High-speed hardware implementations of Elliptic Curve Cryptography: A survey
For the last decade, Elliptic Curve Cryptography (ECC) has gained increasing acceptance in the industry and the academic community and has been the subject of several standards. This interest is mainly due to the high level of security with relatively small keys provided by ECC. To sustain the high...
Saved in:
Published in | Journal of systems architecture Vol. 53; no. 2; pp. 72 - 84 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier B.V
01.02.2007
Elsevier Sequoia S.A |
Subjects | |
Online Access | Get full text |
ISSN | 1383-7621 1873-6165 |
DOI | 10.1016/j.sysarc.2006.09.002 |
Cover
Abstract | For the last decade, Elliptic Curve Cryptography (ECC) has gained increasing acceptance in the industry and the academic community and has been the subject of several standards. This interest is mainly due to the high level of security with relatively small keys provided by ECC. To sustain the high throughput required by applications like network servers, high-speed implementations of public-key cryptosystems are needed. For that purpose, hardware-based accelerators are often the only solution reaching an acceptable performance-cost ratio. The fundamental question that arises is how to choose the appropriate efficiency–flexibility tradeoff.
In this survey, techniques for implementing Elliptic Curve Cryptography at a high-speed are explored. A classification of the work available in the open literature in function of the level of efficiency and flexibility is also proposed. In particular, the subjects of reconfigurable, dedicated, generator, versatile and general purpose scalar multipliers are addressed. Finally, some words about future work that should be tackled are provided. |
---|---|
AbstractList | For the last decade, Elliptic Curve Cryptography (ECC) has gained increasing acceptance in the industry and the academic community and has been the subject of several standards. This interest is mainly due to the high level of security with relatively small keys provided by ECC. To sustain the high throughput required by applications like network servers, high-speed implementations of public-key cryptosystems are needed. For that purpose, hardware-based accelerators are often the only solution reaching an acceptable performance-cost ratio. The fundamental question that arises is how to choose the appropriate efficiency-flexibility tradeoff In this survey, techniques for implementing Elliptic Curve Cryptography at a high-speed are explored. A classification of the work available in the open literature in function of the level of efficiency and flexibility is also proposed. In particular, the subjects of reconfigurable, dedicated, generator, versatile and general purpose scalar multipliers are addressed. Finally, some words about future work that should be tackled are provided. [PUBLICATION ABSTRACT] For the last decade, Elliptic Curve Cryptography (ECC) has gained increasing acceptance in the industry and the academic community and has been the subject of several standards. This interest is mainly due to the high level of security with relatively small keys provided by ECC. To sustain the high throughput required by applications like network servers, high-speed implementations of public-key cryptosystems are needed. For that purpose, hardware-based accelerators are often the only solution reaching an acceptable performance-cost ratio. The fundamental question that arises is how to choose the appropriate efficiency–flexibility tradeoff. In this survey, techniques for implementing Elliptic Curve Cryptography at a high-speed are explored. A classification of the work available in the open literature in function of the level of efficiency and flexibility is also proposed. In particular, the subjects of reconfigurable, dedicated, generator, versatile and general purpose scalar multipliers are addressed. Finally, some words about future work that should be tackled are provided. |
Author | Meurice de Dormale, Guerric Quisquater, Jean-Jacques |
Author_xml | – sequence: 1 givenname: Guerric surname: Meurice de Dormale fullname: Meurice de Dormale, Guerric email: gmeurice@dice.ucl.ac.be – sequence: 2 givenname: Jean-Jacques surname: Quisquater fullname: Quisquater, Jean-Jacques email: quisquater@dice.ucl.ac.be |
BookMark | eNqFkDFPwzAQhS1UJNrCP2CI2BPOTuOkHZCqqFCkSiwwW459bh2lSbDTovx7UoWJAaY7nd57p_fNyKRuaiTknkJEgfLHMvK9l05FDIBHsIwA2BWZ0iyNQ055Mhn2OIvDlDN6Q2belwCQJJRNyW5r94fQt4g6OEinv6TDwB7bCo9Yd7KzTe2DxgSbqrJtZ1WQn9wZg9z1bdfsnWwP_SpYB_5y7W_JtZGVx7ufOScfz5v3fBvu3l5e8_UuVHEcd6E0mjEoZKGoMQmlHAxDUMZQmiKVxrDCLDQanpmkAK2wWCQSUsU111mcynhOHsbc1jWfJ_SdKJuTq4eXgtEsW2aQskG0GkXKNd47NELZsVDnpK0EBXGBJ0oxwhMXeAKWYoA3mBe_zK2zR-n6_2xPow2H9meLTnhlsVaorUPVCd3YvwO-AQTmj7A |
CitedBy_id | crossref_primary_10_1109_LES_2020_3003978 crossref_primary_10_1007_s11277_021_08221_9 crossref_primary_10_1080_09720529_2015_1103017 crossref_primary_10_1016_j_micpro_2008_08_002 crossref_primary_10_1016_j_micpro_2016_12_005 crossref_primary_10_1109_TC_2009_132 crossref_primary_10_1016_j_vlsi_2010_08_001 crossref_primary_10_1016_j_sysarc_2008_04_012 crossref_primary_10_1016_j_micpro_2017_07_001 crossref_primary_10_1145_3696422 crossref_primary_10_32604_cmc_2022_021483 crossref_primary_10_1109_TVLSI_2008_2000728 crossref_primary_10_1002_cta_2295 crossref_primary_10_1109_ACCESS_2018_2881444 crossref_primary_10_1109_TIE_2012_2186104 crossref_primary_10_1155_2016_6371403 crossref_primary_10_1109_JIOT_2014_2360121 crossref_primary_10_4028_www_scientific_net_AMR_459_544 crossref_primary_10_1631_jzus_A0820024 crossref_primary_10_1145_2700834 crossref_primary_10_3390_mi15101238 crossref_primary_10_1016_j_micpro_2015_02_003 crossref_primary_10_1007_s13389_011_0002_2 crossref_primary_10_1016_j_ipl_2016_11_007 crossref_primary_10_1007_s11277_020_07832_y crossref_primary_10_1109_TCSI_2018_2883557 crossref_primary_10_1002_cta_2504 crossref_primary_10_1140_epjst_e2019_900044_x crossref_primary_10_1155_2011_836460 crossref_primary_10_4028_www_scientific_net_AMR_462_116 crossref_primary_10_1109_TVT_2010_2045014 crossref_primary_10_5573_JSTS_2016_16_1_118 crossref_primary_10_1016_j_mejo_2016_03_006 crossref_primary_10_1016_j_mejo_2017_03_009 crossref_primary_10_3923_jas_2012_201_210 crossref_primary_10_32604_iasc_2023_038927 crossref_primary_10_1016_S1005_8885_08_60206_X crossref_primary_10_1109_TCSI_2010_2103190 |
