ATE128297T1 - Verschlüsselungssystem mit öffentlichem schlüssel unter verwendung elliptischer kurven über ringe. - Google Patents

Verschlüsselungssystem mit öffentlichem schlüssel unter verwendung elliptischer kurven über ringe.

Info

Publication number
ATE128297T1
ATE128297T1 AT91103933T AT91103933T ATE128297T1 AT E128297 T1 ATE128297 T1 AT E128297T1 AT 91103933 T AT91103933 T AT 91103933T AT 91103933 T AT91103933 T AT 91103933T AT E128297 T1 ATE128297 T1 AT E128297T1
Authority
AT
Austria
Prior art keywords
computing
selecting
mod
multiplier
integers
Prior art date
Application number
AT91103933T
Other languages
English (en)
Inventor
Ueli Maurer
Original Assignee
Omnisec Ag
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 Omnisec Ag filed Critical Omnisec Ag
Application granted granted Critical
Publication of ATE128297T1 publication Critical patent/ATE128297T1/de

Links

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
    • 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
    • H04L9/32—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
    • H04L9/3234—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 additional secure or trusted devices, e.g. TPM, smartcard, USB or software token
    • 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
    • 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
    • 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
    • H04L2209/72—Signcrypting, i.e. digital signing and encrypting simultaneously

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Optimization (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Signal Processing (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Algebra (AREA)
  • General Engineering & Computer Science (AREA)
  • Storage Device Security (AREA)
  • Computer And Data Communications (AREA)
  • Lock And Its Accessories (AREA)
  • Error Detection And Correction (AREA)
  • Complex Calculations (AREA)
  • Data Exchanges In Wide-Area Networks (AREA)
AT91103933T 1991-03-14 1991-03-14 Verschlüsselungssystem mit öffentlichem schlüssel unter verwendung elliptischer kurven über ringe. ATE128297T1 (de)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
EP91103933A EP0503119B1 (de) 1991-03-14 1991-03-14 Verschlüsselungssystem mit öffentlichem Schlüssel unter Verwendung elliptischer Kurven über Ringe

Publications (1)

Publication Number Publication Date
ATE128297T1 true ATE128297T1 (de) 1995-10-15

Family

ID=8206517

Family Applications (1)

Application Number Title Priority Date Filing Date
AT91103933T ATE128297T1 (de) 1991-03-14 1991-03-14 Verschlüsselungssystem mit öffentlichem schlüssel unter verwendung elliptischer kurven über ringe.

Country Status (4)

Country Link
US (1) US5146500A (de)
EP (1) EP0503119B1 (de)
AT (1) ATE128297T1 (de)
DE (1) DE69113245D1 (de)

