WO2004112307A3 - Multiplication in a finite field - Google Patents

Multiplication in a finite field Download PDF

Info

Publication number
WO2004112307A3
WO2004112307A3 PCT/IB2004/050827 IB2004050827W WO2004112307A3 WO 2004112307 A3 WO2004112307 A3 WO 2004112307A3 IB 2004050827 W IB2004050827 W IB 2004050827W WO 2004112307 A3 WO2004112307 A3 WO 2004112307A3
Authority
WO
WIPO (PCT)
Prior art keywords
multiplication
finite field
index
entries
memory
Prior art date
Application number
PCT/IB2004/050827
Other languages
French (fr)
Other versions
WO2004112307A2 (en
Inventor
Sebastian Egner
Original Assignee
Koninkl Philips Electronics Nv
Sebastian Egner
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 Koninkl Philips Electronics Nv, Sebastian Egner filed Critical Koninkl Philips Electronics Nv
Priority to EP04735781A priority Critical patent/EP1636932A2/en
Publication of WO2004112307A2 publication Critical patent/WO2004112307A2/en
Publication of WO2004112307A3 publication Critical patent/WO2004112307A3/en

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
    • G06F1/00—Details not covered by groups G06F3/00 - G06F13/00 and G06F21/00
    • G06F1/02—Digital function generators
    • G06F1/03—Digital function generators working, at least partly, by table look-up
    • G06F1/0307—Logarithmic or exponential functions

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)
  • Error Detection And Correction (AREA)
  • Complex Calculations (AREA)

Abstract

An apparatus for performing a multiplication in a finite field Fq ={O, 1, α, (α2,..., αq-2 , or, in an index representation, Fq = {x0, x1,..., xq-1 } where each element xj of the field is represented by a respective index j indicated as j=i(xj). A memory 410 includes a logarithm table L 416 with at least q entries L[j] = logα,(xj), for j=0,...,q-1 and an exponent table E with a first part 412 with respective entries E[j] = i(α) for j=0,...,q-2 and a second part 414 immediately subsequent to the first part with respective entries E[j+q-1 ] = (aj) for j=0,...,q-3. A processor 420 provides as the outcome of the multiplication of non-zero elements x, y ∈ Fq an index retrieved from a table entry E[L[i(x)] + L[i(y)]] in the memory.
PCT/IB2004/050827 2003-06-13 2004-06-02 Multiplication in a finite field WO2004112307A2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
EP04735781A EP1636932A2 (en) 2003-06-13 2004-06-02 Multiplication in a finite field

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
EP03101735.3 2003-06-13
EP03101735 2003-06-13

Publications (2)

Publication Number Publication Date
WO2004112307A2 WO2004112307A2 (en) 2004-12-23
WO2004112307A3 true WO2004112307A3 (en) 2005-10-27

Family

ID=33547711

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/IB2004/050827 WO2004112307A2 (en) 2003-06-13 2004-06-02 Multiplication in a finite field

Country Status (2)

Country Link
EP (1) EP1636932A2 (en)
WO (1) WO2004112307A2 (en)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2981471A1 (en) * 2012-07-19 2013-04-19 Continental Automotive France Method for calculating result of operations e.g. multiplication, in Galois field, involves executing algorithm to determine exponent values based on set of numbers, and calculating final result from extended table of exhibitors
US9235554B2 (en) * 2013-03-15 2016-01-12 Echelon Corporation Method and system of improved Galois multiplication
BR112017006236A2 (en) 2014-09-30 2017-12-12 Koninklijke Philips Nv electronic calculating device, ring coding device, table calculating device, electronic calculating method, computer program, and, computer readable media
JP2018503113A (en) * 2014-11-27 2018-02-01 コーニンクレッカ フィリップス エヌ ヴェＫｏｎｉｎｋｌｉｊｋｅ Ｐｈｉｌｉｐｓ Ｎ．Ｖ． Electronic computing device for performing obfuscated operations
RU2710310C2 (en) * 2014-12-12 2019-12-25 Конинклейке Филипс Н.В. Electronic forming device
JP6387466B2 (en) * 2014-12-22 2018-09-05 コーニンクレッカ フィリップス エヌ ヴェＫｏｎｉｎｋｌｉｊｋｅ Ｐｈｉｌｉｐｓ Ｎ．Ｖ． Electronic computing device
EP3488553A1 (en) * 2016-07-21 2019-05-29 Koninklijke Philips N.V. Device and method for performing obfuscated arithmetic

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3326044A1 (en) * 1983-07-20 1985-02-07 Licentia Patent-Verwaltungs-Gmbh, 6000 Frankfurt Method for carrying out the Galois field multiplication or division and circuit arrangement for carrying out the method

