Source: http://www.google.com/patents/US8204232?dq=5,941,947
Timestamp: 2016-12-04 22:23:43
Document Index: 498790681

Matched Legal Cases: ['Application No. 06701572', 'Application No. 06701572', 'Application No. 06701572', 'Application No. 2', 'Application No. 11178908', 'Application No. 06701572', 'Application No. 2007', 'Application No. 2007', 'Application No. 06701572', 'art 1']

Patent US8204232 - Accelerated verification of digital signatures and public keys - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inPatentsAccelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and...http://www.google.com/patents/US8204232?utm_source=gb-gplus-sharePatent US8204232 - Accelerated verification of digital signatures and public keysAdvanced Patent SearchTry the new Google Patents, with machine-classified Google Scholar results, and Japanese and South Korean patents.Publication numberUS8204232 B2Publication typeGrantApplication numberUS 11/333,296Publication dateJun 19, 2012Filing dateJan 18, 2006Priority dateJan 18, 2005Fee statusPaidAlso published asCA2592875A1, CA2592875C, CA2935823A1, EP1842128A1, EP1842128A4, EP1842128B1, EP2395424A1, EP2395424B1, US8788827, US8806197, US20070064932, US20120230494, US20130064367, US20140344579, WO2006076800A1Publication number11333296, 333296, US 8204232 B2, US 8204232B2, US-B2-8204232, US8204232 B2, US8204232B2InventorsMarinus Struik, Daniel R. Brown, Scott A. Vanstone, Robert P. Gallant, Adrian Antipa, Robert J. LambertOriginal AssigneeCerticom Corp.Export CitationBiBTeX, EndNote, RefManPatent Citations (78), Non-Patent Citations (68), Referenced by (9), Classifications (15), Legal Events (3) External Links: USPTO, USPTO Assignment, EspacenetAccelerated verification of digital signatures and public keys
Patent CitationsCited PatentFiling datePublication dateApplicantTitleUS4519036Jan 5, 1983May 21, 1985Emi LimitedProgram storage hardware with security schemeUS4745568May 30, 1985May 17, 1988Onyszchuk Ivan MComputational method and apparatus for finite field multiplicationUS4748668Jul 9, 1986May 31, 1988Yeda Research And Development Company LimitedMethod, apparatus and article for identification and signatureUS4890323May 20, 1987Dec 26, 1989Racal-Guardata LimitedData communication systems and methodsUS4989171Oct 12, 1989Jan 29, 1991U.S. Philips CorporationData processing method and apparatus for calculating a multiplicatively inverted element of a finite fieldUS5146500Mar 22, 1991Sep 8, 1992Omnisec A.G.Public key cryptographic system using elliptic curves over ringsUS5150411Jan 16, 1991Sep 22, 1992OmnisecCryptographic system allowing encrypted communication between users with a secure mutual cipher key determined without user interactionUS5159632Sep 17, 1991Oct 27, 1992Next Computer, Inc.Method and apparatus for public key exchange in a cryptographic systemUS5202995Sep 3, 1992Apr 13, 1993International Business Machines CorporationMethod for removing invariant branches from instruction loops of a computer programUS5218637Jun 11, 1991Jun 8, 1993L'etat Francais Represente Par Le Ministre Des Postes, Des Telecommunications Et De L'espaceMethod of transferring a secret, by the exchange of two certificates between two microcomputers which establish reciprocal authorizationUS5271061Oct 2, 1992Dec 14, 1993Next Computer, Inc.Method and apparatus for public key exchange in a cryptographic systemUS5272755Jun 26, 1992Dec 21, 1993Matsushita Electric Industrial Co., Ltd.Public key cryptosystem with an elliptic curveUS5351297Apr 16, 