomized buffer
US20090046849A1 (en) * 2007-04-23 2009-02-19 Bally Gaming, Inc. Data integrity and non-repudiation method
FR2941115B1 (fr) * 2009-01-14 2011-02-25 Sagem Securite Codage de points d'une courbe elliptique
US20100208884A1 (en) * 2009-02-19 2010-08-19 Thomson Licensing Method and device for hashing onto points of an elliptic curve
EP2222015A1 (en) * 2009-02-19 2010-08-25 Thomson Licensing Method and device for hashing onto points of an elliptic curve
US8787564B2 (en) 2011-11-30 2014-07-22 Certicom Corp. Assessing cryptographic entropy
EP2798773B1 (en) 2011-12-28 2020-08-26 BlackBerry Limited Generating digital signatures
WO2013153628A1 (ja) * 2012-04-11 2013-10-17 株式会社日立製作所 演算処理システムおよび演算結果認証方法
KR102238681B1 (ko) 2013-07-01 2021-04-12 삼성전자주식회사 데이터 인증을 위한 서명 정보 생성 및 검증 방법과 이를 위한 시스템
KR20150017844A (ko) * 2013-08-08 2015-02-23 삼성전자주식회사 페이지 구성 방법 및 이를 지원하는 전자 장치
CN103780382B (zh) * 2014-01-13 2017-01-18 华南理工大学 一种基于超球面的多变量公钥加密/解密系统及方法
CN103825743A (zh) * 2014-02-13 2014-05-28 南京邮电大学 一种具有隐私保护功能的数据安全聚合方法
CN105099693B (zh) * 2014-05-23 2018-10-19 华为技术有限公司 一种传输方法及传输装置
US10129026B2 (en) 2016-05-03 2018-11-13 Certicom Corp. Method and system for cheon resistant static diffie-hellman security
US10320565B2 (en) * 2017-02-28 2019-06-11 Certicom Corp. Generating an elliptic curve point in an elliptic curve cryptographic system
CN109714153B (zh) * 2019-02-01 2022-04-08 铜陵学院 一种高效的聚合签名方法
CN110363509B (zh) * 2019-07-19 2022-03-29 华中师范大学 一种信息保护方法及装置
KR102568418B1 (ko) * 2021-08-26 2023-08-18 하이파이브랩 주식회사 다중 서명을 지원하는 전자 인증 시스템 및 방법
CN116170147A (zh) * 2023-02-01 2023-05-26 上海金仕达软件科技股份有限公司 一种用于国密sm2的获得不存在私钥的非对称加密公钥方法

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US5272755A (en) * 1991-06-28 1993-12-21 Matsushita Electric Industrial Co., Ltd. Public key cryptosystem with an elliptic curve
US5159632A (en) * 1991-09-17 1992-10-27 Next Computer, Inc. Method and apparatus for public key exchange in a cryptographic system
US5577124A (en) * 1995-03-09 1996-11-19 Arithmetica, Inc. Multi-purpose high speed cryptographically secure sequence generator based on zeta-one-way functions
EP0924895B1 (en) * 1997-12-17 2009-07-08 Nippon Telegraph and Telephone Corporation Encryption and decryption devices for public-key cryptosystems and recording medium with their processing programs recorded thereon
CA2257008C (en) * 1998-12-24 2007-12-11 Certicom Corp. A method for accelerating cryptographic operations on elliptic curves
FR2788650B1 (fr) * 1999-01-14 2001-02-16 Gemplus Card Int Procede cryptographique a cles publique et privee
US6507907B1 (en) * 1999-02-26 2003-01-14 Intel Corporation Protecting information in a system
US6959085B1 (en) * 1999-05-03 2005-10-25 Ntru Cryptosystems, Inc. Secure user identification based on ring homomorphisms
US20020199001A1 (en) * 2001-02-25 2002-12-26 Storymail, Inc. System and method for conducting a secure response communication session
US20020194501A1 (en) * 2001-02-25 2002-12-19 Storymail, Inc. System and method for conducting a secure interactive communication session
WO2003017559A2 (en) * 2001-08-13 2003-02-27 Board Of Trustees Of The Leland Stanford Junior University Systems and methods for identity-based encryption and related cryptographic techniques
JP4752176B2 (ja) * 2003-09-11 2011-08-17 日本電信電話株式会社 一方向性関数演算方法及び装置及びプログラム
US7499544B2 (en) * 2003-11-03 2009-03-03 Microsoft Corporation Use of isogenies for design of cryptosystems
US7587605B1 (en) * 2004-03-19 2009-09-08 Microsoft Corporation Cryptographic pairing-based short signature generation and verification
JP4842276B2 (ja) * 2004-11-11 2011-12-21 サーティコム コーポレーション 楕円曲線上の新しいトラップドア１方向性関数と、その、より短い署名及び非対称暗号化への応用

Also Published As

Publication number Publication date
US7844051B2 (en) 2010-11-30
WO2006050605A1 (en) 2006-05-18
JP2008519994A (ja) 2008-06-12
JP4842276B2 (ja) 2011-12-21
EP1815636A4 (en) 2011-03-16
JP2011232782A (ja) 2011-11-17
CN101099329B (zh) 2012-12-26
US8213605B2 (en) 2012-07-03
US20110060909A1 (en) 2011-03-10
JP5190142B2 (ja) 2013-04-24
CA2587474A1 (en) 2006-05-18
CN101099329A (zh) 2008-01-02
EP1815636A1 (en) 2007-08-08
EP1815636B1 (en) 2012-02-22
US20120314855A1 (en) 2012-12-13
US8782400B2 (en) 2014-07-15
US20060140400A1 (en) 2006-06-29
ATE546909T1 (de) 2012-03-15

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