Cites_doi | 10.1007/3-540-36400-5_26 10.1109/ITCC.2004.1286701 10.1007/978-3-540-24660-2_20 10.1007/3-540-44709-1_29 10.1049/cp:20040604 10.1007/3-540-36400-5_36 10.1109/ISCAS.2002.1010824 10.1007/11693383_25 10.1109/JPROC.2005.862438 10.1007/3-540-45537-X_13 10.1007/3-540-36563-X_11 10.1109/FPT.2003.1275732 10.1109/ASAP.2004.1342462 10.1109/ITCC.2004.1286702 10.1023/A:1008013818413 10.1007/3-540-48059-5_24 10.1007/3-540-45537-X_20 10.1109/ASAP.2003.1212867 10.1007/11802839_45 10.1109/DATE.2005.254 10.1109/TC.2003.1190586 10.1007/3-540-44499-8_4 10.1017/CBO9781107360211 10.1109/ITCC.2004.1286717 10.1117/12.506144 10.1007/3-540-36400-5_28 10.1016/0890-5401(88)90024-7 10.1007/3-540-44983-3_9 10.1109/IPDPS.2002.1016557 10.1007/3-540-39799-X_31 10.1109/ITCC.2005.33 10.1007/978-3-540-24660-2_28 10.1109/ASAP.2003.1212866 10.1049/cp:20040606 10.1007/3-540-44499-8_2 10.1007/3-540-44499-8_22 10.1109/ITCC.2005.25 10.1007/978-3-540-30117-2_25 10.1016/j.micpro.2004.03.003 10.1145/988952.989062 10.1109/IWRSP.2001.933834 10.1090/S0025-5718-1987-0866113-7 10.1007/978-3-540-24676-3_16 10.1109/ARITH.2003.1207677 10.1109/TVLSI.2002.801608 10.1007/3-540-48059-5_7 10.1007/3-540-44709-1_12 10.1090/S0025-5718-1987-0866109-5 10.1007/BF02620228 10.1007/3-540-44709-1_11 10.1007/978-3-540-27776-7_29 10.1007/978-3-540-30117-2_115 10.1109/DATE.2005.67 10.1006/jagm.1997.0913 10.1109/FPT.2004.1393285 10.1007/3-540-48059-5_27 10.1007/978-3-540-45146-4_34 10.1007/s00145-001-0011-x 10.1007/3-540-36400-5_41 10.1007/3-540-44709-1_18 10.1007/3-540-45537-X_11 10.1109/TC.2002.1004591 10.1007/3-540-44499-8_3 |
ContentType | Journal Article |
Copyright | 2006 Elsevier B.V. Copyright Elsevier Sequoia S.A. Feb/Mar 2007 |
Copyright_xml | – notice: 2006 Elsevier B.V. – notice: Copyright Elsevier Sequoia S.A. Feb/Mar 2007 |
DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
DOI | 10.1016/j.sysarc.2006.09.002 |
DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
DatabaseTitleList | Computer and Information Systems Abstracts |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Computer Science |
EISSN | 1873-6165 |
EndPage | 84 |
ExternalDocumentID | 1204763401 10_1016_j_sysarc_2006_09_002 S1383762106001044 |
Genre | Feature |
GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1~. 1~5 29L 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABBOA ABFNM ABFRF ABJNI ABMAC ABXDB ABYKQ ACDAQ ACGFO ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADJOM ADMUD ADTZH AEBSH AECPX AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHJVU AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BKOMP BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HVGLF HZ~ IHE J1W JJJVA KOM M41 MO0 MS~ N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 R2- RIG ROL RPZ RXW SBC SDF SDG SDP SES SEW SPC SPCBC SST SSV SSZ T5K TAE TN5 U5U UHS ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD 7SC 8FD AFXIZ AGCQF AGRNS JQ2 L7M L~C L~D SSH |
ID | FETCH-LOGICAL-c333t-afd220babc1ff51160f2e0cff117e1aff2bf4def68f5b0dceb45a07c6d6d837a3 |
IEDL.DBID | .~1 |
ISSN | 1383-7621 |
IngestDate | Fri Jul 25 06:17:20 EDT 2025 Thu Apr 24 23:05:00 EDT 2025 Wed Oct 01 00:46:44 EDT 2025 Fri Feb 23 02:28:01 EST 2024 |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 2 |
Keywords | High-speed hardware implementation Network applications Elliptic Curve Cryptography Public-key cryptography Efficiency–flexibility tradeoffs |
Language | English |
License | https://www.elsevier.com/tdm/userlicense/1.0 |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-c333t-afd220babc1ff51160f2e0cff117e1aff2bf4def68f5b0dceb45a07c6d6d837a3 |
Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
PQID | 218898072 |
PQPubID | 9850 |
PageCount | 13 |
ParticipantIDs | proquest_journals_218898072 crossref_citationtrail_10_1016_j_sysarc_2006_09_002 crossref_primary_10_1016_j_sysarc_2006_09_002 elsevier_sciencedirect_doi_10_1016_j_sysarc_2006_09_002 |
ProviderPackageCode | CITATION AAYXX |
PublicationCentury | 2000 |
PublicationDate | 2007-02-01 |
PublicationDateYYYYMMDD | 2007-02-01 |
PublicationDate_xml | – month: 02 year: 2007 text: 2007-02-01 day: 01 |
PublicationDecade | 2000 |
PublicationPlace | Amsterdam |
PublicationPlace_xml | – name: Amsterdam |
PublicationTitle | Journal of systems architecture |
PublicationYear | 2007 |
Publisher | Elsevier B.V Elsevier Sequoia S.A |
Publisher_xml | – name: Elsevier B.V – name: Elsevier Sequoia S.A |
References | Cilardo, Coppolino, Mazzocca, Romano (bib17) 2006; 94 G. Orlando, C. Paar, A scalable GF K. Itoh, M. Takenaka, N. Torii, S. Temma, and Y. Kurihara, Fast implementation of public-key cryptography on a DSP TMS320C6201, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1717, 1999, pp. 61–72. Leong, Leung (bib44) 2002; 10 Agnew, Beth, Mullin, Vanstone (bib1) 1993; 6 μm CMOS 1.5 K. Järvinen, M. Tommiska, J. Skyttä, A scalable architecture for elliptic curve point multiplication, in: IEEE Field-Programmable Technology (FPT), 2004, pp. 303–306. in: Application-Specific Systems, Architectures, and Processors (ASAP), 2003, pp. 444–454. Gordon (bib30) 1998; 27 Wu (bib80) 2002; 51 Lutz, Hasan (bib46) 2003; 5205 and GF(2 N. Gura, S.C. Shantz, H. Eberle, D. Finchelstein, S. Gupta, V. Gupta, D. Stebila, An end-to-end systems approach to elliptic curve cryptography, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2523, 2002, pp. 349–365. in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1965, 2000, pp. 277–292. S.A. Huss, M. Jung, F. Madlener, High speed elliptic curve crypto processors: design space exploration by means of reconfigurable hardware, International Scientific and Applied Conference – Information Security, 2004. in: Application-Specific Systems, Architectures, and Processors (ASAP), 2003, pp. 433–443. Ecrypt, Vampire lab, The side channel cryptanalysis lounge, 2006. Available from M. Bednara, M. Daldrup, J. Teich, J. von zur Gathen, J. Shokrollahi, Tradeoff analysis of FPGA based elliptic curve cryptography, in: IEEE Symposium on Circuits and Systems (ISCAS), 5, 2002, pp. 797–800. IEEE P1363, Standard specifications for public key cryptography, 1999. B. King, An improved implementation of elliptic curves over GF(2 when using