1993Sep 27, 1994Matsushita Electric Industrial Co., Ltd.Method of privacy communication using elliptic curvesUS5373560Aug 4, 1993Dec 13, 1994Schlafly; RogerPartial modular reduction methodUS5442707Sep 27, 1993Aug 15, 1995Matsushita Electric Industrial Co., Ltd.Method for generating and verifying electronic signatures and privacy communication using elliptic curvesUS5463690Dec 14, 1993Oct 31, 1995Next Computer, Inc.Method and apparatus for public key exchange in a cryptographic systemUS5497423Jun 20, 1994Mar 5, 1996Matsushita Electric Industrial Co., Ltd.Method of implementing elliptic curve cryptosystems in digital signatures or verification and privacy communicationUS5511198Feb 28, 1994Apr 23, 1996Fujitsu LimitedOptimizing compiler for shortening execution time of object programUS5524222Nov 22, 1994Jun 4, 1996Cyrix CorporationMicrosequencer allowing a sequence of conditional jumps without requiring the insertion of NOP or other instructionsUS5627893Dec 20, 1993May 6, 1997Telstra Corporation LimitedCryptographic methodUS5650948Jun 7, 1995Jul 22, 1997Texas Instruments IncorporatedMethod and system for translating a software implementation with data-dependent conditions to a data flow graph with conditional expressionsUS5675645Apr 18, 1995Oct 7, 1997Ricoh Company, Ltd.Method and apparatus for securing executable programs against copyingUS5757918Sep 30, 1996May 26, 1998Tandem Computers IncorporatedMethod and apparatus for user and security device authenticationUS5761305May 17, 1995Jun 2, 1998Certicom CorporationKey agreement and transport protocol with implicit signaturesUS5764772Dec 15, 1995Jun 9, 1998Lotus Development CoporationDifferential work factor cryptography method and systemUS5768389Jun 20, 1996Jun 16, 1998Nippon Telegraph And Telephone CorporationMethod and system for generation and management of secret key of public key cryptosystemUS5778069Apr 10, 1996Jul 7, 1998Microsoft CorporationNon-biased pseudo random number generatorUS5825880Jun 4, 1997Oct 20, 1998Sudia; Frank W.Multi-step digital signature method and systemUS5889865Oct 18, 1996Mar 30, 1999Certicom Corp.Key agreement and transport protocol with implicit signaturesUS5892899Jun 13, 1996Apr 6, 1999Intel CorporationTamper resistant methods and apparatusUS5896455Apr 24, 1998Apr 20, 1999Certicom CorporationKey agreement and transport protocol with implicit signaturesUS5937066Oct 2, 1996Aug 10, 1999International Business Machines CorporationTwo-phase cryptographic key recovery systemUS5987131Aug 18, 1997Nov 16, 1999Picturetel CorporationCryptographic key exchange using pre-computationUS5999626Apr 16, 1996Dec 7, 1999Certicom Corp.Digital signatures on a smartcardUS6122736Nov 7, 1997Sep 19, 2000Certicom Corp.Key agreement and transport protocol with implicit signaturesUS6141420Jan 29, 1997Oct 31, 2000Certicom Corp.Elliptic curve encryption systemsUS6212279Jul 23, 1998Apr 3, 2001The United States Of America As Represented By The United States National Security AgencyMethod of elliptic curve cryptographic key exchange using reduced base tau expansion in non-adjacent formUS6243467 *Jul 23, 1998Jun 5, 2001The United States Of America As Represented By The National Security AgencyMethod of elliptic curve cryptographic digital signature generation and verification using reduced base tau expansion in non-adjacent formUS6279110Nov 10, 1997Aug 21, 2001Certicom CorporationMasked digital signaturesUS6298135Apr 29, 1999Oct 2, 2001Motorola, Inc.Method of preventing power analysis attacks on microelectronic