DE60316586D1 - Effiziente arithmetik in galois-feldern ungerader charakterstik auf binärer hardware - Google Patents

Effiziente arithmetik in galois-feldern ungerader charakterstik auf binärer hardware

Info

Publication number
DE60316586D1
DE60316586D1 DE60316586T DE60316586T DE60316586D1 DE 60316586 D1 DE60316586 D1 DE 60316586D1 DE 60316586 T DE60316586 T DE 60316586T DE 60316586 T DE60316586 T DE 60316586T DE 60316586 D1 DE60316586 D1 DE 60316586D1
Authority
DE
Germany
Prior art keywords
ungerader
galois fields
data bits
binary data
efficient arithmetic
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
DE60316586T
Other languages
English (en)
Other versions
DE60316586T2 (de
Inventor
Rolf Blom
Mats Naeslund
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.)
Telefonaktiebolaget LM Ericsson AB
Original Assignee
Telefonaktiebolaget LM Ericsson AB
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 Telefonaktiebolaget LM Ericsson AB filed Critical Telefonaktiebolaget LM Ericsson AB
Application granted granted Critical
Publication of DE60316586D1 publication Critical patent/DE60316586D1/de
Publication of DE60316586T2 publication Critical patent/DE60316586T2/de
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q20/00—Payment architectures, schemes or protocols
    • G06Q20/38—Payment protocols; Details thereof
    • G06Q20/382—Payment protocols; Details thereof insuring higher security of transaction
    • G06Q20/3829—Payment protocols; Details thereof insuring higher security of transaction involving key management
    • 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
    • H04L9/30—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

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computer Security & Cryptography (AREA)
  • Business, Economics & Management (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Accounting & Taxation (AREA)
  • Strategic Management (AREA)
  • Finance (AREA)
  • General Business, Economics & Management (AREA)
  • Algebra (AREA)
  • General Engineering & Computer Science (AREA)
  • Error Detection And Correction (AREA)
  • Complex Calculations (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)
  • Detection And Correction Of Errors (AREA)
  • Storage Device Security (AREA)
DE60316586T 2002-10-17 2003-10-07 Effiziente arithmetik in galois-feldern ungerader charakterstik auf binärer hardware Expired - Lifetime DE60316586T2 (de)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
US271947 2002-10-17
US10/271,947 US7724898B2 (en) 2002-10-17 2002-10-17 Cryptography using finite fields of odd characteristic on binary hardware
PCT/SE2003/001560 WO2004036413A2 (en) 2002-10-17 2003-10-07 Efficient arithmetic in finite fields of odd characteristic on binary hardware

Publications (2)

Publication Number Publication Date
DE60316586D1 true DE60316586D1 (de) 2007-11-08
DE60316586T2 DE60316586T2 (de) 2008-07-24

Family

ID=32106422

Family Applications (1)

Application Number Title Priority Date Filing Date
DE60316586T Expired - Lifetime DE60316586T2 (de) 2002-10-17 2003-10-07 Effiziente arithmetik in galois-feldern ungerader charakterstik auf binärer hardware

Country Status (6)

Country Link
US (1) US7724898B2 (de)
EP (1) EP1552382B1 (de)
AT (1) ATE374397T1 (de)
AU (1) AU2003267913A1 (de)
DE (1) DE60316586T2 (de)
WO (1) WO2004036413A2 (de)