projective point arithmetic, in: Selected Areas in Cryptography (SAC), LNCS 2259, 2001, pp. 134–150. H. Eberle, N. Gura, S. Chang-Shantz, A cryptographic processor for arbitrary elliptic curves over GF(2 H. Eberle, N. Gura, S.C. Shantz, V. Gupta, L. Rarick, S. Sundaram, A public-key cryptographic processor for RSA and ECC, in: Application-Specific Systems, Architectures, and Processors (ASAP), 2004, pp. 98–110. L. Batina, G. Bruin-Muurling, S.B. Örs, Flexible hardware design for RSA and elliptic curve cryptosystems, in: The Cryptographer’s Track at RSA Conference (CT-RSA), LNCS 2964, 2004, pp. 250–263. . J.A. Solinas, Low-weight binary representations for pairs of integers, Tech. Report CORR 01-41, Department of Combinatorics & Optimization. Available from GHz elliptic curve public key cryptosystem chip, in: Symposium on Advanced Research in Asynchronous Circuits and Systems (ASYNC), 2000, pp. 188–197. in: Irish Signals and Systems Conference (ISSC), 2004, pp. 589–594. T. Akishita, Fast simultaneous scalar multiplication on elliptic curve with montgomery form, in: Selected Areas in Cryptography (SAC), LNCS 2259, 2001, pp. 255–267. Z. Dyka, P. Langendoerfer, Area efficient hardware implementation of elliptic curve cryptography by iteratively applying Karatsuba’s method, in: Design, Automation and Test in Europe (DATE), 3, 2005, pp. 70–75. A. Menezes, E. Teske, A. Weng, Weak fields for ECC, in: The Cryptographer’s Track at RSA Conference (CT-RSA), LNCS 2964, 2004, pp. 366–386. Song, Parhi (bib74) 1998; 19 Mentens, Örs, Preneel (bib50) 2004 B. Möller, Algorithms for multi-exponentiation, in: Selected Areas in Cryptography (SAC), LNCS 2259, 2001, pp. 165–180. S.B. Örs, L. Batina, B. Preneel, J. Vandewalle, Hardware implementation of an elliptic curve processor over GF Montgomery (bib53) 1987; 48 N.P. Smart, The hessian form of an elliptic curve, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2162, 2001, pp. 118–125. Certicom Research, SEC 2: Recommended elliptic curve domain parameters, v1.0, 2000. Available from B. Canvel, A. Hiltgen, S. Vaudenay, M. Vuagnoux, Password interception in a SSL/TLS channel, in: Cryptology Conference (CRYPTO), LNCS 2729, 2003, pp. 583–599. A. K. Daneshbeh, M.A. Hasan, Area efficient high speed elliptic curve cryptoprocessor for random curves, in: IEEE Symposium on Information Technology: Coding and Computing (ITCC), 2, 2004, pp. 588–592. S. Okada, N. Torii, K. Itoh, M. Takenaka, Implementation of elliptic curve cryptographic coprocessor over GF(2 T. Kerins, W.P. Marnane, E.M. Popovici, An FPGA implementation of a flexible secure elliptic curve cryptography processor, in: Reconfigurable Computing: Architectures and Applications (ARC), 2005. N. Telle, W. Luk, R.C.C. Cheung, Customising hardware designs for elliptic curve cryptography, in: Computer Systems: Architectures, Modeling, and Simulation (SAMOS), 2004, pp. 274–283. Gaudry, Hess, Smart (bib29) 2002; 15 N. Nguyen, K. Gaj, D. Caliga, T. El-Ghazawi, Implementation of elliptic curve cryptosystems on a reconfigurable computer, in: IEEE Field-Programmable Technology (FPT), 2003, pp. 60–67. J. López, R. Dahab, Fast multiplication on elliptic curves over GF(2 H. Wu, On complexity of polynomial basis squaring in in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2523, 2002, pp. 500–514. G. Bertoni, J. Guajardo, S. Kumar, G. Orlando, C. Paar, T. Wollinger, Efficient GF J. Großschädl, A bit-serial unified multiplier architecture for finite fields GF L. Batina, S.B. Örs, B. Preneel, J. Vandewalle, Hardware architectures for public key cryptography, Elsevier Integration, the VLSI Journal, special issue on Embedded Cryptographic Hardware, 34 (2003) 1–2, pp. 1–64. I. Blake, G. Seroussi, N.P. Smart, Elliptic curves in cryptography, London Mathematical Society Lecture Note Series, 1999. V. Miller, Uses of elliptic curves in cryptography, in: Cryptology Conference (CRYPTO), LNCS 218, 1985, pp. 417–426. in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2523, 2002, pp. 381–399. on an FPGA, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1965, 2000, pp. 25–40. arithmetic architectures for cryptographic applications, in: The Cryptographer’s Track at RSA Conference (CT-RSA), LNCS 2612, 2003, pp. 158–175. F. Rodríguez-Henríquez, Ç.K. Koç, On fully parallel karatsuba multipliers for GF(2 G. Bai, G. Chen, H. Chen, Fast scalar multiplications of elliptic curve cryptosystems over binary fields, in: SKLOIS Information Security and Cryptology (CISC), 2005, pp. 315–323. R.C.C. Cheung, W. Luk, P.Y.K. Cheung, Reconfigurable elliptic curve cryptosystems on a chip, in: Design, Automation and Test in Europe (DATE), 1, 2005, pp. 24–29. novel algorithm and implementations on FPGA, in: Reconfigurable Computing: Architectures and Applications (ARC), LNCS 3985, 2006, pp. 370–382. K. Okeya, K. Sakurai, Fast multi-scalar multiplication methods on elliptic curves with precomputation strategy using montgomery trick, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2523, 2002, pp. 564–578. in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1965, 2000, pp. 41–56. G. Meurice de Dormale, J.-J. Quisquater, Iterative modular division over GF(2 J.-C. Bajard, L. Imbert, C. Negre, T. Plantard, Efficient multiplication in GF affine coordinates application, in: Field-Programmable Logic and Applications (FPL), LNCS 3203, 2004, pp. 231–240. elliptic curve processor architecture for programmable hardware, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2162, 2001, pp. 356–371. U.S. Department of Commerce/National Institute of Standards and Technology (NIST), Digital Signature Standard (DSS), FIPS PUB 182-2change1, 2000. C. Grabbe, M. Bednara, J. von zur Gathen, J. Shokrollahi, J. Teich, A high performance vliw processor for finite field arithmetic, in: Reconfigurable Architectures Workshop (RAW), 2003. J. Wolkerstorfer, Dual-field arithmetic unit for GF Koblitz (bib43) 1987; 48 2001. N.A. Saqib, F. Rodríguez-Henríquez, A. Díaz-Pérez, A parallel architecture for computing scalar multiplication on hessian elliptic curves, in: Symposium on Information Technology: Coding and Computing (ITCC), 2, 2004, pp. 493–497. C. McIvor, M. McLoone, J. McCanny, An FPGA elliptic curve cryptographic accelerator over GF N.A. Saqib, F. Rodríguez-Henríquez, A. Díaz-Pérez, A