WO2004036413A3 - Efficient arithmetic in finite fields of odd characteristic on binary hardware - Google Patents

Efficient arithmetic in finite fields of odd characteristic on binary hardware Download PDF

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Publication number
WO2004036413A3
WO2004036413A3 PCT/SE2003/001560 SE0301560W WO2004036413A3 WO 2004036413 A3 WO2004036413 A3 WO 2004036413A3 SE 0301560 W SE0301560 W SE 0301560W WO 2004036413 A3 WO2004036413 A3 WO 2004036413A3
Authority
WO
WIPO (PCT)
Prior art keywords
odd
field
finite fields
data bits
binary data
Prior art date
Application number
PCT/SE2003/001560
Other languages
French (fr)
Other versions
WO2004036413A2 (en
Inventor
Rolf Blom
Mats Naeslund
Original Assignee
Ericsson Telefon Ab L M
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 Ericsson Telefon Ab L M filed Critical Ericsson Telefon Ab L M
Priority to DE60316586T priority Critical patent/DE60316586T2/en
Priority to EP03748852A priority patent/EP1552382B1/en
Priority to AU2003267913A priority patent/AU2003267913A1/en
Publication of WO2004036413A2 publication Critical patent/WO2004036413A2/en
Publication of WO2004036413A3 publication Critical patent/WO2004036413A3/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
    • 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

Abstract

A method of processing binary data representing field elements of an odd-characteristic finite field GF(pk) is described. The method comprises storing binary data representing at least a portion of a field element of an odd-characteristic finite field GF(pk) in a register, p being an odd prime number, the field element comprising k coefficients in accordance with a polynomial-basis representation, the binary data comprising plural groups of data bits, wherein each group of data bits represents an associated one of the k coefficients. The method also comprises executing at least one operation on contents of the register such that the plural groups of data bits are processed in parallel. An apparatus comprising a memory and a processing unit coupled to the memory to carry out the method is also described.
PCT/SE2003/001560 2002-10-17 2003-10-07 Efficient arithmetic in finite fields of odd characteristic on binary hardware WO2004036413A2 (en)

Priority Applications (3)

Application Number Priority Date Filing Date Title
DE60316586T DE60316586T2 (en) 2002-10-17 2003-10-07 EFFICIENT ARITHMETIC IN GALOIS FIELDS OF UNGERADER CHARACTERISTICS ON BINARY HARDWARE
EP03748852A EP1552382B1 (en) 2002-10-17 2003-10-07 Efficient arithmetic in finite fields of odd characteristic on binary hardware
AU2003267913A AU2003267913A1 (en) 2002-10-17 2003-10-07 Efficient arithmetic in finite fields of odd characteristic on binary hardware

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US10/271,947 US7724898B2 (en) 2002-10-17 2002-10-17 Cryptography using finite fields of odd characteristic on binary hardware
US10/271,947 2002-10-17

Publications (2)

Publication Number Publication Date
WO2004036413A2 WO2004036413A2 (en) 2004-04-29
WO2004036413A3 true WO2004036413A3 (en) 2004-06-24

Family

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Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/SE2003/001560 WO2004036413A2 (en) 2002-10-17 2003-10-07 Efficient arithmetic in finite fields of odd characteristic on binary hardware

Country Status (6)

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

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DE102005028662B4 (en) * 2005-03-04 2022-06-02 Ihp Gmbh - Innovations For High Performance Microelectronics / Leibniz-Institut Für Innovative Mikroelektronik Method and device for calculating a polynomial multiplication, in particular for elliptic curve cryptography
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
WO2008087734A1 (en) * 2007-01-19 2008-07-24 Mitsubishi Electric Corporation Cryptogram generating device, cryptogram communication system, and group parameter generating device
US8527781B2 (en) * 2007-05-09 2013-09-03 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
US8499168B2 (en) * 2007-05-09 2013-07-30 Kingston Technology Corporation Secure and scalable solid state disk system
EP2195761B1 (en) * 2007-10-01 2013-04-03 Research In Motion Limited Substitution table masking for cryptographic processes
WO2009104260A1 (en) * 2008-02-20 2009-08-27 三菱電機株式会社 Verifying device
CN102187617B (en) * 2008-05-20 2014-10-08 爱迪德有限责任公司 cryptographic system
JP5354994B2 (en) * 2008-08-25 2013-11-27 株式会社東芝 Apparatus and program for performing data compression processing using algebraic torus
US8345864B1 (en) 2008-12-12 2013-01-01 Emc Corporation Elliptic curve cryptography scalar multiplication with on demand acceleration table generation
US7773000B1 (en) 2009-02-27 2010-08-10 Red Hat, Inc. Efficient coding of integers in non-power-of-two ranges
JPWO2011148558A1 (en) * 2010-05-28 2013-07-25 日本電気株式会社 Signature generation apparatus, signature method, and signature generation program
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
US9698977B2 (en) * 2013-01-16 2017-07-04 Mitsubishi Electric Corporation Information processing apparatus, information processing method, and program
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
US11755288B2 (en) * 2016-11-08 2023-09-12 Koninklijke Philips N.V. Secure transformation from a residue number system to a radix representation
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

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US4587627A (en) * 1981-11-30 1986-05-06 Omnet Associates Computational method and apparatus for finite field arithmetic
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Also Published As

Publication number Publication date
AU2003267913A8 (en) 2004-05-04
EP1552382A2 (en) 2005-07-13
ATE374397T1 (en) 2007-10-15
DE60316586D1 (en) 2007-11-08
DE60316586T2 (en) 2008-07-24
US7724898B2 (en) 2010-05-25
EP1552382B1 (en) 2007-09-26
AU2003267913A1 (en) 2004-05-04
WO2004036413A2 (en) 2004-04-29
US20060072743A1 (en) 2006-04-06

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