Families Citing this family (79)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5272755A (en) * 1991-06-28 1993-12-21 Matsushita Electric Industrial Co., Ltd. Public key cryptosystem with an elliptic curve
US5351297A (en) * 1991-06-28 1994-09-27 Matsushita Electric Industrial Co., Ltd. Method of privacy communication using elliptic curves
US6307935B1 (en) * 1991-09-17 2001-10-23 Apple Computer, Inc. Method and apparatus for fast elliptic encryption with direct embedding
US5271061A (en) * 1991-09-17 1993-12-14 Next Computer, Inc. Method and apparatus for public key exchange in a cryptographic system
US5159632A (en) * 1991-09-17 1992-10-27 Next Computer, Inc. Method and apparatus for public key exchange in a cryptographic system
NZ240019A (en) * 1991-09-30 1996-04-26 Peter John Smith Public key encrypted communication with non-multiplicative cipher
US5442707A (en) * 1992-09-28 1995-08-15 Matsushita Electric Industrial Co., Ltd. Method for generating and verifying electronic signatures and privacy communication using elliptic curves
US5627893A (en) * 1992-12-22 1997-05-06 Telstra Corporation Limited Cryptographic method
WO1994021066A1 (en) * 1993-03-05 1994-09-15 Telstra Corporation Limited A method and apparatus for generating a digital message authentication code
US5497423A (en) * 1993-06-18 1996-03-05 Matsushita Electric Industrial Co., Ltd. Method of implementing elliptic curve cryptosystems in digital signatures or verification and privacy communication
DE69327238T2 (de) * 1993-08-17 2000-09-07 Entrust Technologies ( Switzerland) Ltd. Liab. Co., Glattzentrum Verfahren zur digitalen Unterschrift und Verfahren zur Schlüsselübereinkunft
WO1996004602A1 (en) * 1994-07-29 1996-02-15 Certicom Corp. Elliptic curve encryption systems
US5606609A (en) * 1994-09-19 1997-02-25 Scientific-Atlanta Electronic document verification system and method
US5870470A (en) * 1996-02-20 1999-02-09 International Business Machines Corporation Method and apparatus for encrypting long blocks using a short-block encryption procedure
US5999626A (en) * 1996-04-16 1999-12-07 Certicom Corp. Digital signatures on a smartcard
US7567669B2 (en) 1996-05-17 2009-07-28 Certicom Corp. Strengthened public key protocol
US5737424A (en) * 1996-06-04 1998-04-07 Software Security, Inc. Method and system for secure distribution of protected data using elliptic curve systems
US6088798A (en) * 1996-09-27 2000-07-11 Kabushiki Kaisha Toshiba Digital signature method using an elliptic curve, a digital signature system, and a program storage medium having the digital signature method stored therein
JPH10133576A (ja) * 1996-10-31 1998-05-22 Hitachi Ltd 公開鍵暗号方法および装置
US5974151A (en) * 1996-11-01 1999-10-26 Slavin; Keith R. Public key cryptographic system having differential security levels
US6154541A (en) * 1997-01-14 2000-11-28 Zhang; Jinglong F Method and apparatus for a robust high-speed cryptosystem
US6782100B1 (en) 1997-01-29 2004-08-24 Certicom Corp. Accelerated finite field operations on an elliptic curve
GB2321741B (en) 1997-02-03 2000-10-04 Certicom Corp Data card verification system
US6266771B1 (en) 1997-02-10 2001-07-24 The Regents Of The University Of California Probabilistic signature scheme
US6587563B1 (en) 1997-02-15 2003-07-01 Apple Computer, Inc. Cryptographic system using chaotic dynamics
US6252959B1 (en) * 1997-05-21 2001-06-26 Worcester Polytechnic Institute Method and system for point multiplication in elliptic curve cryptosystem
US6240183B1 (en) 1997-06-19 2001-05-29 Brian E. Marchant Security apparatus for data transmission with dynamic random encryption
US6236728B1 (en) 1997-06-19 2001-05-22 Brian E. Marchant Security apparatus for data transmission with dynamic random encryption
US6094486A (en) * 1997-06-19 2000-07-25 Marchant; Brian E. Security apparatus for data transmission with dynamic random encryption
AU9426598A (en) * 1997-10-14 1999-05-03 Certicom Corp. Key validation scheme
DE19748954A1 (de) * 1997-10-29 1999-05-06 Francotyp Postalia Gmbh Verfahren für eine digital druckende Frankiermaschine zur Erzeugung und Überprüfung eines Sicherheitsabdruckes
WO2000010285A1 (en) * 1998-08-13 2000-02-24 Teledyne Technologies Incorporated Deterministically generating block substitution tables which meet a given standard of nonlinearity
US7292693B1 (en) 1998-08-13 2007-11-06 Teledyne Technologies Incorporated Deterministically generating block substitution tables which meet a given standard of nonlinearity
US7483699B2 (en) * 1998-09-22 2009-01-27 Qualcomm Incorporated Overhead message update with decentralized control
US7215773B1 (en) 1998-10-14 2007-05-08 Certicom.Corp. Key validation scheme
US6611597B1 (en) * 1999-01-25 2003-08-26 Matsushita Electric Industrial Co., Ltd. Method and device for constructing elliptic curves
US7519178B1 (en) * 1999-02-24 2009-04-14 International Business Machines Corporation Method, system and apparatus for ensuring a uniform distribution in key generation
JP3833412B2 (ja) * 1999-04-09 2006-10-11 富士通株式会社 有限体演算における表現データ生成装置および方法
EP1164744A1 (de) * 2000-06-16 2001-12-19 Koninklijke KPN N.V. Kryptografischer Vergleich von innerhalb eines kleinen Zahlenintervalls ausgewählten Werten