parallel architecture for fast computation of elliptic curve scalar multiplication over GF(2 D. Naccache, N.P. Smart, J. Stern, Projective coordinates leak, in: Theory and Applications of Cryptographic Techniques (EUROCRYPT), LNCS 3027, 2004, pp. 257–267. F. Sozzani, G. Bertoni, S. Turcato, L. Breveglieri, A parallelized design for an elliptic curve cryptosystem coprocessor, in: Symposium on Information Technology: Coding and Computing (ITCC), 1, 2005, pp. 626–630. Itoh, Tsujii (bib38) 1988; 78 S. Bajracharya, C. Shu, K. Gaj, T. El-Ghazawi, Implementation of elliptic curve cryptosystems over GF(2 for elliptic curve cryptography, in: IEEE Symposium on Computer Arithmetic (ARITH-16), 2003, pp. 181–187. J. von zur Gathen, J. Shokrollahi, Efficient FPGA-based karatsuba multipliers for polynomials over M.J. Potgieter, B.J. van Dyk, Two hardware implementations of the group operations necessary for implementing an elliptic curve cryptosystem over a characteristic two finite field, in: IEEE Africon Conference in Africa (AFRICON), 2002. B. Ansari, M. Anwar Hasan, High performance architecture of elliptic curve scalar multiplication, Tech. Report CACR 2006-01, 2006. Available from J.W. Chung, S.G. Sim, P.J. Lee, Fast implementation of elliptic curve defined over GF K. Okeya, K. Sakurai, Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1717, 1999, pp. 316–327. H. Wu, Low complexity bit-parallel finite field arithmetic using polynomial basis, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1717, 1999, pp. 280–291. in optimal normal basis on a reconfigurable computer, in: Field-Programmable Logic and Applications (FPL), LNCS 3203, 2004, pp. 1001–1005. in: Selected Areas in Cryptography (SAC), LNCS 3897, 2005, pp. 359–369. Satoh, Takano (bib68) 2003; 52 E. Savas, A.F. Tenca, Ç.K. Ko 10.1016/j.sysarc.2006.09.002_bib45 10.1016/j.sysarc.2006.09.002_bib42 10.1016/j.sysarc.2006.09.002_bib49 10.1016/j.sysarc.2006.09.002_bib48 10.1016/j.sysarc.2006.09.002_bib47 Wu (10.1016/j.sysarc.2006.09.002_bib80) 2002; 51 10.1016/j.sysarc.2006.09.002_bib41 10.1016/j.sysarc.2006.09.002_bib40 Hankerson (10.1016/j.sysarc.2006.09.002_bib33) 2004 Mentens (10.1016/j.sysarc.2006.09.002_bib50) 2004 Agnew (10.1016/j.sysarc.2006.09.002_bib1) 1993; 6 10.1016/j.sysarc.2006.09.002_bib12 10.1016/j.sysarc.2006.09.002_bib56 10.1016/j.sysarc.2006.09.002_bib11 10.1016/j.sysarc.2006.09.002_bib55 10.1016/j.sysarc.2006.09.002_bib10 10.1016/j.sysarc.2006.09.002_bib54 10.1016/j.sysarc.2006.09.002_bib16 10.1016/j.sysarc.2006.09.002_bib15 10.1016/j.sysarc.2006.09.002_bib59 10.1016/j.sysarc.2006.09.002_bib14 10.1016/j.sysarc.2006.09.002_bib58 10.1016/j.sysarc.2006.09.002_bib13 10.1016/j.sysarc.2006.09.002_bib57 Itoh (10.1016/j.sysarc.2006.09.002_bib38) 1988; 78 10.1016/j.sysarc.2006.09.002_bib52 10.1016/j.sysarc.2006.09.002_bib51 Song (10.1016/j.sysarc.2006.09.002_bib74) 1998; 19 Koblitz (10.1016/j.sysarc.2006.09.002_bib43) 1987; 48 10.1016/j.sysarc.2006.09.002_bib19 10.1016/j.sysarc.2006.09.002_bib18 10.1016/j.sysarc.2006.09.002_bib23 10.1016/j.sysarc.2006.09.002_bib67 10.1016/j.sysarc.2006.09.002_bib22 10.1016/j.sysarc.2006.09.002_bib66 10.1016/j.sysarc.2006.09.002_bib21 10.1016/j.sysarc.2006.09.002_bib65 10.1016/j.sysarc.2006.09.002_bib20 Leong (10.1016/j.sysarc.2006.09.002_bib44) 2002; 10 10.1016/j.sysarc.2006.09.002_bib64 10.1016/j.sysarc.2006.09.002_bib27 10.1016/j.sysarc.2006.09.002_bib26 10.1016/j.sysarc.2006.09.002_bib25 10.1016/j.sysarc.2006.09.002_bib69 10.1016/j.sysarc.2006.09.002_bib24 10.1016/j.sysarc.2006.09.002_bib63 10.1016/j.sysarc.2006.09.002_bib62 10.1016/j.sysarc.2006.09.002_bib61 10.1016/j.sysarc.2006.09.002_bib60 10.1016/j.sysarc.2006.09.002_bib8 Cilardo (10.1016/j.sysarc.2006.09.002_bib17) 2006; 94 10.1016/j.sysarc.2006.09.002_bib9 10.1016/j.sysarc.2006.09.002_bib6 10.1016/j.sysarc.2006.09.002_bib7 10.1016/j.sysarc.2006.09.002_bib4 10.1016/j.sysarc.2006.09.002_bib5 10.1016/j.sysarc.2006.09.002_bib2 10.1016/j.sysarc.2006.09.002_bib3 10.1016/j.sysarc.2006.09.002_bib28 Montgomery (10.1016/j.sysarc.2006.09.002_bib53) 1987; 48 Lutz (10.1016/j.sysarc.2006.09.002_bib46) 2003; 5205 10.1016/j.sysarc.2006.09.002_bib34 10.1016/j.sysarc.2006.09.002_bib78 10.1016/j.sysarc.2006.09.002_bib77 10.1016/j.sysarc.2006.09.002_bib32 10.1016/j.sysarc.2006.09.002_bib76 10.1016/j.sysarc.2006.09.002_bib31 10.1016/j.sysarc.2006.09.002_bib75 10.1016/j.sysarc.2006.09.002_bib37 10.1016/j.sysarc.2006.09.002_bib36 10.1016/j.sysarc.2006.09.002_bib35 10.1016/j.sysarc.2006.09.002_bib79 Gaudry (10.1016/j.sysarc.2006.09.002_bib29) 2002; 15 10.1016/j.sysarc.2006.09.002_bib70 10.1016/j.sysarc.2006.09.002_bib73 10.1016/j.sysarc.2006.09.002_bib72 10.1016/j.sysarc.2006.09.002_bib71 Satoh (10.1016/j.sysarc.2006.09.002_bib68) 2003; 52 10.1016/j.sysarc.2006.09.002_bib39 Gordon (10.1016/j.sysarc.2006.09.002_bib30) 1998; 27 |
References_xml | – reference: F. Sozzani, G. Bertoni, S. Turcato, L. Breveglieri, A parallelized design for an elliptic curve cryptosystem coprocessor, in: Symposium on Information Technology: Coding and Computing (ITCC), 1, 2005, pp. 626–630. – reference: -coordinate on a montgomery-form elliptic curve, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2162, 2001, pp. 126–141. – reference: ) on CalmRISC with MAC2424 coprocessor, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1965, 2000, pp. 57–70. – reference: N. Telle, W. Luk, R.C.C. Cheung, Customising hardware designs for elliptic curve cryptography, in: Computer Systems: Architectures, Modeling, and Simulation (SAMOS), 2004, pp. 274–283. – reference: T. Kerins, W.P. Marnane, E.M. Popovici, An FPGA implementation of a flexible secure elliptic curve cryptography processor, in: Reconfigurable Computing: Architectures and Applications (ARC), 2005. – reference: ), in: Irish Signals and Systems Conference (ISSC), 2004, pp. 589–594. – reference: ), in: Application-Specific Systems, Architectures, and Processors (ASAP), 2003, pp. 444–454. – reference: C. Shu, K. Gaj, T. El-Ghazawi, Low latency elliptic curve cryptography accelerators for NIST curves on binary fields, in: IEEE Field-Programmable Technology (FPT), 2005, pp. 309–310. – reference: G. Bai, G. Chen, H. Chen, Fast scalar multiplications of elliptic curve cryptosystems over binary fields, in: SKLOIS Information Security and Cryptology (CISC), 2005, pp. 315–323. – year: 2004 ident: bib33 article-title: Guide to elliptic curve cryptography – reference: J.