AU2001273653A1 - Method and apparatus for incomplete modular arithmetic - Google Patents

Method and apparatus for incomplete modular arithmetic

Info

Publication number
AU2001273653A1
AU2001273653A1 AU2001273653A AU7365301A AU2001273653A1 AU 2001273653 A1 AU2001273653 A1 AU 2001273653A1 AU 2001273653 A AU2001273653 A AU 2001273653A AU 7365301 A AU7365301 A AU 7365301A AU 2001273653 A1 AU2001273653 A1 AU 2001273653A1
Authority
AU
Australia
Prior art keywords
modular arithmetic
incomplete
incomplete modular
arithmetic
modular
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
AU2001273653A
Inventor
Cetin K. Koc
Erkay Savas
Tugrul Yanik
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.)
State Of Oregon Acting By And Through State Board Of Higher Education On Behalf Of Theuniversity Of Oregon
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 AU2001273653A1 publication Critical patent/AU2001273653A1/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
    • 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
    • G06F7/722—Modular multiplication
    • 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
AU2001273653A 2000-06-29 2001-06-29 Method and apparatus for incomplete modular arithmetic Abandoned AU2001273653A1 (en)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
US21520600P 2000-06-29 2000-06-29
US60215206 2000-06-29
PCT/US2001/041208 WO2002003608A1 (en) 2000-06-29 2001-06-29 Method and apparatus for incomplete modular arithmetic

Publications (1)

Publication Number Publication Date
AU2001273653A1 true AU2001273653A1 (en) 2002-01-14

Family

ID=22802084

Family Applications (1)

Application Number Title Priority Date Filing Date
AU2001273653A Abandoned AU2001273653A1 (en) 2000-06-29 2001-06-29 Method and apparatus for incomplete modular arithmetic

Country Status (3)

Country Link
US (1) US7080109B2 (en)
AU (1) AU2001273653A1 (en)
WO (1) WO2002003608A1 (en)

Families Citing this family (16)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6978016B2 (en) * 2000-12-19 2005-12-20 International Business Machines Corporation Circuits for calculating modular multiplicative inverse
US6973470B2 (en) * 2001-06-13 2005-12-06 Corrent Corporation Circuit and method for performing multiple modulo mathematic operations
DE10222212A1 (en) * 2002-05-16 2003-12-04 Giesecke & Devrient Gmbh Spying-proof modular inversion
GB0227793D0 (en) * 2002-11-29 2003-01-08 Koninkl Philips Electronics Nv Multiplier with look up tables
GB0314557D0 (en) * 2003-06-21 2003-07-30 Koninkl Philips Electronics Nv Improved reduction calculations
US7715551B2 (en) * 2004-04-29 2010-05-11 Stmicroelectronics Asia Pacific Pte. Ltd. Apparatus and method for consistency checking public key cryptography computations
US7664810B2 (en) * 2004-05-14 2010-02-16 Via Technologies, Inc. Microprocessor apparatus and method for modular exponentiation
US8532288B2 (en) 2006-12-01 2013-09-10 International Business Machines Corporation Selectively isolating processor elements into subsets of processor elements
US7890559B2 (en) * 2006-12-22 2011-02-15 International Business Machines Corporation Forward shifting of processor element processing for load balancing
US7755766B1 (en) 2007-03-27 2010-07-13 Itt Manufacturing Enterprises, Inc. Telescope interferometric maintenance evaluation tool
US7978846B2 (en) * 2007-06-30 2011-07-12 Intel Corporation Scale-invariant barrett reduction for elliptic-curve cyrptography
US8005210B2 (en) * 2007-06-30 2011-08-23 Intel Corporation Modulus scaling for elliptic-curve cryptography
US7986779B2 (en) * 2007-06-30 2011-07-26 Intel Corporation Efficient elliptic-curve cryptography based on primality of the order of the ECC-group
KR102132261B1 (en) 2014-03-31 2020-08-06 삼성전자주식회사 Method and apparatus for computing montgomery multiplication performing final reduction wihhout comparator
DE102020102453A1 (en) * 2020-01-31 2021-08-05 Infineon Technologies Ag Integrated circuit for the modular multiplication of two whole numbers for a cryptographic method and method for the cryptographic processing of data based on modular multiplication
US20240012615A1 (en) * 2022-07-07 2024-01-11 International Business Machines Corporation Fast modular multiplication of large integers

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5270956A (en) * 1991-03-18 1993-12-14 University Of Maryland System and method for performing fast algebraic operations on a permutation network
US5274707A (en) * 1991-12-06 1993-12-28 Roger Schlafly Modular exponentiation and reduction device and method
JPH0720778A (en) * 1993-07-02 1995-01-24 Fujitsu Ltd Remainder calculating device, table generating device, and multiplication remainder calculating device
US6009450A (en) * 1997-12-24 1999-12-28 Motorola, Inc. Finite field inverse circuit
GB2352309B (en) * 1999-07-21 2004-02-11 Advanced Risc Mach Ltd A system and method for performing modular multiplication

Also Published As

Publication number Publication date
US20020059353A1 (en) 2002-05-16
US7080109B2 (en) 2006-07-18
WO2002003608A1 (en) 2002-01-10

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