BR9815161A - Método para produzir um produto de multiplicação de curva elìptica; método para otimizar o cálculo de uma expressão, método para produção de um produto de adição de curva elìptica; aparelho para produção de um produto de multiplicação de ponto de curva elìptica - Google Patents
Método para produzir um produto de multiplicação de curva elìptica; método para otimizar o cálculo de uma expressão, método para produção de um produto de adição de curva elìptica; aparelho para produção de um produto de multiplicação de ponto de curva elìpticaInfo
- Publication number
- BR9815161A BR9815161A BR9815161-4A BR9815161A BR9815161A BR 9815161 A BR9815161 A BR 9815161A BR 9815161 A BR9815161 A BR 9815161A BR 9815161 A BR9815161 A BR 9815161A
- Authority
- BR
- Brazil
- Prior art keywords
- producing
- product
- calculation
- elliptically
- present
- Prior art date
Links
Classifications
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- 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
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- 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
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- 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
- G06F7/728—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 using Montgomery reduction
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- 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
- H04L9/3073—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 involving pairings, e.g. identity based encryption [IBE], bilinear mappings or bilinear pairings, e.g. Weil or Tate pairing
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
- Y04S40/20—Information technology specific aspects, e.g. CAD, simulation, modelling, system security
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Computational Mathematics (AREA)
- Mathematical Physics (AREA)
- Computing Systems (AREA)
- General Engineering & Computer Science (AREA)
- Algebra (AREA)
- Computer Security & Cryptography (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Complex Calculations (AREA)
Abstract
<B>"MéTODO PARA PRODUZIR UM PRODUTO DE MULTIPLICAçãO DE CURVA ELìPTICA; MéTODO PARA OTIMIZAR O CáLCULO DE UMA EXPRESSãO; MéTODO PARA PRODUçãO DE UM PRODUTO DE ADIçãO DE CURVA ELìPTICA; APARELHO PARA PRODUçãO DE UM PRODUTO DE MULTIPLICAçãO DE PONTO DE CURVA ELìPTICA"<D> A presente invenção provê um método de transformação para obter implementações otimizadas em hardware e software de sistemas criptográficos baseados em curva elíptica, incluindo criptografia, descriptografia e funções de assinatura. O método é aplicável a qualquer grupo G de curva elíptica definido sobre qualquer campo F. Mais especificamente, a presente invenção é caracterizada por acelerar a operação de multiplicação de ponto de curva elíptica, que consiste no cálculo Q = eP, onde P é um membro de G e e é um número inteiro. Isto é obtido transformando-se P = (x, y) em um ponto P' = (x', y') a fim de se computar Q'= (u, v = eP'). O ponto P' não está necessariamente na curva elíptica, mas desempenhando-se o cálculo em P' e transformando-se o Q' resultante de volta em G, pode ser possível calcular Q mais eficientemente do que utilizando-se um método direto. A presente invenção também inclui um método para otimizar o cálculo de operações criptográficas envolvendo expressões arbitrárias em aritmética de campo finito através de um método de transformação que permite a utilização de qualquer campo F de um modo eficiente. A invenção inclui um método para otimizar cálculo finito arbitrário em um campo finito. A presente invenção ensina um conjunto de transformações de cálculos criptográficos que permite a utilização de outras técnicas conhecidas as quais, anteriormente à esta invenção, tinham apenas sido aplicáveis a certos casos especiais limitados.
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US6931497P | 1997-12-05 | 1997-12-05 | |
PCT/US1998/025824 WO1999030458A1 (en) | 1997-12-05 | 1998-12-04 | Transformation methods for optimizing elliptic curve cryptographic computations |
Publications (1)
Publication Number | Publication Date |
---|---|
BR9815161A true BR9815161A (pt) | 2000-10-10 |
Family
ID=22088145
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
BR9815161-4A BR9815161A (pt) | 1997-12-05 | 1998-12-04 | Método para produzir um produto de multiplicação de curva elìptica; método para otimizar o cálculo de uma expressão, método para produção de um produto de adição de curva elìptica; aparelho para produção de um produto de multiplicação de ponto de curva elìptica |
Country Status (7)
Country | Link |
---|---|
EP (1) | EP1038371A4 (pt) |
JP (1) | JP2001526416A (pt) |
CN (1) | CN1280726A (pt) |
AU (1) | AU758621B2 (pt) |
BR (1) | BR9815161A (pt) |
