DE60005284D1 - Berechnungsverfahren für kryptographie mittels elliptischer kurven - Google Patents
Berechnungsverfahren für kryptographie mittels elliptischer kurvenInfo
- Publication number
- DE60005284D1 DE60005284D1 DE60005284T DE60005284T DE60005284D1 DE 60005284 D1 DE60005284 D1 DE 60005284D1 DE 60005284 T DE60005284 T DE 60005284T DE 60005284 T DE60005284 T DE 60005284T DE 60005284 D1 DE60005284 D1 DE 60005284D1
- Authority
- DE
- Germany
- Prior art keywords
- cryptography
- calculation method
- elliptic curves
- 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.)
- Expired - Lifetime
Links
Classifications
-
- 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
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Computational Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computing Systems (AREA)
- Mathematical Physics (AREA)
- General Engineering & Computer Science (AREA)
- Complex Calculations (AREA)
- Error Detection And Correction (AREA)
- Optical Communication System (AREA)
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FR9908949A FR2796177B1 (fr) | 1999-07-09 | 1999-07-09 | Procede de cryptographie mis en oeuvre entre deux entites echangeant des informations |
FR9908949 | 1999-07-09 | ||
PCT/FR2000/001979 WO2001004742A1 (fr) | 1999-07-09 | 2000-07-07 | Procede de calcul pour la cryptographie a courbe elliptique |
Publications (2)
Publication Number | Publication Date |
---|---|
DE60005284D1 true DE60005284D1 (de) | 2003-10-23 |
DE60005284T2 DE60005284T2 (de) | 2004-07-01 |
Family
ID=9547945
Family Applications (2)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
DE1110140T Pending DE1110140T1 (de) | 1999-07-09 | 2000-07-07 | Berechnungsverfahren für kryptographie mittels elliptischer kurven |
DE60005284T Expired - Lifetime DE60005284T2 (de) | 1999-07-09 | 2000-07-07 | Berechnungsverfahren für kryptographie mittels elliptischer kurven |
Family Applications Before (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
DE1110140T Pending DE1110140T1 (de) | 1999-07-09 | 2000-07-07 | Berechnungsverfahren für kryptographie mittels elliptischer kurven |
Country Status (8)
Country | Link |
---|---|
US (1) | US7079650B1 (de) |
EP (1) | EP1110140B1 (de) |
JP (1) | JP4704640B2 (de) |
CA (1) | CA2342737C (de) |
DE (2) | DE1110140T1 (de) |
ES (1) | ES2159274T3 (de) |
FR (1) | FR2796177B1 (de) |
WO (1) | WO2001004742A1 (de) |
Families Citing this family (34)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO1998053637A1 (en) * | 1997-05-21 | 1998-11-26 | E.S.P. Communications, Inc. | System, method and apparatus for 'caller only' initiated two-way wireless communication with caller generated billing |
US7200225B1 (en) | 1999-11-12 | 2007-04-03 | Richard Schroeppel | Elliptic curve point ambiguity resolution apparatus and method |
US7308097B2 (en) * | 2001-12-07 | 2007-12-11 | Ntru Cryptosystems, Inc. | Digital signature and authentication method and apparatus |
US7298839B2 (en) | 2003-07-25 | 2007-11-20 | Microsoft Corporation | Squared Weil and Tate pairing techniques for use with elliptic curves |
US7769167B2 (en) | 2003-07-25 | 2010-08-03 | Microsoft Corporation | Weil and Tate pairing techniques using parabolas |
US7440569B2 (en) * | 2003-07-28 | 2008-10-21 | Microsoft Corporation | Tate pairing techniques for use with hyperelliptic curves |
KR100530372B1 (ko) * | 2003-12-20 | 2005-11-22 | 삼성전자주식회사 | 사이드채널 공격을 방지할 수 있는 타원곡선 암호화 방법 |
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 |
US7742596B2 (en) * | 2004-08-24 | 2010-06-22 | General Dynamics C4 Systems, Inc. | Reliable elliptic curve cryptography computation |
JP4752313B2 (ja) | 2004-09-30 | 2011-08-17 | ソニー株式会社 | 暗号処理演算方法、および暗号処理装置、並びにコンピュータ・プログラム |
US7598855B2 (en) | 2005-02-01 | 2009-10-06 | Location Based Technologies, Inc. | Apparatus and method for locating individuals and objects using tracking devices |
US20070229350A1 (en) * | 2005-02-01 | 2007-10-04 | Scalisi Joseph F | Apparatus and Method for Providing Location Information on Individuals and Objects using Tracking Devices |
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 |
DE102006002891B4 (de) * | 2006-01-20 | 2009-06-04 | Siemens Ag | Verfahren, Vorrichtung und System zum Verifizieren von auf einer elliptischen Kurve ermittelten Punkten |
KR20080012633A (ko) * | 2006-08-04 | 2008-02-12 | 삼성전자주식회사 | 고속 몽고메리 전력 래더 알고리즘에서 사용되는 폴트 검출동작을 구현하기 위한 소수 유한 영역에서의 포인트 덧셈방법 및 덧셈 연산 장치 |
US8102256B2 (en) | 2008-01-06 | 2012-01-24 | Location Based Technologies Inc. | Apparatus and method for determining location and tracking coordinates of a tracking device |
