AU2001247826A1 - Scalable and unified multiplication methods and apparatus - Google Patents

Scalable and unified multiplication methods and apparatus

Info

Publication number
AU2001247826A1
AU2001247826A1 AU2001247826A AU4782601A AU2001247826A1 AU 2001247826 A1 AU2001247826 A1 AU 2001247826A1 AU 2001247826 A AU2001247826 A AU 2001247826A AU 4782601 A AU4782601 A AU 4782601A AU 2001247826 A1 AU2001247826 A1 AU 2001247826A1
Authority
AU
Australia
Prior art keywords
scalable
multiplication methods
unified
unified multiplication
methods
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
AU2001247826A
Inventor
Cetin K. Koc
Erkay Savas
Alexandre F. Tenca
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.)
Oregon State University
Original Assignee
Oregon State Board of Higher Education
Oregon State
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 Oregon State Board of Higher Education, Oregon State filed Critical Oregon State Board of Higher Education
Publication of AU2001247826A1 publication Critical patent/AU2001247826A1/en
Abandoned 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
    • 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
    • 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

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Complex Calculations (AREA)
AU2001247826A 2000-03-31 2001-03-27 Scalable and unified multiplication methods and apparatus Abandoned AU2001247826A1 (en)

Applications Claiming Priority (5)

Application Number Priority Date Filing Date Title
US19367600P 2000-03-31 2000-03-31
US60193676 2000-03-31
US09/637,229 US7240204B1 (en) 2000-03-31 2000-08-11 Scalable and unified multiplication methods and apparatus
US09637229 2000-08-11
PCT/US2001/009812 WO2001076132A1 (en) 2000-03-31 2001-03-27 Scalable and unified multiplication methods and apparatus

Publications (1)

Publication Number Publication Date
AU2001247826A1 true AU2001247826A1 (en) 2001-10-15

Family

ID=26889234

Family Applications (1)

Application Number Title Priority Date Filing Date
AU2001247826A Abandoned AU2001247826A1 (en) 2000-03-31 2001-03-27 Scalable and unified multiplication methods and apparatus

Country Status (3)

Country Link
US (1) US7240204B1 (en)
AU (1) AU2001247826A1 (en)
WO (1) WO2001076132A1 (en)

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DE60208926T2 (en) * 2001-12-14 2006-08-31 Koninklijke Philips Electronics N.V. FLOW BAND IN A MONTGOMERY MULTIPLIER
US7532720B2 (en) * 2003-10-15 2009-05-12 Microsoft Corporation Utilizing SIMD instructions within montgomery multiplication
US20060059219A1 (en) * 2004-09-16 2006-03-16 Koshy Kamal J Method and apparatus for performing modular exponentiations
US7539718B2 (en) * 2004-09-16 2009-05-26 Intel Corporation Method and apparatus for performing Montgomery multiplications
JP4351987B2 (en) * 2004-11-19 2009-10-28 株式会社東芝 Montgomery conversion device, arithmetic device, IC card, encryption device, decryption device, and program
FR2884005B1 (en) * 2005-04-01 2007-06-01 Thales Sa METHOD FOR IMPLEMENTING MODULAR MONTGOMERY MULTIPLICATION AND DEVICE THEREOF
US7693925B2 (en) * 2005-09-30 2010-04-06 Intel Corporation Multiplicand shifting in a linear systolic array modular multiplier
US7725624B2 (en) 2005-12-30 2010-05-25 Intel Corporation System and method for cryptography processing units and multiplier
US20070157030A1 (en) 2005-12-30 2007-07-05 Feghali Wajdi K Cryptographic system component
US10498532B2 (en) * 2016-10-01 2019-12-03 Intel Corporation Parallel computation techniques for accelerated cryptographic capabilities
US11165578B1 (en) * 2018-08-16 2021-11-02 Pqsecure Technologies, Llc Efficient architecture and method for arithmetic computations in post-quantum cryptography
CN111190571B (en) * 2019-12-30 2022-03-22 华南师范大学 Modular multiplication circuit based on binary domain expansion and control method thereof
CN111835517B (en) * 2020-06-29 2023-12-22 易兆微电子(杭州)股份有限公司 Double-domain elliptic curve point multiplication hardware accelerator