US20020041683A1 (en) * 2000-09-29 2002-04-11 Hopkins Dale W. Method for selecting optimal number of prime factors of a modulus for use in a cryptographic system
FI111491B (fi) * 2000-11-28 2003-07-31 Setec Oy Avainparin generointi
IL142962A (en) * 2001-05-03 2006-07-05 Nds Ltd OSS signing program
US7113594B2 (en) 2001-08-13 2006-09-26 The Board Of Trustees Of The Leland Stanford University Systems and methods for identity-based encryption and related cryptographic techniques
FR2828779B1 (fr) * 2001-08-17 2004-01-16 Gemplus Card Int Procede de calcul universel applique a des points d'une courbe elliptique
US7840806B2 (en) * 2002-10-16 2010-11-23 Enterprise Information Management, Inc. System and method of non-centralized zero knowledge authentication for a computer network
US8239917B2 (en) * 2002-10-16 2012-08-07 Enterprise Information Management, Inc. Systems and methods for enterprise security with collaborative peer to peer architecture
ATE352830T1 (de) 2002-10-26 2007-02-15 Additional Director Ipr Defenc Verfahren zur elliptische-kurven-verschlüsselung
CN100452695C (zh) * 2002-11-29 2009-01-14 北京华大信安科技有限公司 椭圆曲线加密解密方法和装置
GB2413465B (en) * 2004-04-23 2007-04-04 Hewlett Packard Development Co Cryptographic method and apparatus
EP1815636B1 (de) * 2004-11-11 2012-02-22 Certicom Corp. Neue falltür-einwegefunktion auf elliptischen kurven und ihre anwendung für asymmetrische verschlüsselung und kürzere signaturen
US7607019B2 (en) * 2005-02-03 2009-10-20 Apple Inc. Small memory footprint fast elliptic encryption
US8467535B2 (en) * 2005-01-18 2013-06-18 Certicom Corp. Accelerated verification of digital signatures and public keys
US8204232B2 (en) 2005-01-18 2012-06-19 Certicom Corp. Accelerated verification of digital signatures and public keys
KR100817048B1 (ko) * 2005-03-05 2008-03-26 삼성전자주식회사 여러 가지 포인트 표현을 기반으로 한 ｅｃｃ에서 ｄｆａ대책을 위한 암호화 방법 및 장치
US8139765B2 (en) * 2008-12-29 2012-03-20 King Fahd University Of Petroleum & Minerals Elliptical polynomial-based message authentication code
US8184803B2 (en) 2008-12-29 2012-05-22 King Fahd University Of Petroleum And Minerals Hash functions using elliptic curve cryptography
US8705740B2 (en) 2008-12-30 2014-04-22 King Fahd University Of Petroleum And Minerals Elliptic curve-based message authentication code system and method
US8165287B2 (en) * 2008-12-30 2012-04-24 King Fahd University Of Petroleum & Minerals Cryptographic hash functions using elliptic polynomial cryptography
US20100169658A1 (en) * 2008-12-30 2010-07-01 Lahouari Ghouti Elliptic curve-based message authentication code
US8170203B2 (en) * 2008-12-31 2012-05-01 King Fahd University Of Petroleum & Minerals Message authentication code with elliptic polynomial hopping
US8189771B2 (en) 2009-01-12 2012-05-29 King Fahd University Of Petroleum & Minerals Hash functions with elliptic polynomial hopping
US8189775B2 (en) * 2010-02-18 2012-05-29 King Fahd University Of Petroleum & Minerals Method of performing cipher block chaining using elliptic polynomial cryptography
US8331558B2 (en) * 2010-02-18 2012-12-11 King Fahd University Of Petroleum And Minerals Method of cipher block chaining using elliptic curve cryptography
US8332651B2 (en) 2010-02-18 2012-12-11 King Fahd University Of Petroleum And Minerals Method of generating a password protocol using elliptic polynomial cryptography
US8351601B2 (en) * 2010-02-18 2013-01-08 King Fahd University Of Petroleum And Minerals Elliptic polynomial cryptography with secret key embedding
US8385541B2 (en) * 2010-02-18 2013-02-26 King Fahd University Of Petroleum And Minerals Method of performing elliptic polynomial cryptography with elliptic polynomial hopping
US8699701B2 (en) 2010-12-01 2014-04-15 King Fahd University Method of performing XZ-elliptic curve cryptography for use with network security protocols
US8509426B1 (en) 2010-12-01 2013-08-13 King Fahd University Of Petroleum And Minerals XZ-elliptic curve cryptography system and method
ITGE20110091A1 (it) 2011-08-10 2013-02-11 Carlo Pes Metodo di cifratura e decifratura
US8745376B2 (en) 2011-10-14 2014-06-03 Certicom Corp. Verifying implicit certificates and digital signatures
CN105915514B (zh) * 2016-04-13 2020-09-11 中国电力科学研究院 计量用合并单元加密验证装置及方法
WO2017203992A1 (ja) * 2016-05-23 2017-11-30 ソニー株式会社 暗号化装置、暗号化方法、復号化装置、及び復号化方法
DE102017109423A1 (de) * 2017-05-03 2018-11-08 Osram Gmbh Verschlüsselung von Baken
US10637656B2 (en) 2017-11-28 2020-04-28 Blackberry Limited Method and system for key agreement utilizing semigroups
US11522718B2 (en) * 2019-11-28 2022-12-06 Crypto Lab Inc. Methods of generating encryption key and digital signature based on lattices
US11569987B2 (en) * 2021-02-12 2023-01-31 Blackberry Limited Method and system for key agreement utilizing plactic monoids
US11956370B2 (en) 2021-06-23 2024-04-09 Blackberry Limited Method and system for digital signatures utilizing multiplicative semigroups
CN113868607B (zh) * 2021-09-07 2024-10-18 中国联合网络通信集团有限公司 一种一次性身份标识使用方法及装置
IT202300025482A1 (it) 2023-11-29 2025-05-29 Massimo Bertaccini Sistema per la trasmissione di un messaggio criptato tramite canale quantistico e relativo metodo

