{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T13:18:03Z","timestamp":1758892683834},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T00:00:00Z","timestamp":1622505600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T00:00:00Z","timestamp":1625011200000},"content-version":"vor","delay-in-days":29,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Electron Test"],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Montgomery <jats:italic>kP<\/jats:italic> algorithm i.e. the Montgomery ladder is reported in literature as resistant against simple SCA due to the fact that the processing of each key bit value of the scalar <jats:italic>k<\/jats:italic> is done using the same sequence of operations. We implemented the Montgomery <jats:italic>kP<\/jats:italic> algorithm using Lopez-Dahab projective coordinates for the NIST elliptic curve <jats:italic>B-233<\/jats:italic>. We instantiated the same VHDL code for a wide range of clock frequencies for the same target FPGA and using the same compiler options. We measured electromagnetic traces of the <jats:italic>kP<\/jats:italic> executions using the same input data, i.e. scalar <jats:italic>k<\/jats:italic> and elliptic curve point <jats:italic>P<\/jats:italic>, and measurement setup. Additionally, we synthesized the same VHDL code for two IHP CMOS technologies, for a broad spectrum of frequencies. We simulated the power consumption of each synthesized design during an execution of the <jats:italic>kP<\/jats:italic> operation, always using the same scalar <jats:italic>k<\/jats:italic> and elliptic curve point <jats:italic>P<\/jats:italic> as inputs. Our experiments clearly show that the success of simple electromagnetic analysis attacks against FPGA implementations as well as the one of simple power analysis attacks against synthesized ASIC designs depends on the target frequency for which the design was implemented and at which it is executed significantly. In our experiments the scalar <jats:italic>k<\/jats:italic> was successfully revealed via simple visual inspection of the electromagnetic traces of the FPGA for frequencies from 40 to 100\u00a0MHz when standard compile options were used as well as from 50\u00a0MHz up to 240\u00a0MHz when performance optimizing compile options were used. We obtained similar results attacking the power traces simulated for the ASIC. Despite the significant differences of the here investigated technologies the designs\u2019 resistance against the attacks performed is similar: only a few points in the traces represent strong leakage sources allowing to reveal the key at very low and very high frequencies. For the \u201cmiddle\u201d frequencies the number of points which allow to successfully reveal the key increases when increasing the frequency.<\/jats:p>","DOI":"10.1007\/s10836-021-05951-3","type":"journal-article","created":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T04:02:37Z","timestamp":1625025757000},"page":"289-303","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice"],"prefix":"10.1007","volume":"37","author":[{"given":"Ievgen","family":"Kabin","sequence":"first","affiliation":[]},{"given":"Zoya","family":"Dyka","sequence":"additional","affiliation":[]},{"given":"Dan","family":"Klann","sequence":"additional","affiliation":[]},{"given":"Marcin","family":"Aftowicz","sequence":"additional","affiliation":[]},{"given":"Peter","family":"Langendoerfer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"key":"5951_CR1","doi-asserted-by":"publisher","unstructured":"Federal Information Processing Standard (FIPS) (2013) Digital Signature Standard; Request for Comments on the NIST-Recommended Elliptic Curves: 