assembliesUS6304658Dec 31, 1998Oct 16, 2001Cryptography Research, Inc.Leak-resistant cryptographic method and apparatusUS6334189Nov 20, 1998Dec 25, 2001Jamama, LlcUse of pseudocode to protect software from unauthorized useUS6411715Nov 10, 1998Jun 25, 2002Rsa Security, Inc.Methods and apparatus for verifying the cryptographic security of a selected private and public key pair without knowing the private keyUS6419159Jun 14, 1999Jul 16, 2002Microsoft CorporationIntegrated circuit device with power analysis protection circuitryUS6430588Sep 3, 1999Aug 6, 2002Nippon Telegraph And Telephone CorporationApparatus and method for elliptic-curve multiplication and recording medium having recorded thereon a program for implementing the methodUS6446207Jan 29, 1998Sep 3, 2002Certicom CorporationVerification protocolUS6496929Apr 12, 2002Dec 17, 2002Citibank, NaGenerating RSA moduli including a predetermined portionUS6724894Nov 5, 1999Apr 20, 2004Pitney Bowes Inc.Cryptographic device having reduced vulnerability to side-channel attack and method of operating sameUS6816594Sep 8, 1999Nov 9, 2004Hitachi, Ltd.Elliptic curve generating method and device, elliptic encryption system and recording mediumUS6829356 *May 17, 2000Dec 7, 2004Verisign, Inc.Server-assisted regeneration of a strong secret from a weak secretUS6873706Sep 29, 1999Mar 29, 2005Hitachi, Ltd.Processing apparatus, program, or system of secret informationUS7110538Jun 22, 2001Sep 19, 2006Certicom Corp.Method for accelerating cryptographic operations on elliptic curvesUS7127063Jan 29, 2002Oct 24, 2006Certicom Corp.Method and apparatus for computing a shared secret keyUS7215780Jan 29, 2002May 8, 2007Certicom Corp.Method and apparatus for elliptic curve scalar multiplicationUS7421074Oct 8, 2004Sep 2, 2008Samsung Electronics Co., Ltd.Security system using RSA algorithm and method thereofUS7486789 *Dec 9, 2002Feb 3, 2009Panasonic CorporationDevice and method for calculation on elliptic curveUS7599491Apr 11, 2002Oct 6, 2009Certicom Corp.Method for strengthening the implementation of ECDSA against power analysisUS7613660Jun 6, 2003Nov 3, 2009Pitney Bowes Inc.System and method for mail destination address information encoding, protection and recovery in postal paymentUS20010053220Aug 15, 2001Dec 20, 2001Cryptography Research, Inc.Cryptographic computation using masking to prevent differential power analysis and other attacksUS20020044649Jun 22, 2001Apr 18, 2002Certicom Corp.Method for accelerating cryptographic operations on elliptic curvesUS20020057796Aug 17, 2001May 16, 2002Lambert Robert J.Method for accelerating cryptographic operations on elliptic curvesUS20020166058Sep 26, 2001Nov 7, 2002Fujitsu LimitedSemiconductor integrated circuit on IC card protected against tamperingUS20030021410 *Sep 24, 2002Jan 30, 2003Hitachi, Ltd.IC card equipped with elliptic curve encryption processing facilityUS20030044003Aug 31, 2001Mar 6, 2003International Business Machines CorporationSpace-efficient, side-channel attack resistant table lookupsUS20030048903Dec 28, 2001Mar 13, 2003Fujitsu LimitedEncryption secured against DPAUS20030059042 *Jul 17, 2002Mar 27, 2003Katsuyuki OkeyaElliptic scalar multiplication systemUS20030059043Jul 18, 2002Mar 27, 2003Katsuyuki OkeyaElliptic curve signature verification method and apparatus and a storage medium for implementing the sameUS20030061498Dec 20, 2000Mar 27, 2003Hermann DrexlerPortable data carrier provided with access protection by dividing up codesUS20050135606 *Oct 28, 2004Jun 23, 2005Brown Daniel