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4200770A (en) * 1977-09-06 1980-04-29 Stanford University Cryptographic apparatus and method
US4405829A (en) * 1977-12-14 1983-09-20 Massachusetts Institute Of Technology Cryptographic communications system and method
US4885777A (en) * 1985-09-04 1989-12-05 Hitachi, Ltd. Electronic transaction system
US4748668A (en) * 1986-07-09 1988-05-31 Yeda Research And Development Company Limited Method, apparatus and article for identification and signature
EP0383985A1 (de) * 1989-02-24 1990-08-29 Claus Peter Prof. Dr. Schnorr Verfahren zur Identifikation von Teilnehmern sowie zur Generierung und Verifikation von elektronischen Unterschriften in einem Datenaustauschsystem
CA2011396C (en) * 1989-03-03 1995-01-03 Kazue Tanaka Cipher-key distribution system

Also Published As

Publication number Publication date
US5146500A (en) 1992-09-08
EP0503119A1 (de) 1992-09-16
EP0503119B1 (de) 1995-09-20
DE69113245D1 (de) 1995-10-26

Similar Documents

Publication Publication Date Title
DE69113245D1 (de) Verschlüsselungssystem mit öffentlichem Schlüssel unter Verwendung elliptischer Kurven über Ringe.
Naor et al. Visual cryptography
US6415032B1 (en) Encryption technique using stream cipher and block cipher
US6487661B2 (en) Key agreement and transport protocol
Nguyen et al. Lattice reduction in cryptology: An update
US8275124B2 (en) Threshold secret sharing apparatus, threshold secret sharing scheme, secret information decryption method, and program for the same
US6636968B1 (en) Multi-node encryption and key delivery
CA2176866A1 (en) Strengthened public key protocol
EP0739105A1 (de) Verfahren zur Unterschrift und zur Sitzungsschlüsselerzeugung
CA2068488A1 (en) Hybrid public key algorithm/data encryption algorithm key distribution method based on control vectors
ATE183315T1 (de) Verfahren und gerät zum verschlüsseln und entschlüsseln von kommunikationsdaten
CA2150683A1 (en) A Cryptographic Method
ATE403992T1 (de) Kryptografisches gerät und verfahren
WO1999034548A3 (en) System and method for deriving an appropriate initialization vector for secure communications
RU98102447A (ru) Дешифрирование повторно переданных данных в системе связи с шифрованием
EP0936776A3 (de) Netzwerksystem unter Verwendung eines Verfahrens zur Rückgewinnung eines verteilten Geheimnisses mit Schwellwert
US7062043B1 (en) Method of elliptic curve digital signature using coefficient splitting
Ding The differential cryptanalysis and design of natural stream ciphers
Biehl et al. Protocols for collusion-secure asymmetric fingerprinting
ElGamal Cryptography and logarithms over finite fields
DE69737806D1 (de) Datenverschlüsselungsverfahren
US6728376B1 (en) System for encrypting documents with stencils
ATE331360T1 (de) Verschlüsselungs- und entschlüsselungsverfahren von elektronischen informationen unter verwendung von zufälligen permutationen
US7024559B1 (en) Method of elliptic curve digital signature using expansion in joint sparse form
US7505585B2 (en) Method of generating cryptographic key using elliptic curve and expansion in joint sparse form and using same

Legal Events

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