AU2001254878A1 - Cryptography method on elliptic curves - Google Patents

Cryptography method on elliptic curves

Info

Publication number
AU2001254878A1
AU2001254878A1 AU2001254878A AU5487801A AU2001254878A1 AU 2001254878 A1 AU2001254878 A1 AU 2001254878A1 AU 2001254878 A AU2001254878 A AU 2001254878A AU 5487801 A AU5487801 A AU 5487801A AU 2001254878 A1 AU2001254878 A1 AU 2001254878A1
Authority
AU
Australia
Prior art keywords
elliptic curves
cryptography method
cryptography
elliptic
curves
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.)
Abandoned
Application number
AU2001254878A
Inventor
Jean-Sebastien Coron
Christophe Tymen
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Gemplus SA
Original Assignee
Gemplus Card International SA
Gemplus SA
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 Gemplus Card International SA, Gemplus SA filed Critical Gemplus Card International SA
Publication of AU2001254878A1 publication Critical patent/AU2001254878A1/en
Abandoned legal-status Critical Current

Links

Classifications

    • 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
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
    • H04L9/0841—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these involving Diffie-Hellman or related key agreement protocols
    • 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
    • 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
    • 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
    • H04L2209/08—Randomization, e.g. dummy operations or using noise

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Algebra (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Physics & Mathematics (AREA)
  • Computing Systems (AREA)
  • Complex Calculations (AREA)
  • Storage Device Security (AREA)
AU2001254878A 2000-04-18 2001-04-18 Cryptography method on elliptic curves Abandoned AU2001254878A1 (en)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
FR0005006 2000-04-18
FR0005006A FR2807898B1 (en) 2000-04-18 2000-04-18 ELLIPTICAL CURVE CRYPTOGRAPHY PROCESS
PCT/FR2001/001195 WO2001080481A1 (en) 2000-04-18 2001-04-18 Cryptography method on elliptic curves

Publications (1)

Publication Number Publication Date
AU2001254878A1 true AU2001254878A1 (en) 2001-10-30

Family

ID=8849392

Family Applications (1)

Application Number Title Priority Date Filing Date
AU2001254878A Abandoned AU2001254878A1 (en) 2000-04-18 2001-04-18 Cryptography method on elliptic curves

Country Status (8)

Country Link
US (1) US7218735B2 (en)
EP (1) EP1277307A1 (en)
JP (1) JP2004501385A (en)
CN (1) CN1425231A (en)
AU (1) AU2001254878A1 (en)
FR (1) FR2807898B1 (en)
MX (1) MXPA02010310A (en)
WO (1) WO2001080481A1 (en)

Families Citing this family (22)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7308096B2 (en) * 2000-05-30 2007-12-11 Hitachi, Ltd. Elliptic scalar multiplication system
CN1902853B (en) 2003-10-28 2012-10-03 塞尔蒂卡姆公司 Method and apparatus for verifiable generation of public keys
US9621539B2 (en) * 2004-01-30 2017-04-11 William H. Shawn Method and apparatus for securing the privacy of a computer network
WO2005107141A1 (en) * 2004-04-30 2005-11-10 Research In Motion Limited Systems and methods to securely generate shared keys
US7483533B2 (en) * 2004-08-05 2009-01-27 King Fahd University Of Petroleum Elliptic polynomial cryptography with multi x-coordinates embedding
US7483534B2 (en) * 2004-08-05 2009-01-27 King Fahd University Of Petroleum Elliptic polynomial cryptography with multi y-coordinates embedding
US7607019B2 (en) * 2005-02-03 2009-10-20 Apple Inc. Small memory footprint fast elliptic encryption
WO2006076800A1 (en) * 2005-01-18 2006-07-27 Certicom Corp. Accelerated verification of digital signatures and public keys
US8396213B2 (en) 2005-01-21 2013-03-12 Certicom Corp. Elliptic curve random number generation
CA2542556C (en) * 2005-06-03 2014-09-16 Tata Consultancy Services Limited An authentication system executing an elliptic curve digital signature cryptographic process
US7587047B2 (en) * 2005-06-22 2009-09-08 Apple Inc. Chaos generator for accumulation of stream entropy
US8165286B2 (en) * 2008-04-02 2012-04-24 Apple Inc. Combination white box/black box cryptographic processes and apparatus
EP2151947A1 (en) * 2008-08-05 2010-02-10 Irdeto Access B.V. Signcryption scheme based on elliptic curve cryptography
CN101582170B (en) * 2009-06-09 2011-08-31 上海大学 Remote sensing image encryption method based on elliptic curve cryptosystem
CN102546162A (en) * 2010-12-29 2012-07-04 北京数字太和科技有限责任公司 Data safety processing method
US10129026B2 (en) * 2016-05-03 2018-11-13 Certicom Corp. Method and system for cheon resistant static diffie-hellman security
US10361855B2 (en) * 2016-05-27 2019-07-23 Nxp B.V. Computing a secure elliptic curve scalar multiplication using an unsecured and secure environment
WO2018135511A1 (en) * 2017-01-18 2018-07-26 日本電信電話株式会社 Secure computation method, secure computation system, secure computation device, and program
EP3376705A1 (en) * 2017-03-17 2018-09-19 Koninklijke Philips N.V. Elliptic curve point multiplication device and method in a white-box context
KR102329580B1 (en) * 2020-11-10 2021-11-23 주식회사 아톰릭스랩 Crypto Key distribution and recovery method for multiple 3rd parties managed systems
KR102328896B1 (en) * 2020-11-10 2021-11-22 주식회사 아톰릭스랩 Crypto Key distribution and recovery method for 3rd party managed system
KR102536397B1 (en) * 2022-10-26 2023-05-26 주식회사 시옷 Signature verification method performed in a computing device and a computing device performing the same method

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5999626A (en) * 1996-04-16 1999-12-07 Certicom Corp. Digital signatures on a smartcard
US5854759A (en) * 1997-05-05 1998-12-29 Rsa Data Security, Inc. Methods and apparatus for efficient finite field basis conversion
ATE325478T1 (en) * 1998-01-02 2006-06-15 Cryptography Res Inc LEAK RESISTANT CRYPTOGRAPHIC METHOD AND APPARATUS
CA2257008C (en) * 1998-12-24 2007-12-11 Certicom Corp. A method for accelerating cryptographic operations on elliptic curves
US6611597B1 (en) * 1999-01-25 2003-08-26 Matsushita Electric Industrial Co., Ltd. Method and device for constructing elliptic curves

Also Published As

Publication number Publication date
US20030152218A1 (en) 2003-08-14
US7218735B2 (en) 2007-05-15
CN1425231A (en) 2003-06-18
JP2004501385A (en) 2004-01-15
WO2001080481A1 (en) 2001-10-25
FR2807898A1 (en) 2001-10-19
MXPA02010310A (en) 2003-04-25
FR2807898B1 (en) 2002-06-28
EP1277307A1 (en) 2003-01-22

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