-C. Bajard, L. Imbert, C. Negre, T. Plantard, Efficient multiplication in GF( – reference: R.C.C. Cheung, W. Luk, P.Y.K. Cheung, Reconfigurable elliptic curve cryptosystems on a chip, in: Design, Automation and Test in Europe (DATE), 1, 2005, pp. 24–29. – reference: M. Bednara, M. Daldrup, J. von zur Gathen, J. Shokrollahi, J. Teich, Reconfigurable implementation of elliptic curve crypto algorithms, in: Reconfigurable Architectures Workshop (RAW), 2002. – reference: ), in: Application-Specific Systems, Architectures, and Processors (ASAP), 2003, pp. 433–443. – reference: ), in: Parallel & Distributed Processing Symposium (IPDPS), 2004. – reference: ), in: Computer Science and Technology (CST), 2003, pp. 405–410. – reference: G. Bertoni, J. Guajardo, S. Kumar, G. Orlando, C. Paar, T. Wollinger, Efficient GF( – reference: G. Meurice de Dormale, J.-J. Quisquater, Iterative modular division over GF(2 – reference: I. Blake, G. Seroussi, N.P. Smart, Elliptic curves in cryptography, London Mathematical Society Lecture Note Series, 1999. – reference: H. Eberle, N. Gura, S.C. Shantz, V. Gupta, L. Rarick, S. Sundaram, A public-key cryptographic processor for RSA and ECC, in: Application-Specific Systems, Architectures, and Processors (ASAP), 2004, pp. 98–110. – reference: ), in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1965, 2000, pp. 277–292. – reference: J. von zur Gathen, J. Shokrollahi, Efficient FPGA-based karatsuba multipliers for polynomials over – reference: U.S. Department of Commerce/National Institute of Standards and Technology (NIST), Digital Signature Standard (DSS), FIPS PUB 182-2change1, 2000. – reference: C. McIvor, M. McLoone, J. McCanny, An FPGA elliptic curve cryptographic accelerator over GF( – reference: . – reference: Ecrypt, Vampire lab, The side channel cryptanalysis lounge, 2006. Available from: – reference: G. Meurice de Dormale, P. Bulens, J.-J. Quisquater, Efficient modular division implementation: ECC over GF( – volume: 5205 start-page: 541 year: 2003 end-page: 551 ident: bib46 article-title: High-performance finite field multiplier for cryptographic applications publication-title: Advanced Signal Processing Algorithms, Architectures, and Implementations XIII – SPIE – reference: M.J. Potgieter, B.J. van Dyk, Two hardware implementations of the group operations necessary for implementing an elliptic curve cryptosystem over a characteristic two finite field, in: IEEE Africon Conference in Africa (AFRICON), 2002. – reference: O. Hauck, A. Katoch, S.A. Huss, VLSI system design using asynchronous wave pipelines: A 0.35 – reference: G. Orlando, C. Paar, A scalable GF( – reference: ) for elliptic curve cryptography, in: IEEE Symposium on Computer Arithmetic (ARITH-16), 2003, pp. 181–187. – reference: J.A. Solinas, Low-weight binary representations for pairs of integers, Tech. Report CORR 01-41, Department of Combinatorics & Optimization. Available from: – reference: IEEE P1363, Standard specifications for public key cryptography, 1999. – reference: D. Naccache, N.P. Smart, J. Stern, Projective coordinates leak, in: Theory and Applications of Cryptographic Techniques (EUROCRYPT), LNCS 3027, 2004, pp. 257–267. – reference: K. Okeya, K. Sakurai, Fast multi-scalar multiplication methods on elliptic curves with precomputation strategy using montgomery trick, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2523, 2002, pp. 564–578. – reference: , 2001. – reference: B. Canvel, A. Hiltgen, S. Vaudenay, M. Vuagnoux, Password interception in a SSL/TLS channel, in: Cryptology Conference (CRYPTO), LNCS 2729, 2003, pp. 583–599. – reference: S. Bajracharya, C. Shu, K. Gaj, T. El-Ghazawi, Implementation of elliptic curve cryptosystems over GF(2 – reference: J. Wolkerstorfer, Dual-field arithmetic unit for GF( – reference: ANSI, ANSI X9.62 The elliptic curve digital signature algorithm (ECDSA). Available from: – volume: 78 start-page: 171 year: 1988 end-page: 177 ident: bib38 article-title: A fast algorithm for computing multiplicative inverses in GF(2 publication-title: Information and Computation – volume: 48 start-page: 243 year: 1987 end-page: 264 ident: bib53 article-title: Speeding the pollard and elliptic curve methods of factorization publication-title: Mathematics of Computation – reference: N.P. Smart, The hessian form of an elliptic curve, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2162, 2001, pp. 118–125. – volume: 94 start-page: 395 year: 2006 end-page: 406 ident: bib17 article-title: Elliptic curve cryptography engineering publication-title: Proceedings of the IEEE – reference: J.W. Chung, S.G. Sim, P.J. Lee, Fast implementation of elliptic curve defined over GF( – reference: ), in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1965, 2000, pp. 41–56. – reference: ) elliptic curve processor architecture for programmable hardware, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2162, 2001, pp. 356–371. – reference: N. Gura, S.C. Shantz, H. Eberle, D. Finchelstein, S. Gupta, V. Gupta, D. Stebila, An end-to-end systems approach to elliptic curve cryptography, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2523, 2002, pp. 349–365. – reference: M. Ernst, M. Jung, F. Madlener, S. Huss, R. Blümel, A reconfigurable system on chip implementation for elliptic curve cryptography over GF(2 – reference: ) on an FPGA, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1965, 2000, pp. 25–40. – volume: 52 start-page: 449 year: 2003 end-page: 460 ident: bib68 article-title: A scalable dual-field elliptic curve cryptographic processor publication-title: IEEE Transactions Computers – volume: 6 start-page: 3 year: 1993 end-page: 13 ident: bib1 article-title: Arithmetic operations in GF(2 publication-title: Journal of Cryptology – reference: ): novel algorithm and implementations on FPGA, in: Reconfigurable Computing: Architectures and Applications (ARC), LNCS 3985, 2006, pp. 370–382. – reference: K. Okeya, K. Sakurai, Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the – reference: F. Crowe, A. Daly, W. Marnane, A scalable dual mode arithmetic unit for public key cryptosystems, in: IEEE Symposium on Information Technology: Coding and Computing (ITCC), 1, 2005, pp. 