Families Citing this family (25)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100486726B1 (ko) * 2002-11-09 2005-05-03 삼성전자주식회사 유한 체에서의 기저 변환 방법 및 기저 변환 장치
FR2867289A1 (fr) * 2004-03-02 2005-09-09 France Telecom Procede et dispositif pour accomplir une operation cryptographique
DE102005028662B4 (de) * 2005-03-04 2022-06-02 Ihp Gmbh - Innovations For High Performance Microelectronics / Leibniz-Institut Für Innovative Mikroelektronik Verfahren und Vorrichtung zum Berechnen einer Polynom-Multiplikation, insbesondere für die elliptische Kurven-Kryptographie
US7983415B2 (en) * 2006-12-19 2011-07-19 King Fahd University Of Petroleum And Minerals Method for performing iterative scalar multiplication which is protected against address bit attack
US8607070B2 (en) * 2006-12-20 2013-12-10 Kingston Technology Corporation Secure storage system and method of use
US8290146B2 (en) * 2007-01-19 2012-10-16 Mitsubishi Electric Corporation Ciphertext generating apparatus, cryptographic communication system, and group parameter generating apparatus
US8527781B2 (en) * 2007-05-09 2013-09-03 Kingston Technology Corporation Secure and scalable solid state disk system
US8499168B2 (en) * 2007-05-09 2013-07-30 Kingston Technology Corporation Secure and scalable solid state disk system
US8010768B2 (en) * 2007-05-09 2011-08-30 Kingston Technology Corporation Secure and scalable solid state disk system
CA2688592C (en) * 2007-10-01 2014-04-15 Research In Motion Limited Substitution table masking for cryptographic processes
WO2009104260A1 (ja) * 2008-02-20 2009-08-27 三菱電機株式会社 検証装置
KR101582806B1 (ko) * 2008-05-20 2016-01-07 이르데토 비.브이. 암호화 시스템
JP5354994B2 (ja) * 2008-08-25 2013-11-27 株式会社東芝 代数的トーラスを用いたデータ圧縮処理を行う装置およびプログラム
US8498411B1 (en) * 2008-12-12 2013-07-30 Emc Corporation Using multiples above two with running totals and reference values other than 0 and 2 (window size) in elliptic curve cryptography scalar multiplication acceleration tables
US7773000B1 (en) 2009-02-27 2010-08-10 Red Hat, Inc. Efficient coding of integers in non-power-of-two ranges
WO2011148558A1 (ja) * 2010-05-28 2011-12-01 日本電気株式会社 署名生成装置、署名方法、及び署名生成プログラムが格納された非一時的なコンピュータ可読媒体
TW201243643A (en) * 2011-04-22 2012-11-01 Inst Information Industry Hierarchical encryption/decryption device and method thereof
CA2838203C (en) 2011-06-06 2021-04-06 Certicom Corp. Squaring binary finite field elements
US10148285B1 (en) 2012-07-25 2018-12-04 Erich Schmitt Abstraction and de-abstraction of a digital data stream
WO2014112170A1 (ja) * 2013-01-16 2014-07-24 三菱電機株式会社 情報処理装置及び情報処理方法及びプログラム
US10795858B1 (en) 2014-02-18 2020-10-06 Erich Schmitt Universal abstraction and de-abstraction of a digital data stream
US9553723B2 (en) * 2014-11-14 2017-01-24 Unsene, ehf. Multi-dimensional encryption
JP6670421B1 (ja) * 2016-11-08 2020-03-18 コーニンクレッカ フィリップス エヌ ヴェＫｏｎｉｎｋｌｉｊｋｅ Ｐｈｉｌｉｐｓ Ｎ．Ｖ． 剰余数系表現を基数表現に変換する電子計算装置
WO2020036598A1 (en) * 2018-08-16 2020-02-20 Pqsecure Technologies, Llc An efficient architecture and method for arithmetic computations in post-quantum cryptography
US11206136B1 (en) * 2020-05-27 2021-12-21 Nxp B.V. Method for multiplying polynomials for a cryptographic operation