R.Method and apparatus for verifiable generation of public keysEP0588339A2Sep 16, 1993Mar 23, 1994Nippon Telegraph And Telephone CorporationMethod and apparatus for settlement of accounts by IC cardsFR2536928A1 Title not availableFR2672402A1 Title not availableJP2002328602A Title not availableJP2004163687A Title not availableWO1991016691A1Apr 10, 1991Oct 31, 1991Jonhig LimitedValue transfer systemWO1998000771A1Jun 27, 1997Jan 8, 1998Northern Telecom LimitedDistribution and controlled use of software productsWO1998052319A1May 12, 1998Nov 19, 1998Yeda Research And Development Co. Ltd.Improved method and apparatus for protecting public key schemes from timing and fault attacksWO2000042733A1Jan 14, 2000Jul 20, 2000Certicom Corp.Method and apparatus for masking cryptographic operations* Cited by examinerNon-Patent CitationsReference1A. Antipa, D. R. L. Brown, R. P. Gallant, R. Lambert, R. Struik and S. A. Vanstone. Accelerated verification of ECDSA signatures. In B. Preneel and S. Tavares (eds.), Selected Areas in Cryptography: SAC 2005, Lecture Notes in Computer Science 3897, pp. 307-318. Springer, Aug. 2005.2Ansi, X9.62/1998, Public Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA), Jan. 1999, 195 pages.3Bleichenbacher, "Compressing Rabin Signatures", Lecture Notes in Computer Science, Springer, Berlin, 2004, pp. 124-126, ISBN 3-540-20996-4.4Cheon, J.H. et al.; "Two Efficient Algorithms for Arithmetic of Elliptic Curves Using Frobenius Map"; Public Key Cryptography; First International Workshop on Practice and Theory in Public Key Cryptography - PCK 98; 1998; pp. 195-202.5Ciet, M. et al.; "Improved Algorithms for Efficient Arithmetic on Elliptic Curves Using Fast Endomorphisms"; May 4, 2003; pp. 388 to 400; LNCS 2656; Advances in Cryptology-Eurocypt; International Conference on the Theory and Application of Cyptographic Techniques; Springer-Verlag; Germany.6Ciet, M. et al.; "Improved Algorithms for Efficient Arithmetic on Elliptic Curves Using Fast Endomorphisms"; May 4, 2003; pp. 388 to 400; LNCS 2656; Advances in Cryptology—Eurocypt; International Conference on the Theory and Application of Cyptographic Techniques; Springer-Verlag; Germany.7Communication Pursuant to Article 94(3) EPC issued in European Application No. 06701572.7 on Jul. 16, 2010; 4 pages.8Communication Pursuant to Article 94(3) EPC issued in European Application No. 06701572.7 on Mar. 8, 2010; 4 pages.9Communication under Rule 71(3) Epc issued in European Application No. 06701572.7 on Apr. 4, 2011; 6 pages.10D.J. Johnson, A.J. Menezes, S.A. Vanstone, The Elliptic Curve Digital Signature Algorithm (ECDSA),' International Journal of Information Security, vol. 1, pp. 36-63, 2001.11Deitel, H.M. et al., "C++ How to Program", 1994, Prentice-Hall, pp. 58-62.12Dirichlet, "Bericht über die zur Bekanntmachung geeigneten Verhandlungen der Königl. Preufs. Akademie der Wissenschaften zu Berlin", 1842, 4 pages; Certification and English Translation: "Report Concerning the Negotiations of the Royal Prussian Academy of Sciences at Berlin Suitable to be Announced", 1842, 5 pages.13Examiner's Report issued in Canadian Application No. 2,259,089 on Feb. 2, 2009; 3 pages.14Extended European Search Report issued in European Application No. 11178908.7 on Nov. 15, 2011; 6 pages.15G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, Fifth Edition, Oxford: Oxford University Press, 2000, pp. 169-170.16Hankerson, Darrel et al.; "Guide to Elliptic Curve Cryptography"; ISBN 0-387-95273-X; 2004; 332 pages.17Henry Cohen, A