568–573. – reference: J. López, R. Dahab, Fast multiplication on elliptic curves over GF(2 – reference: ), in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1717, 1999, pp. 316–327. – reference: V. Miller, Uses of elliptic curves in cryptography, in: Cryptology Conference (CRYPTO), LNCS 218, 1985, pp. 417–426. – volume: 51 start-page: 521 year: 2002 end-page: 529 ident: bib80 article-title: Montgomery multiplier and squarer for a class of finite fields publication-title: IEEE Transactions on Computers – reference: C. Grabbe, M. Bednara, J. von zur Gathen, J. Shokrollahi, J. Teich, A high performance vliw processor for finite field arithmetic, in: Reconfigurable Architectures Workshop (RAW), 2003. – reference: Certicom Research, SEC 2: Recommended elliptic curve domain parameters, v1.0, 2000. Available from: – reference: K. Järvinen, M. Tommiska, J. Skyttä, A scalable architecture for elliptic curve point multiplication, in: IEEE Field-Programmable Technology (FPT), 2004, pp. 303–306. – reference: S. Okada, N. Torii, K. Itoh, M. Takenaka, Implementation of elliptic curve cryptographic coprocessor over GF(2 – reference: K. Itoh, M. Takenaka, N. Torii, S. Temma, and Y. Kurihara, Fast implementation of public-key cryptography on a DSP TMS320C6201, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1717, 1999, pp. 61–72. – reference: J. Lutz, M.A. Hasan, High performance FPGA based elliptic curve cryptographic co-processor, in: IEEE Symposium on Information Technology: Coding and Computing (ITCC), 2, 2004, pp. 486–492. – reference: N. Nguyen, K. Gaj, D. Caliga, T. El-Ghazawi, Implementation of elliptic curve cryptosystems on a reconfigurable computer, in: IEEE Field-Programmable Technology (FPT), 2003, pp. 60–67. – reference: E. Savas, A.F. Tenca, Ç.K. Koç, A scalable and unified multiplier architecture for finite fields GF( – volume: 15 start-page: 19 year: 2002 end-page: 46 ident: bib29 article-title: Constructive and destructive facets of Weil descent on elliptic curves publication-title: Journal of Cryptology – reference: A. K. Daneshbeh, M.A. Hasan, Area efficient high speed elliptic curve cryptoprocessor for random curves, in: IEEE Symposium on Information Technology: Coding and Computing (ITCC), 2, 2004, pp. 588–592. – reference: M. Bednara, M. Daldrup, J. Teich, J. von zur Gathen, J. Shokrollahi, Tradeoff analysis of FPGA based elliptic curve cryptography, in: IEEE Symposium on Circuits and Systems (ISCAS), 5, 2002, pp. 797–800. – volume: 19 start-page: 149 year: 1998 end-page: 166 ident: bib74 article-title: Low energy digit-serial/parallel finite field multipliers publication-title: Journal of VLSI Signal Processing – reference: N.A. Saqib, F. Rodríguez-Henríquez, A. Díaz-Pérez, A parallel architecture for fast computation of elliptic curve scalar multiplication over GF(2 – reference: H. Wu, Low complexity bit-parallel finite field arithmetic using polynomial basis, in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 1717, 1999, pp. 280–291. – reference: L. Batina, G. Bruin-Muurling, S.B. Örs, Flexible hardware design for RSA and elliptic curve cryptosystems, in: The Cryptographer’s Track at RSA Conference (CT-RSA), LNCS 2964, 2004, pp. 250–263. – reference: J. Großschädl, A bit-serial unified multiplier architecture for finite fields GF( – reference: B. Möller, Algorithms for multi-exponentiation, in: Selected Areas in Cryptography (SAC), LNCS 2259, 2001, pp. 165–180. – reference: T. Akishita, Fast simultaneous scalar multiplication on elliptic curve with montgomery form, in: Selected Areas in Cryptography (SAC), LNCS 2259, 2001, pp. 255–267. – reference: B. King, An improved implementation of elliptic curves over GF(2 – reference: M. Ernst, S. Klupsch, O. Hauck, S.A. Huss, Rapid prototyping for hardware accelerated elliptic curve public-key cryptosystems, in: IEEE Rapid System Prototyping (RSP), 2001, pp. 24–31. – reference: N.A. Saqib, F. Rodríguez-Henríquez, A. Díaz-Pérez, A parallel architecture for computing scalar multiplication on hessian elliptic curves, in: Symposium on Information Technology: Coding and Computing (ITCC), 2, 2004, pp. 493–497. – reference: μm CMOS 1.5 – volume: 10 start-page: 550 year: 2002 end-page: 559 ident: bib44 article-title: A microcoded elliptic curve processor using FPGA technology publication-title: IEEE Transactions on VLSI Systems – reference: S.A. Huss, M. Jung, F. Madlener, High speed elliptic curve crypto processors: design space exploration by means of reconfigurable hardware, International Scientific and Applied Conference – Information Security, 2004. – reference: , in: Selected Areas in Cryptography (SAC), LNCS 2012, 2000, pp. 118–129. – reference: H. Eberle, N. Gura, S. Chang-Shantz, A cryptographic processor for arbitrary elliptic curves over GF(2 – reference: ), in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2523, 2002, pp. 500–514. – reference: GHz elliptic curve public key cryptosystem chip, in: Symposium on Advanced Research in Asynchronous Circuits and Systems (ASYNC), 2000, pp. 188–197. – reference: A. Menezes, E. Teske, A. Weng, Weak fields for ECC, in: The Cryptographer’s Track at RSA Conference (CT-RSA), LNCS 2964, 2004, pp. 366–386. – reference: ) when using projective point arithmetic, in: Selected Areas in Cryptography (SAC), LNCS 2259, 2001, pp. 134–150. – reference: ) affine coordinates application, in: Field-Programmable Logic and Applications (FPL), LNCS 3203, 2004, pp. 231–240. – reference: S.B. Örs, L. Batina, B. Preneel, J. Vandewalle, Hardware implementation of an elliptic curve processor over GF( – reference: B. Ansari, M. Anwar Hasan, High performance architecture of elliptic curve scalar multiplication, Tech. Report CACR 2006-01, 2006. Available from: – volume: 48 start-page: 203 year: 1987 end-page: 209 ident: bib43 article-title: Elliptic curve cryptosystem publication-title: Mathematics of Computation – reference: ) arithmetic architectures for cryptographic applications, in: The Cryptographer’s Track at RSA Conference (CT-RSA), LNCS 2612, 2003, pp. 158–175. – reference: ) in optimal normal basis on a reconfigurable computer, in: Field-Programmable Logic and Applications (FPL), LNCS 3203, 2004, pp. 1001–1005. – reference: , in: Selected Areas in Cryptography (SAC), LNCS 3897, 2005, pp. 359–369. – reference: G. Orlando, C. Paar, A high-performance reconfigurable elliptic curve processor for GF(2 – start-page: 454 year: 2004 end-page: 457 ident: bib50 article-title: An FPGA implementation of an elliptic curve processor GF(2 publication-title: ACM Great Lakes Symposium on VLSI – reference: Z. Dyka, P. Langendoerfer, Area efficient hardware implementation of elliptic curve cryptography by iteratively applying Karatsuba’s method, in: Design, Automation and Test in Europe (DATE), 3, 2005, pp. 70–75. – reference: ), in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2162, 2001, pp. 202–219. – reference: H. Wu, On complexity of polynomial basis squaring in – reference: T. Kerins, W. Marnane, E. Popovici, Design for reuse of elliptic curve cryptosystem processors for FPGAs, in: Irish Signals and Systems Conference (ISSC), 2004, pp. 577–582. – reference: ), in: Cryptographic Hardware and Embedded Systems (CHES), LNCS 2523, 2002, pp. 381–399. – reference: ) and GF(2 – reference: F. Rodríguez-Henríquez, Ç.K. Koç, On fully parallel karatsuba multipliers for GF(2 – reference: L. Batina, S.B. Örs, B. Preneel, J. Vandewalle, Hardware architectures for public key cryptography, Elsevier Integration, the VLSI Journal, special issue on Embedded Cryptographic Hardware, 34 (2003) 1–2, pp. 1–64. – volume: 27 start-page: 129 year: 1998 end-page: 146 ident: bib30 article-title: A survey of fast exponentiation methods publication-title: Journal of Algorithms – ident: 10.1016/j.sysarc.2006.09.002_bib32 doi: 10.1007/3-540-36400-5_26 – ident: 10.1016/j.sysarc.2006.09.002_bib47 doi: 10.1109/ITCC.2004.1286701 – ident: 10.1016/j.sysarc.2006.09.002_bib8 doi: 10.1007/978-3-540-24660-2_20 – ident: 10.1016/j.sysarc.2006.09.002_bib61 doi: 10.1007/3-540-44709-1_29 – ident: 10.1016/j.sysarc.2006.09.002_bib63 – ident: 10.1016/j.sysarc.2006.09.002_bib40 doi: 10.1049/cp:20040604 – ident: 10.1016/j.sysarc.2006.09.002_bib77 doi: 10.1007/3-540-36400-5_36 – ident: 10.1016/j.sysarc.2006.09.002_bib10 doi: 10.1109/ISCAS.2002.1010824 – ident: 10.1016/j.sysarc.2006.09.002_bib5 – ident: 10.1016/j.sysarc.2006.09.002_bib9 – ident: 10.1016/j.sysarc.2006.09.002_bib28 doi: 10.1007/11693383_25 – volume: 94 start-page: 395 issue: 2 year: 2006 ident: 10.1016/j.sysarc.2006.09.002_bib17 article-title: Elliptic curve cryptography engineering publication-title: Proceedings of the IEEE doi: 10.1109/JPROC.2005.862438 – ident: 10.1016/j.sysarc.2006.09.002_bib52 doi: 10.1007/3-540-45537-X_13 – ident: 10.1016/j.sysarc.2006.09.002_bib12 doi: 10.1007/3-540-36563-X_11 – ident: 10.1016/j.sysarc.2006.09.002_bib55 doi: 10.1109/FPT.2003.1275732 – ident: 10.1016/j.sysarc.2006.09.002_bib24 doi: 10.1109/ASAP.2004.1342462 – ident: 10.1016/j.sysarc.2006.09.002_bib66 doi: 10.1109/ITCC.2004.1286702 – ident: 10.1016/j.sysarc.2006.09.002_bib73 – volume: 19 start-page: 149 issue: 2 year: 1998 ident: 10.1016/j.sysarc.2006.09.002_bib74 article-title: Low energy digit-serial/parallel finite field multipliers publication-title: Journal of VLSI Signal Processing doi: 10.1023/A:1008013818413 – ident: 10.1016/j.sysarc.2006.09.002_bib78 doi: 10.1007/3-540-48059-5_24 – ident: 10.1016/j.sysarc.2006.09.002_bib35 – ident: 10.1016/j.sysarc.2006.09.002_bib2 doi: 10.1007/3-540-45537-X_20 – ident: 10.1016/j.sysarc.2006.09.002_bib23 doi: 10.1109/ASAP.2003.1212867 – ident: 10.1016/j.sysarc.2006.09.002_bib21 doi: 10.1007/11802839_45 – ident: 10.1016/j.sysarc.2006.09.002_bib15 doi: 10.1109/DATE.2005.254 – volume: 52 start-page: 449 issue: 4 year: 2003 ident: 10.1016/j.sysarc.2006.09.002_bib68 article-title: A scalable dual-field elliptic curve cryptographic processor publication-title: IEEE Transactions Computers doi: 10.1109/TC.2003.1190586 – ident: 10.1016/j.sysarc.2006.09.002_bib16 doi: 10.1007/3-540-44499-8_4 – ident: 10.1016/j.sysarc.2006.09.002_bib13 doi: 10.1017/CBO9781107360211 – ident: 10.1016/j.sysarc.2006.09.002_bib19 doi: 10.1109/ITCC.2004.1286717 – volume: 5205 start-page: 541 year: 2003 ident: 10.1016/j.sysarc.2006.09.002_bib46 article-title: High-performance finite field multiplier for cryptographic applications publication-title: Advanced Signal Processing Algorithms, Architectures, and Implementations XIII – SPIE doi: 10.1117/12.506144 – ident: 10.1016/j.sysarc.2006.09.002_bib25 doi: 10.1007/3-540-36400-5_28 – volume: 78 start-page: 171 issue: 3 year: 1988 ident: 10.1016/j.sysarc.2006.09.002_bib38 article-title: A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases publication-title: Information and Computation doi: 10.1016/0890-5401(88)90024-7 – ident: 10.1016/j.sysarc.2006.09.002_bib41 – ident: 10.1016/j.sysarc.2006.09.002_bib79 doi: 10.1007/3-540-44983-3_9 – ident: 10.1016/j.sysarc.2006.09.002_bib11 doi: 10.1109/IPDPS.2002.1016557 – ident: 10.1016/j.sysarc.2006.09.002_bib51 doi: 10.1007/3-540-39799-X_31 – ident: 10.1016/j.sysarc.2006.09.002_bib18 doi: 10.1109/ITCC.2005.33 – ident: 10.1016/j.sysarc.2006.09.002_bib27 – ident: 10.1016/j.sysarc.2006.09.002_bib49 doi: 10.1007/978-3-540-24660-2_28 – ident: 10.1016/j.sysarc.2006.09.002_bib62 doi: 10.1109/ASAP.2003.1212866 – ident: 10.1016/j.sysarc.2006.09.002_bib48 doi: 10.1049/cp:20040606 – ident: 10.1016/j.sysarc.2006.09.002_bib57 doi: 10.1007/3-540-44499-8_2 – ident: 10.1016/j.sysarc.2006.09.002_bib34 – ident: 10.1016/j.sysarc.2006.09.002_bib69 doi: 10.1007/3-540-44499-8_22 – ident: 10.1016/j.sysarc.2006.09.002_bib75 doi: 10.1109/ITCC.2005.25 – ident: 10.1016/j.sysarc.2006.09.002_bib20 doi: 10.1007/978-3-540-30117-2_25 – ident: 10.1016/j.sysarc.2006.09.002_bib67 doi: 10.1016/j.micpro.2004.03.003 – start-page: 454 year: 2004 ident: 10.1016/j.sysarc.2006.09.002_bib50 article-title: An FPGA implementation of an elliptic curve processor GF(2m) publication-title: ACM Great Lakes Symposium on VLSI doi: 10.1145/988952.989062 – ident: 10.1016/j.sysarc.2006.09.002_bib26 doi: 10.1109/IWRSP.2001.933834 – volume: 48 start-page: 243 issue: 177 year: 1987 ident: 10.1016/j.sysarc.2006.09.002_bib53 article-title: Speeding the pollard and elliptic curve methods of factorization publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1987-0866113-7 – ident: 10.1016/j.sysarc.2006.09.002_bib65 – ident: 10.1016/j.sysarc.2006.09.002_bib54 doi: 10.1007/978-3-540-24676-3_16 – ident: 10.1016/j.sysarc.2006.09.002_bib3 – ident: 10.1016/j.sysarc.2006.09.002_bib6 doi: 