US8774827B2 (en) | 2007-04-05 | 2014-07-08 | Location Based Technologies, Inc. | Apparatus and method for generating position fix of a tracking device in accordance with a subscriber service usage profile to conserve tracking device power |
US8244468B2 (en) * | 2007-11-06 | 2012-08-14 | Location Based Technology Inc. | System and method for creating and managing a personalized web interface for monitoring location information on individuals and objects using tracking devices |
US8224355B2 (en) | 2007-11-06 | 2012-07-17 | Location Based Technologies Inc. | System and method for improved communication bandwidth utilization when monitoring location information |
US8497774B2 (en) | 2007-04-05 | 2013-07-30 | Location Based Technologies Inc. | Apparatus and method for adjusting refresh rate of location coordinates of a tracking device |
US9111189B2 (en) * | 2007-10-31 | 2015-08-18 | Location Based Technologies, Inc. | Apparatus and method for manufacturing an electronic package |
US8654974B2 (en) | 2007-10-18 | 2014-02-18 | Location Based Technologies, Inc. | Apparatus and method to provide secure communication over an insecure communication channel for location information using tracking devices |
US20170207918A1 (en) * | 2009-06-16 | 2017-07-20 | Morpho | Cryptography on an elliptical curve |
US20140314229A1 (en) * | 2011-12-09 | 2014-10-23 | Morpho | Cryptography on a simplified elliptical curve |
US8548160B2 (en) * | 2010-01-13 | 2013-10-01 | Microsoft Corporation | Determination of pairings on a curve using aggregated inversions |
US8731187B2 (en) * | 2010-12-21 | 2014-05-20 | Microsoft Corporation | Computing genus-2 curves using general isogenies |
US10148285B1 (en) | 2012-07-25 | 2018-12-04 | Erich Schmitt | Abstraction and de-abstraction of a digital data stream |
CN103124213B (zh) * | 2013-03-05 | 2015-09-16 | 丁勇 | 基于椭圆曲线密码的传感器网络密钥管理方法 |
US10795858B1 (en) | 2014-02-18 | 2020-10-06 | Erich Schmitt | Universal abstraction and de-abstraction of a digital data stream |
US10673631B2 (en) * | 2016-11-07 | 2020-06-02 | Infosec Global Inc. | Elliptic curve isogeny-based cryptographic scheme |
US11157240B2 (en) * | 2019-02-15 | 2021-10-26 | International Business Machines Corporation | Perform cryptographic computation scalar multiply instruction |
CN111106937A (zh) * | 2019-12-31 | 2020-05-05 | 深圳职业技术学院 | 一种基于随机素数的双通道交换的超奇异椭圆曲线算法的密钥交换方法 |
WO2021225578A1 (en) | 2020-05-04 | 2021-11-11 | Pqsecure Technologies, Llc | An efficient hardware architecture for highly secure isogeny-based cryptosystems |
Family Cites Families (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP0804758B1 (de) * | 1994-07-29 | 2005-11-09 | Certicom Corp. | Verschlüsselungssystem für elliptische kurve |
US6490352B1 (en) * | 1999-03-05 | 2002-12-03 | Richard Schroeppel | Cryptographic elliptic curve apparatus and method |
JP3639153B2 (ja) * | 1999-08-16 | 2005-04-20 | 日本電信電話株式会社 | 逐次拡大を用いた楕円曲線演算装置及びプログラム記録媒体 |
US20020055962A1 (en) * | 1999-11-12 | 2002-05-09 | Richard Schroeppel | Automatically solving equations in finite fields |
EP1323027A1 (de) * | 2000-08-29 | 2003-07-02 | NTRU Cryptosystems, Inc. | Kryptographisches verfahren und kryptographische vorrichtung mit verbesserter geschwindigkeit |
CA2439736C (en) * | 2002-09-03 | 2013-05-21 | Certicom Corp. | Method and apparatus for performing validation of elliptic curve public keys |
-
1999
- 1999-07-09 FR FR9908949A patent/FR2796177B1/fr not_active Expired - Lifetime
-
2000
- 2000-07-07 DE DE1110140T patent/DE1110140T1/de active Pending
- 2000-07-07 US US09/786,756 patent/US7079650B1/en not_active Expired - Lifetime
- 2000-07-07 CA CA002342737A patent/CA2342737C/fr not_active Expired - Lifetime
- 2000-07-07 WO PCT/FR2000/001979 patent/WO2001004742A1/fr active IP Right Grant
- 2000-07-07 ES ES00949685T patent/ES2159274T3/es not_active Expired - Lifetime
- 2000-07-07 EP EP00949685A patent/EP1110140B1/de not_active Expired - Lifetime
- 2000-07-07 JP JP2001510082A patent/JP4704640B2/ja not_active Expired - Fee Related
- 2000-07-07 DE DE60005284T patent/DE60005284T2/de not_active Expired - Lifetime
Also Published As
Publication number | Publication date |
---|---|
FR2796177A1 (fr) | 2001-01-12 |
JP4704640B2 (ja) | 2011-06-15 |
JP2003504695A (ja) | 2003-02-04 |
CA2342737A1 (fr) | 2001-01-18 |
DE1110140T1 (de) | 2002-02-21 |
US7079650B1 (en) | 2006-07-18 |
EP1110140A1 (de) | 2001-06-27 |
WO2001004742A1 (fr) | 2001-01-18 |
CA2342737C (fr) | 2004-06-01 |
FR2796177B1 (fr) | 2001-10-12 |
ES2159274T3 (es) | 2004-05-16 |
ES2159274T1 (es) | 2001-10-01 |
DE60005284T2 (de) | 2004-07-01 |
EP1110140B1 (de) | 2003-09-17 |
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Legal Events
Date | Code | Title | Description |
---|---|---|---|
8364 | No opposition during term of opposition |