Course in Computational Algebraic Number Theory, Springer, ISBN 0-387-55640-0, pp. 83-96.18IEEE P1363a/D12 (Draft Version 12), Jul. 16, 2003, 177 pages.19International Preliminary Report on Patentability issued in International Application No. PCT/CA2006/00058 on Aug. 2, 2007; 8 pages.20International Search Report and Written Opinion of the International Searching Authority issued in International Application No. PCT/CA2006/00058 on May 1, 2006; 11 pages.21J. Solinas, ‘Low-Weight Binary Representations for Pairs of Integers,’ Centre for Applied Cryptographic Research, Corr 2001-41, University of Waterloo, Ontario, Canada, 2001, 24 pages.22J. Solinas, 'Low-Weight Binary Representations for Pairs of Integers,' Centre for Applied Cryptographic Research, Corr 2001-41, University of Waterloo, Ontario, Canada, 2001, 24 pages.23Johnson, D. et al.; "The Elliptic Curve Digital Signature Algorithm (ECDSA)"; Aug. 1, 2001; pp. 36 to 53; International Journal of Information Security; vol. 1, No. 1; Published on-line Jul. 27, 2001.24Johnson, D. et al.; "The Elliptic Curve Digital Signature Algorithm (ECDSA)"; Certricom Corporation White Paper; 2001; pp. 2-56.25Kelsy, J. et al.; "Side Channel Cryptanalysis of Product Ciphers"; Journal of Computer Security 8; 2000,; pp. 141-158.26Koblitz, Neal; "CM-Curves with Good Cryptographic Properties"; Advances in Cryptography-CRYPTO '91; 1991; pp. 279-287.27Koblitz, Neal; "Elliptic Curve Cryptosystems"; Mathematics of Computation,; vol. 48, No. 177; 1987; pp. 203-209.28Koblitz, Neal; "CM-Curves with Good Cryptographic Properties"; Advances in Cryptography—CRYPTO '91; 1991; pp. 279-287.29Kocher, P. et al.; "Differential Power Analysis"; Advances in Cryptology-CRYPTO '99; Proceedings of the 19th Annual International Cryptology Conference; 1999; pp. 388-397.30Kocher, P. et al.; "Introduction to Differential Power Analysis and Related Attacks"; Cryptography Research; 1998, 5 pages.31Kocher, Paul C.; "Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems", Advances in Cryptology-CRYPTO '96; Proceedings of the 16th Annual International Cryptology Conference; vol. 1109; 1996; pp.32Koyama, K. et al.; "Elliptic Curve Cryptosystems and Their Applications"; IEICE Transactions on Information and Systems; vol. E75-D, No. 1; 1992; pp. 50-57.33L. Lov'asz, ‘An Algorithmic Theory of Numbers, Graphs and Convexity,’ CBMSNSF Regional Conference Series in Applied Mathematics, Band 50, SIAM Publications, 1986, 98 pages.34L. Lov'asz, 'An Algorithmic Theory of Numbers, Graphs and Convexity,' CBMSNSF Regional Conference Series in Applied Mathematics, Band 50, SIAM Publications, 1986, 98 pages.35Leendert, P.; Supplementary European Search Report from corresponding EP Application No. 06701572.7; completed Sep. 24, 2009; received by applicant's agent Oct. 6, 2009.36Lercier, R.; "Finding Good Random Elliptic Curves for Cryptosystems Defined over Finite Fields"; Advances in Cryptography-EUROPCRYPT '97; vol. 1233; 1997; pp. 379-392.37Lercier, R.; "Finding Good Random Elliptic Curves for Cryptosystems Defined over Finite Fields"; Advances in Cryptography—EUROPCRYPT '97; vol. 1233; 1997; pp. 379-392.38Menezes, A. et al.; "The Implementation of Elliptic Curve Cryptosystems" of "Lecture Notes in Computer Science"; Advances in Cryptology-AUSCRYPT '90; International Conference on Cryptology; vol. 453; 1990; 14 pages.39Menezes, Alfred. J.; "Handbook of Applied Cryptography"; CRC Press; 1997; pp. 613, 614, 618.40Menezes, Alfred; "Elliptic Curve Cryptosystems"; A