10.1109/ARITH.2003.1207677 – volume: 10 start-page: 550 issue: 5 year: 2002 ident: 10.1016/j.sysarc.2006.09.002_bib44 article-title: A microcoded elliptic curve processor using FPGA technology publication-title: IEEE Transactions on VLSI Systems doi: 10.1109/TVLSI.2002.801608 – year: 2004 ident: 10.1016/j.sysarc.2006.09.002_bib33 – ident: 10.1016/j.sysarc.2006.09.002_bib37 doi: 10.1007/3-540-48059-5_7 – ident: 10.1016/j.sysarc.2006.09.002_bib58 doi: 10.1007/3-540-44709-1_12 – volume: 48 start-page: 203 year: 1987 ident: 10.1016/j.sysarc.2006.09.002_bib43 article-title: Elliptic curve cryptosystem publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1987-0866109-5 – ident: 10.1016/j.sysarc.2006.09.002_bib56 – ident: 10.1016/j.sysarc.2006.09.002_bib71 – volume: 6 start-page: 3 issue: 1 year: 1993 ident: 10.1016/j.sysarc.2006.09.002_bib1 article-title: Arithmetic operations in GF(2m) publication-title: Journal of Cryptology doi: 10.1007/BF02620228 – ident: 10.1016/j.sysarc.2006.09.002_bib64 – ident: 10.1016/j.sysarc.2006.09.002_bib72 doi: 10.1007/3-540-44709-1_11 – ident: 10.1016/j.sysarc.2006.09.002_bib76 doi: 10.1007/978-3-540-27776-7_29 – ident: 10.1016/j.sysarc.2006.09.002_bib7 doi: 10.1007/978-3-540-30117-2_115 – ident: 10.1016/j.sysarc.2006.09.002_bib22 doi: 10.1109/DATE.2005.67 – ident: 10.1016/j.sysarc.2006.09.002_bib4 – volume: 27 start-page: 129 year: 1998 ident: 10.1016/j.sysarc.2006.09.002_bib30 article-title: A survey of fast exponentiation methods publication-title: Journal of Algorithms doi: 10.1006/jagm.1997.0913 – ident: 10.1016/j.sysarc.2006.09.002_bib39 doi: 10.1109/FPT.2004.1393285 – ident: 10.1016/j.sysarc.2006.09.002_bib45 doi: 10.1007/3-540-48059-5_27 – ident: 10.1016/j.sysarc.2006.09.002_bib14 doi: 10.1007/978-3-540-45146-4_34 – volume: 15 start-page: 19 year: 2002 ident: 10.1016/j.sysarc.2006.09.002_bib29 article-title: Constructive and destructive facets of Weil descent on elliptic curves publication-title: Journal of Cryptology doi: 10.1007/s00145-001-0011-x – ident: 10.1016/j.sysarc.2006.09.002_bib59 doi: 10.1007/3-540-36400-5_41 – ident: 10.1016/j.sysarc.2006.09.002_bib31 doi: 10.1007/3-540-44709-1_18 – ident: 10.1016/j.sysarc.2006.09.002_bib42 doi: 10.1007/3-540-45537-X_11 – volume: 51 start-page: 521 issue: 5 year: 2002 ident: 10.1016/j.sysarc.2006.09.002_bib80 article-title: Montgomery multiplier and squarer for a class of finite fields publication-title: IEEE Transactions on Computers doi: 10.1109/TC.2002.1004591 – ident: 10.1016/j.sysarc.2006.09.002_bib70 – ident: 10.1016/j.sysarc.2006.09.002_bib36 – ident: 10.1016/j.sysarc.2006.09.002_bib60 doi: 10.1007/3-540-44499-8_3 |
SSID | ssj0005512 |
Score | 2.0797896 |
Snippet | For the last decade, Elliptic Curve Cryptography (ECC) has gained increasing acceptance in the industry and the academic community and has been the subject of... |
SourceID | proquest crossref elsevier |
SourceType | Aggregation Database Enrichment Source Index Database Publisher |
StartPage | 72 |
SubjectTerms | Computer peripherals Cryptography Efficiency–flexibility tradeoffs Elliptic Curve Cryptography High-speed hardware implementation Network applications Public-key cryptography Studies |
Title | High-speed hardware implementations of Elliptic Curve Cryptography: A survey |
URI | https://dx.doi.org/10.1016/j.sysarc.2006.09.002 https://www.proquest.com/docview/218898072 |
Volume | 53 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Complete Freedom Collection [SCCMFC] customDbUrl: eissn: 1873-6165 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0005512 issn: 1383-7621 databaseCode: ACRLP dateStart: 19960101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection customDbUrl: eissn: 1873-6165 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0005512 issn: 1383-7621 databaseCode: .~1 dateStart: 19960901 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals [SCFCJ] customDbUrl: eissn: 1873-6165 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0005512 issn: 1383-7621 databaseCode: AIKHN dateStart: 19960101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals customDbUrl: mediaType: online eissn: 1873-6165 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0005512 issn: 1383-7621 databaseCode: AKRWK dateStart: 19960101 isFulltext: true providerName: Library Specific Holdings |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NS8MwFA9jXrz4Lc7pyMFrXNqm7eptFMf82kUHu4UkfYGJbmPtlF38203adKgIgtfwUsrLy3svye_9HkIXHmhgAjJCGfiEiYARqeKEhCCENOHWZNC2OPlhFA3H7HYSThoorWthLKzS-f7Kp5fe2o10nTa7i-m0--jZw1VkjixRSTJjOUEt-5ex6cuPLzCPsHrxNMLEStflcyXGK1_nxpzck0SyuVz5JTz9cNRl9BnsoR2XNuJ-9Wf7qAGzA7Rbt2TAboceonuL2yD5wsQkbOup3sUS8PS1BomXRobnGluohnEWCqer5RvgdLleFI68-gr3cW5H10doPLh-SofENUwgKgiCggid-T6VQipPa5NJRVT7QJXWnheDJ7T2LSwPdNTToaSZAslCQWMVZVFmdCmCY9SczWdwgnDYSySLpQchEyajYkJTmQBQ6SXKngFbKKj1xJVjE7dNLV54DRt75pV2baPLiNOEG-22ENnMWlRsGn_Ix_US8G9WwY3D_2Nmu14x7nZlzk0600t6NPZP__3dNtqubnctoOUMNYvlCs5NWlLITml3HbTVv7kbjj4BJEPknA |
linkProvider | Elsevier |
linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8MwDLbGOMCFN-JNDlyjpW3artymCTRg24UhcYuS1JGGYEzrAO3fk7TpEAgJiWuUVJXjfLaTzzbARYAGucScMo4h5TLiVOk0ozFKqay5tR60S04eDJPeA799jB8b0K1zYRyt0mN_heklWvuRlpdmazoet-4DF1wlNmRJyiIzfAVWeWwxuQmrnZu73vCL6RFXj552PnUL6gy6kuZVLAqrUf5VIlver_xioX5gdWmArrdgw3uOpFP93DY0cLIDm3VXBuIP6S70HXWDFlNrlohLqfqQMyTjl5onXuoZeTXEsTUsXmjSfZu9I-nOFtO5r199STqkcKOLPXi4vhp1e9T3TKA6iqI5lSYPQ6ak0oEx1plKmAmRaWOCIMVAGhM6Zh6apG1ixXKNiseSpTrJk9yKU0b70Jy8TvAASNzOFE9VgDGX1qni0jCVITIVZNqFgYcQ1XIS2hcUd30tnkXNHHsSlXRdr8tEsExY6R4CXa6aVgU1_pif1lsgvimGsJj_x8rjeseEP5iFsB5NO2uzNDz693fPYa03GvRF_2Z4dwzr1WWv47ecQHM-e8NT66XM1ZnXwk_s3OdH |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=High-speed+hardware+implementations+of+Elliptic+Curve+Cryptography%3A+A+survey&rft.jtitle=Journal+of+systems+architecture&rft.au=Guerric+Meurice+de+Dormale&rft.au=Jean-Jacques+Quisquater&rft.date=2007-02-01&rft.pub=Elsevier+Sequoia+S.A&rft.issn=1383-7621&rft.eissn=1873-6165&rft.volume=53&rft.issue=2%2F3&rft.spage=72&rft_id=info:doi/10.1016%2Fj.sysarc.2006.09.002&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=1204763401 |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1383-7621&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1383-7621&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1383-7621&client=summon |