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3326044A1 (en) * 1983-07-20 1985-02-07 Licentia Patent-Verwaltungs-Gmbh, 6000 Frankfurt Method for carrying out the Galois field multiplication or division and circuit arrangement for carrying out the method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
SUT E ET AL: "Comparison of Reed-Solomon decoder implementations based on two different microprocessors", ELECTROTECHNICAL CONFERENCE, 1991. PROCEEDINGS., 6TH MEDITERRANEAN LJUBLJANA, SLOVENIA 22-24 MAY 1991, NEW YORK, NY, USA,IEEE, US, 22 May 1991 (1991-05-22), pages 614 - 617, XP010039970, ISBN: 0-87942-655-1 *
TOSHIYA TODOROKI ET AL INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS SOCIEDADE BRASILIERA DE TELECOMUNICACOES: "DESIGN OF A REED-SOLOMON DECODER USING A DIGITAL SIGNAL PROCESSOR (DSP)", SBT/IEEE INTERNATIONAL TELECOMMUNICATIONS SYMPOSIUM. RIO DE JANEIRO, SEPT. 3 - 6, 1990, NEW YORK, IEEE, US, vol. SYMP. 1, 3 September 1990 (1990-09-03), pages 443 - 445, XP000245460 *

Also Published As

Publication number Publication date
WO2004112307A2 (en) 2004-12-23
EP1636932A2 (en) 2006-03-22

Similar Documents

Publication Publication Date Title
WO2004023248A3 (en) Polymorphic computational system and method in signals intelligence analysis
WO2009035108A1 (en) Correspondence learning apparatus and method and correspondence learning program, annotation apparatus and method and annotation program, and retrieval apparatus and method and retrieval program
Pearson Coefficient
WO2007082277A3 (en) Transforms with reduce complexity and/or improve precision by means of common factors
WO2004112307A3 (en) Multiplication in a finite field
EP2045716A3 (en) Exponentiation calculation apparatus and exponentiation calculation method
CN101232572A (en) Method and apparatus for denoising digital picture
WO2005033870A3 (en) Method for creating and using text objects as control devices
CA2329104A1 (en) Method and apparatus for calculating a reciprocal
WO2009020216A1 (en) Arithmetic operation method and arithmetic operation device
AU2003241350A1 (en) "emod" a fast modulus calculation for computer systems
EP1441277A3 (en) Electronic control apparatus
TW200612329A (en) Galois field multiplier and multiplication method thereof
Wei Convergence of numerical solutions for variable delay differential equations driven by Poisson random jump measure
EP2028837A3 (en) Video signal processing device, video signal processing method and display device
WO2020080689A3 (en) Apparatus and method for generating index value for comparing body composition change performance
Li et al. Approximation numbers of composition operators on Hp
Linde Kolmogorov numbers of Riemann–Liouville operators over small sets and applications to Gaussian processes
WO2002048901A3 (en) Method and circuit arrangement for carrying out a fast fourier transformation and the use thereof
Gatica et al. Vinyltrimethylsilane-co-methylmethacrylate copolymers. Synthesis and reactivity ratios
WO2003075144A3 (en) Input apparatus for a computer system
DE60316200D1 (en) MODULAR TRAFFIC INFORMATION SYSTEM
Mattarei Exponential functions in prime characteristic
Ştefănescu Computation of dominant real roots of polynomials
Arnab Estimation of a finite population total in varying probability sampling for multi-character surveys

Legal Events

Date Code Title Description
AK Designated states

Kind code of ref document: A2

Designated state(s): AE AG AL AM AT AU AZ BA BB BG BR BW BY BZ CA CH CN CO CR CU CZ DE DK DM DZ EC EE EG ES FI GB GD GE GH GM HR HU ID IL IN IS JP KE KG KP KR KZ LC LK LR LS LT LU LV MA MD MG MK MN MW MX MZ NA NI NO NZ OM PG PH PL PT RO RU SC SD SE SG SK SL SY TJ TM TN TR TT TZ UA UG US UZ VC VN YU ZA ZM ZW

AL Designated countries for regional patents

Kind code of ref document: A2

Designated state(s): BW GH GM KE LS MW MZ NA SD SL SZ TZ UG ZM ZW AM AZ BY KG KZ MD RU TJ TM AT BE BG CH CY CZ DE DK EE ES FI FR GB GR HU IE IT LU MC NL PL PT RO SE SI SK TR BF BJ CF CG CI CM GA GN GQ GW ML MR NE SN TD TG

121 Ep: the epo has been informed by wipo that ep was designated in this application
WWE Wipo information: entry into national phase

Ref document number: 2004735781

Country of ref document: EP

WWP Wipo information: published in national office

Ref document number: 2004735781

Country of ref document: EP

WWW Wipo information: withdrawn in national office

Ref document number: 2004735781

Country of ref document: EP