thesis presented to the University of Waterloo; 1992; pp. 1-121.41Miller, Victor C.; "Use of Elliptic Curves in Cryptography"; CRYPTO '85; LNCS 218; 1985; pp. 417-426.42Miyaji, A.; "Elliptic Curves Suitable for Cryptosystems"; IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences; vol. E77-A, No. 1; 1994; pp. 98-104.43Moller, Bodo; "Algorithms for Multi-Exponentiation"; Selected Areas in Cryptography-SAC 2001; LNCS 2259; pp. 165-180.44Mueller, Volker; "Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two"; Submitted to Journal of Cryptology; 1997; pp. 1-19.45Official Action issued in Japanese Application No. 2007-550647 on Jul. 19, 2011 (3 pages); with English translation (5 pages).46Official Action issued in Japanese Application No. 2007-550647 on Nov. 25, 2011; 4 pages.47P. Nguyen, D. Stehl'e, ‘Low-Dimensional Lattice-Basis Reduction Revisited,’ ACM Transactions on Algorithms, vol. 5, No. 4, Article 46, Publication date: Oct. 2009, 48 pages.48P. Nguyen, D. Stehl'e, ‘Low-Dimensional Lattice-Basis Reduction Revisited,’ ANTS 2004, Lecture Notes in Computer Science, vol. 3076, pp. 338-357, 2004.49P. Nguyen, D. Stehl'e, 'Low-Dimensional Lattice-Basis Reduction Revisited,' ACM Transactions on Algorithms, vol. 5, No. 4, Article 46, Publication date: Oct. 2009, 48 pages.50P. Nguyen, D. Stehl'e, 'Low-Dimensional Lattice-Basis Reduction Revisited,' ANTS 2004, Lecture Notes in Computer Science, vol. 3076, pp. 338-357, 2004.51Park, Y-H, et al.; "An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves"; Jan. 1, 2002; pp. 323 to 334; LNCS 2274; Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems; Springer-Verlag; Germany.52Proceeding further with the European Application Pursuant to Rule 70(2) EPC issued in European Application No. 06701572.7 on Oct. 23, 2009; 6 pages.53Public-Key Cryptography for the Financial Services Industry: Digital Signature Algorithms Providing Partial Message Recovery: Part 1: Elliptic Curve Pintsov-Vanstone Signatures (ECPVS), Draft American National Standard X9.92/2002, 2002, 65 pages.54R. Gallant, R. Lambert, S.A. Vanstone, ‘Fast Point Multiplication on Elliptic Curves with Efficient Endomorphisms,’ in Proceedings of Advances in Cryptology—CRYPTO 2001, Lecture Notes in Computer Science, vol. 2139, pp. 190-200, 2001.55R. Gallant, R. Lambert, S.A. Vanstone, 'Fast Point Multiplication on Elliptic Curves with Efficient Endomorphisms,' in Proceedings of Advances in Cryptology-CRYPTO 2001, Lecture Notes in Computer Science, vol. 2139, pp. 190-200, 2001.56Sakai, Y. et al.; "Algorithms for Efficient Simultaneous Elliptic Scalar Multiplication with Reduced Joint Hamming Weight Representation of Scalars"; Sep. 30, 2002; pp. 484 to 499; LNCS 2433; Proceedings of the 5th International Conference on Information Security; Springer-Verlag; Germany.57Schnorr, C.P.; "Efficient Signature Generation by Smart Cards"; Journal of Cryptology; vol. 4, No. 3; 1991; pp. 161-174.58Solinas, Jerome A.; "An Improved Algorithm for Arithmetic on a Family of Elliptic Curves" of "Lecture Notes in Computer Science"; Advances in Cryptology-CRYPTO '97; 17th Annual International Cryptology Conference; 1997; pp. 357-371.59Solinas, Jerome A.; "Improved Algorithms for Arithmetic on Anormalous Binary Curves"; Technical Report; 1999; 69 pages.60Solinas, Jerome A.; "An Improved Algorithm for Arithmetic on a Family of Elliptic Curves" of "Lecture Notes in Computer Science"; Advances in Cryptology—CRYPTO '97; 17th Annual International Cryptology Conference; 1997; pp. 