CA (1) | CA2310588A1 (pt) |
WO (1) | WO1999030458A1 (pt) |
Families Citing this family (20)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6307935B1 (en) * | 1991-09-17 | 2001-10-23 | Apple Computer, Inc. | Method and apparatus for fast elliptic encryption with direct embedding |
US6343305B1 (en) | 1999-09-14 | 2002-01-29 | The State Of Oregon Acting By And Through The State Board Of Higher Education On Behalf Of Oregon State University | Methods and apparatus for multiplication in a galois field GF (2m), encoders and decoders using same |
FR2821944B1 (fr) * | 2001-03-12 | 2003-05-30 | Gemplus Card Int | Procede de protection contre les attaques par mesure de courant ou de rayonnement electromagnetique |
FR2821945B1 (fr) * | 2001-03-12 | 2003-05-30 | Gemplus Card Int | Procede de protection contre les attaques par mesure de courant ou de rayonnement electromagnetique |
FR2824210B1 (fr) * | 2001-04-27 | 2003-05-30 | Gemplus Card Int | Procede de contre-mesure dans un composant electronique mettant en oeuvre un algorithme cryptographique du type a cle publique sur une courbe elliptique |
FR2824653B1 (fr) * | 2001-05-11 | 2003-08-08 | Gemplus Card Int | Dispositif destine a realiser des calculs d'exponentiation appliques a des points d'une courbe elliptique |
US7209555B2 (en) * | 2001-10-25 | 2007-04-24 | Matsushita Electric Industrial Co., Ltd. | Elliptic curve converting device, elliptic curve converting method, elliptic curve utilization device and elliptic curve generating device |
CN100440776C (zh) * | 2002-11-29 | 2008-12-03 | 北京华大信安科技有限公司 | 椭圆曲线签名和验证签名方法和装置 |
US7499544B2 (en) | 2003-11-03 | 2009-03-03 | Microsoft Corporation | Use of isogenies for design of cryptosystems |
US7664957B2 (en) | 2004-05-20 | 2010-02-16 | Ntt Docomo, Inc. | Digital signatures including identity-based aggregate signatures |
CN101065924B (zh) * | 2004-11-24 | 2011-06-08 | 惠普开发有限公司 | 具有加密功能的智能卡和使用这种卡的方法和系统 |
US7602907B2 (en) * | 2005-07-01 | 2009-10-13 | Microsoft Corporation | Elliptic curve point multiplication |
CN100414492C (zh) * | 2005-11-04 | 2008-08-27 | 北京浦奥得数码技术有限公司 | 一种椭圆曲线密码系统及实现方法 |
US8311214B2 (en) * | 2006-04-24 | 2012-11-13 | Motorola Mobility Llc | Method for elliptic curve public key cryptographic validation |
CN101079701B (zh) * | 2006-05-22 | 2011-02-02 | 北京华大信安科技有限公司 | 高安全性的椭圆曲线加解密方法和装置 |
US8548160B2 (en) * | 2010-01-13 | 2013-10-01 | Microsoft Corporation | Determination of pairings on a curve using aggregated inversions |
CN103078732B (zh) * | 2013-01-08 | 2015-10-21 | 武汉大学 | 一种素域椭圆曲线加密的点乘加速电路 |
CN104601322A (zh) * | 2013-10-31 | 2015-05-06 | 上海华虹集成电路有限责任公司 | 用于密码芯片中三元扩域的蒙哥马利阶梯算法 |
CN104267926B (zh) * | 2014-09-29 | 2018-03-09 | 北京宏思电子技术有限责任公司 | 获取椭圆曲线密码数据的方法和装置 |
CN108337091A (zh) * | 2018-03-22 | 2018-07-27 | 北京中电华大电子设计有限责任公司 | 一种SM9椭圆曲线扭曲线上特定点的p倍点计算方法 |
Family Cites Families (8)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
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 |
US5373560A (en) * | 1991-12-06 | 1994-12-13 | Schlafly; Roger | Partial modular reduction method |
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 |
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 |
US5577124A (en) * | 1995-03-09 | 1996-11-19 | Arithmetica, Inc. | Multi-purpose high speed cryptographically secure sequence generator based on zeta-one-way functions |
US5854759A (en) * | 1997-05-05 | 1998-12-29 | Rsa Data Security, Inc. | Methods and apparatus for efficient finite field basis conversion |
CA2321478A1 (en) * | 1998-02-18 | 1999-08-26 | Erwin Hess | Method and device for cryptographic processing with the aid or an elliptic curve on a computer |
-
1998
- 1998-12-04 BR BR9815161-4A patent/BR9815161A/pt not_active Application Discontinuation
- 1998-12-04 JP JP2000524894A patent/JP2001526416A/ja active Pending
- 1998-12-04 CN CN98811822A patent/CN1280726A/zh active Pending
- 1998-12-04 AU AU21983/99A patent/AU758621B2/en not_active Ceased
- 1998-12-04 WO PCT/US1998/025824 patent/WO1999030458A1/en not_active Application Discontinuation
- 1998-12-04 CA CA002310588A patent/CA2310588A1/en not_active Abandoned
- 1998-12-04 EP EP98965973A patent/EP1038371A4/en not_active Withdrawn
Also Published As
Publication number | Publication date |
---|---|
EP1038371A4 (en) | 2002-01-30 |
CA2310588A1 (en) | 1999-06-17 |
AU758621B2 (en) | 2003-03-27 |
AU2198399A (en) | 1999-06-28 |
JP2001526416A (ja) | 2001-12-18 |
WO1999030458A1 (en) | 1999-06-17 |
EP1038371A1 (en) | 2000-09-27 |
CN1280726A (zh) | 2001-01-17 |
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Legal Events
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FA10 | Dismissal: dismissal - article 33 of industrial property law | ||
B11Y | Definitive dismissal acc. article 33 of ipl - extension of time limit for request of examination expired |