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SE7714587L (en) * 1977-12-21 1979-06-22 Brendstrom Hugo COMMUNICATION SYSTEM
US4763332A (en) * 1987-03-02 1988-08-09 Data Systems Technology Corp. Shared circuitry for the encoding and syndrome generation functions of a Reed-Solomon code
KR19990024971A (en) 1997-09-09 1999-04-06 정선종 Modular multiplier
US5144574A (en) 1989-01-30 1992-09-01 Nippon Telegraph And Telephone Corporation Modular multiplication method and the system for processing data
US5321752A (en) * 1991-09-05 1994-06-14 Canon Kabushiki Kaisha Method of and apparatus for encryption and decryption of communication data
US5513133A (en) 1992-11-30 1996-04-30 Fortress U&T Ltd. Compact microelectronic device for performing modular multiplication and exponentiation over large numbers
US5349551A (en) 1993-07-30 1994-09-20 The United States Of America As Represented By The Director Of National Security Agency Device for and method of preforming an N-bit modular multiplication in approximately N/2 steps
FR2726667B1 (en) * 1994-11-08 1997-01-17 Sgs Thomson Microelectronics METHOD FOR IMPLEMENTING MODULAR MULTIPLICATION ACCORDING TO THE MONTGOMERY METHOD
GB9510035D0 (en) * 1995-05-18 1995-08-02 Cryptech Systems Inc Strengthened public key protocols
US6209016B1 (en) 1996-10-31 2001-03-27 Atmel Research Co-processor for performing modular multiplication
KR100218683B1 (en) 1996-12-04 1999-09-01 정선종 Modular multiplication device
GB9627069D0 (en) 1996-12-30 1997-02-19 Certicom Corp A method and apparatus for finite field multiplication
FR2758195B1 (en) * 1997-01-09 1999-02-26 Sgs Thomson Microelectronics MODULAR ARITHMETIC CO-PACKER COMPRISING TWO MULTIPLICATION CIRCUITS OPERATING IN PARALLEL
KR100684134B1 (en) * 1997-05-04 2007-02-16 엠시스템스 리미티드 Improved apparatus ? method for modular multiplication ? exponentiation based on montgomery multiplication
US6252959B1 (en) * 1997-05-21 2001-06-26 Worcester Polytechnic Institute Method and system for point multiplication in elliptic curve cryptosystem
US5974580A (en) * 1997-07-23 1999-10-26 Cirrus Logic, Inc. Concurrent row/column syndrome generator for a product code
JP3292107B2 (en) * 1997-08-28 2002-06-17 日本電気株式会社 Double vector adder, double vector doubler and double vector integer multiplier
US6061706A (en) * 1997-10-10 2000-05-09 United Microelectronics Corp. Systolic linear-array modular multiplier with pipeline processing elements
DE69826963T2 (en) * 1997-11-04 2005-11-17 Nippon Telegraph And Telephone Corp. Device for modular inversion for securing information
KR100267009B1 (en) 1997-11-18 2000-09-15 윤종용 Method and device for modular multiplication
US6356636B1 (en) * 1998-07-22 2002-03-12 Motorola, Inc. Circuit and method for fast modular multiplication
US6182104B1 (en) * 1998-07-22 2001-01-30 Motorola, Inc. Circuit and method of modulo multiplication
US6397241B1 (en) * 1998-12-18 2002-05-28 Motorola, Inc. Multiplier cell and method of computing
FR2791155B1 (en) * 1999-03-17 2001-05-11 St Microelectronics Sa DEVICE AND METHOD FOR IMPLEMENTING AN ELEMENTARY MODULAR OPERATION ACCORDING TO THE MONTGOMERY METHOD
US6925563B1 (en) * 1999-09-22 2005-08-02 Raytheon Company Multiplication of modular numbers
US7046800B1 (en) * 2000-03-31 2006-05-16 State Of Oregon Acting By And Through The State Board Of Higher Education On Behalf Of Oregon State University Scalable methods and apparatus for Montgomery multiplication
US6691143B2 (en) * 2000-05-11 2004-02-10 Cyberguard Corporation Accelerated montgomery multiplication using plural multipliers
AU5871201A (en) * 2000-05-15 2001-11-26 M-Systems Flash Disk Pioneers Ltd. Extending the range of computational fields of integers
DE60208926T2 (en) * 2001-12-14 2006-08-31 Koninklijke Philips Electronics N.V. FLOW BAND IN A MONTGOMERY MULTIPLIER

Also Published As

Publication number Publication date
WO2001076132A1 (en) 2001-10-11
US7240204B1 (en) 2007-07-03

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