Family Cites Families (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE2512270A1 (de) * 1975-03-20 1976-09-23 Siemens Ag Steuereinheit eines durch mikroprogramme steuerbaren prozessors einer datenverarbeitungsanlage und verfahren zu ihrem betrieb
US4200770A (en) * 1977-09-06 1980-04-29 Stanford University Cryptographic apparatus and method
JPS588348A (ja) * 1981-07-07 1983-01-18 Sony Corp 出力表示用メモリの制御回路
EP0080528A1 (de) 1981-11-30 1983-06-08 Omnet Associates Berechnungsverfahren und Gerät für Arithmetik endlicher Felder
EP0085130A1 (de) * 1982-02-02 1983-08-10 Omnet Associates Verfahren und Einrichtung zur Aufrechterhaltung der Geheimhaltung von durch öffentliche Übertragung übermittelten Nachrichten
US4587657A (en) * 1983-12-16 1986-05-06 Rockwell International Corporation Suppression of high-frequency acoustic waves in E-beam lasers
US4875211A (en) * 1986-12-10 1989-10-17 Matsushita Electric Industrial Co., Ltd. Galois field arithmetic logic unit
US4891781A (en) * 1987-03-04 1990-01-02 Cylink Corporation Modulo arithmetic processor chip
DE69534603T2 (de) * 1994-07-29 2006-08-03 Certicom Corp., Mississauga Verschlüsselungssystem für elliptische kurve
US6643765B1 (en) * 1995-08-16 2003-11-04 Microunity Systems Engineering, Inc. Programmable processor with group floating point operations
US5854759A (en) * 1997-05-05 1998-12-29 Rsa Data Security, Inc. Methods and apparatus for efficient finite field basis conversion
US7069287B2 (en) * 2000-09-19 2006-06-27 Worcester Polytechnic Institute Method for efficient computation of odd characteristic extension fields
DE10107376A1 (de) * 2001-02-16 2002-08-29 Infineon Technologies Ag Verfahren und Vorrichtung zum modularen Multiplizieren und Rechenwerk zum modularen Multiplizieren
US7046803B2 (en) * 2001-10-06 2006-05-16 Samsung Electronics Co., Ltd. Random keystream generation apparatus and method for use in an encryption system

Also Published As

Publication number Publication date
DE60316586T2 (de) 2008-07-24
EP1552382A2 (de) 2005-07-13
ATE374397T1 (de) 2007-10-15
WO2004036413A3 (en) 2004-06-24
US20060072743A1 (en) 2006-04-06
AU2003267913A1 (en) 2004-05-04
AU2003267913A8 (en) 2004-05-04
US7724898B2 (en) 2010-05-25
EP1552382B1 (de) 2007-09-26
WO2004036413A2 (en) 2004-04-29

Similar Documents

Publication Publication Date Title
ATE374397T1 (de) Effiziente arithmetik in galois-feldern ungerader charakterstik auf binärer hardware
Wang et al. FPGA-based Niederreiter cryptosystem using binary Goppa codes
EP1248409B1 (de) Angriffsresistente kryptographische Verfahren und Vorrichtung
EP1449063B1 (de) Galoisfeld-multiplizierersystem
US8422685B2 (en) Method for elliptic curve scalar multiplication
Chou McBits revisited
Roy et al. Compact and side channel secure discrete Gaussian sampling
US7835517B2 (en) Encryption processing apparatus, encryption processing method, and computer program
Huo et al. High performance table-based architecture for parallel CRC calculation
WO2004001701A1 (ja) 符号演算装置
EP1456745A1 (de) Galoisfeld-multiplizier-/multiplizier-addier-multiplizier-akkumulierung
KR20050061544A (ko) 이진 하드웨어에서 홀수 표수의 유한 필드를 사용하는암호화
US9886597B2 (en) Method for encoding data on a chip card by means of constant-weight codes
Morales‐Sandoval et al. Scalable GF (p) Montgomery multiplier based on a digit–digit computation approach
Talapatra et al. Unified digit serial systolic Montgomery multiplication architecture for special classes of polynomials over GF (2m)
Bhaskar et al. Efficient Galois field arithmetic on SIMD architectures
US20030041300A1 (en) Universal device for processing Reed-Solomon forward error-correction encoded messages
Hodjat et al. A scalable and high performance elliptic curve processor with resistance to timing attacks
Morales-Sandoval et al. Area/performance evaluation of digit-digit GF (2 K) multipliers on FPGAS
Ibraimov et al. Hardware implementation of the coding algorithm based on FPGA
Chou McBits revisited: toward a fast constant-time code-based KEM
Sreekanth et al. Implementation of area-efficient AES using FPGA for IOT applications
Sajid et al. AREEBA: An Area Efficient Binary Huff-Curve Architecture. Electronics 2021, 10, 1490
WO2004059851A1 (en) An encoder for high rate parallel encoding
CN116781267A (zh) 一种用于有限域GF(2m)的可配置模乘方法及系统

Legal Events

Date Code Title Description
8364 No opposition during term of opposition