357-371.61U.S. Department of Commerce/National Institute of Standards and Technology; Federal Information Processing Standards Publication (FIPS PUB 180-2); "Secure Hash Standard"; Aug. 1, 2002; 75 pages.62U.S. Department of Commerce/National Institute of Standards and Technology; Federal Information Processing Standards Publication (FIPS PUB 186-2); "Digital Signature Standard (DSS)"; Jan. 27, 2000; 76 pages.63Waleffe, D. et al.; "CORSAIR: A Smart Card for Public Key Cryptosystems", Advances in Cryptology-CRYPTO '90; 1990; pp. 502-513.64Waleffe, D. et al.; "CORSAIR: A Smart Card for Public Key Cryptosystems", Advances in Cryptology—CRYPTO '90; 1990; pp. 502-513.65Wang, C. et al.; "VLSI Architectures for Computing Multiplications and Inverses in GF (2m)"; IEEE Transactions on Computers; vol. C-34, No. 8; 1985; pp. 709-717.66Website: http://cr.yp.to/sigs/compress.html. Publication date of website: unknown. Retrieved on Jul. 15, 2009.67Wharton, John; "An Introduction to the Intel-MCS-51 Single-Chip Microcomputer Family"; Intel Corporation; Intel Application No. AP-69; 1980; 30 pages.68Yen, S.M, et al.; "Multi-Exponentiation"; IEEE Proceedings Comput. Digit. Tech.; vol. 141, No. 6; 1994; pp. 325-326.Referenced byCiting PatentFiling datePublication dateApplicantTitleUS8411855 *Dec 8, 2009Apr 2, 2013Emc CorporationSize optimization for large elliptic curve cryptography scalar multiplication acceleration tablesUS8428252Dec 8, 2009Apr 23, 2013Emc CorporationUsing multiples above two with running totals in elliptic curve cryptography scalar multiplication acceleration tablesUS8498411Sep 29, 2009Jul 30, 2013Emc CorporationUsing multiples above two with running totals and reference values other than 0 and 2 (window size) in elliptic curve cryptography scalar multiplication acceleration tablesUS8788827 *Sep 14, 2012Jul 22, 2014Certicom Corp.Accelerated verification of digital signatures and public keysUS8806197 *May 23, 2012Aug 12, 2014Certicom Corp.Accelerated verification of digital signatures and public keysUS9191210 *Sep 26, 2011Nov 17, 2015Kabushiki Kaisha ToshibaAuthenticator, authenticatee and authentication methodUS20120230494 *May 23, 2012Sep 13, 2012Marinus StruikAccelerated Verification of Digital Signatures and Public KeysUS20130064367 *Sep 14, 2012Mar 14, 2013Marinus StruikAccelerated verification of digital signatures and public keysUS20140075190 *Sep 26, 2011Mar 13, 2014Yuji NagaiAuthenticator, authenticatee and authentication method* Cited by examinerClassifications U.S. Classification380/282, 713/171, 713/169, 380/28, 380/277, 380/30, 713/168, 713/172International ClassificationH04L9/08Cooperative ClassificationH04L9/3066, H04L9/3252, H04L9/30, G06F7/725European ClassificationH04L9/32S, G06F7/72F1Legal EventsDateCodeEventDescriptionJul 5, 2006ASAssignmentOwner name: CERTICOM CORP., CANADAFree format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:STRUIK, MARINUS;BROWN, DANIEL R.;VANSTONE, SCOTT A.;AND OTHERS;REEL/FRAME:017878/0907;SIGNING DATES FROM 20060404 TO 20060608Owner name: CERTICOM CORP., CANADAFree format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:STRUIK, MARINUS;BROWN, DANIEL R.;VANSTONE, SCOTT A.;AND OTHERS;SIGNING DATES FROM 20060404 TO 20060608;REEL/FRAME:017878/0907Feb 26, 2013CCCertificate of correctionDec 21, 2015FPAYFee paymentYear of fee payment: 4RotateOriginal ImageGoogle Home - Sitemap - USPTO Bulk Downloads - Privacy Policy - Terms of Service - About Google Patents - Send FeedbackData provided by IFI CLAIMS Patent Services