186\u2013184. https:\/\/doi.org\/10.6028\/NIST.FIPS.186-4","DOI":"10.6028\/NIST.FIPS.186-4"},{"key":"5951_CR2","unstructured":"Hankerson D, Menezes A, Vanstone S (2004) Guide to Elliptic Curve Cryptography. Springer-Verlag New York, Inc., ISBN 0-387-95273-X"},{"key":"5951_CR3","doi-asserted-by":"crossref","unstructured":"Kabin I, Dyka Z, Kreiser D, Langendoerfer P (2018) Horizontal Address-Bit DEMA against ECDSA. In: 2018 9th IFIP International Conference on New Technologies, Mobility and Security (NTMS), p 1\u20137","DOI":"10.1109\/NTMS.2018.8328695"},{"key":"5951_CR4","unstructured":"NXP Application note AN11875: A1006 Host Reference Implementation for LPC1115.\u00a0Rev. 0.2 \u2014 10 August 2016"},{"key":"#cr-split#-5951_CR5.1","unstructured":"L\u00f3pez J, Dahab R (1999) Fast Multiplication on Elliptic Curves Over GF"},{"key":"#cr-split#-5951_CR5.2","unstructured":"(2m) without precomputation. In:. Ko\u00e7 \u00c7K, Paar C (eds) Cryptographic Hardware and Embedded Systems, vol. 1717. Berlin, Heidelberg: Springer Berlin Heidelberg, p 316-327"},{"key":"5951_CR6","doi-asserted-by":"publisher","unstructured":"Hankerson D, L\u00f3pez J, Menezes A (2000) Software Implementation of Elliptic Curve Cryptography over Binary Fields. In Cryptographic Hardware and Embedded Systems \u2014 CHES 2000, p 1\u201324. https:\/\/doi.org\/10.1007\/3-540-44499-8_1","DOI":"10.1007\/3-540-44499-8_1"},{"key":"5951_CR7","first-page":"291","volume":"2002","author":"M Joye","year":"2002","unstructured":"Joye M, Yen S-M (2002) The Montgomery Powering Ladder. Cryptographic Hardware and Embedded Systems - CHES 2002:291\u2013302","journal-title":"Cryptographic Hardware and Embedded Systems - CHES"},{"key":"5951_CR8","doi-asserted-by":"crossref","unstructured":"Fan J, Guo X, De Mulder E, Schaumont P, Preneel B, Verbauwhede I (2010) State-of-the-art of secure ECC implementations: a survey on known side-channel attacks and countermeasures. In: 2010 IEEE International Symposium on Hardware-Oriented Security and Trust (HOST), p 76\u201387","DOI":"10.1109\/HST.2010.5513110"},{"key":"5951_CR9","doi-asserted-by":"crossref","unstructured":"Itoh K, Izu T, Takenaka M (2002) Address-Bit Differential Power Analysis of Cryptographic Schemes OK-ECDH and OK-ECDSA. In: Cryptographic Hardware and Embedded Systems - CHES 2002, p 129\u2013143","DOI":"10.1007\/3-540-36400-5_11"},{"key":"5951_CR10","doi-asserted-by":"crossref","unstructured":"Kabin I, Dyka Z, Kreiser D, Langendoerfer P (2017) Horizontal address-bit DPA against montgomery kP implementation. In: 2017 International Conference on ReConFigurable Computing and FPGAs (ReConFig), p 1\u20138","DOI":"10.1109\/RECONFIG.2017.8279800"},{"key":"5951_CR11","doi-asserted-by":"publisher","unstructured":"Kabin I, Dyka Z, Aftowicz M, Klann D, Langendoerfer P (2020) Resistance of the Montgomery kP Algorithm against Simple SCA: Theory and Practice. In 2020 IEEE Latin-American Test Symposium (LATS), p 1\u20136. https:\/\/doi.org\/10.1109\/LATS49555.2020.9093678","DOI":"10.1109\/LATS49555.2020.9093678"},{"key":"5951_CR12","doi-asserted-by":"crossref","unstructured":"Bock EA, Dyka Z, Langendoerfer P (2016) Increasing the Robustness of the Montgomery kP-Algorithm Against SCA by Modifying Its Initialization. In: Innovative Security Solutions for Information Technology and Communications. Springer, Cham, p 167\u2013178","DOI":"10.1007\/978-3-319-47238-6_12"},{"key":"5951_CR13","doi-asserted-by":"crossref","unstructured":"Dyka Z, Bock EA, Kabin I, Langendoerfer P (2016) Inherent Resistance of Efficient ECC Designs against SCA Attacks,\u201d in 2016 8th IFIP International Conference on New Technologies, Mobility and Security (NTMS), p 1\u20135","DOI":"10.1109\/NTMS.2016.7792457"},{"key":"5951_CR14","doi-asserted-by":"crossref","unstructured":"Dyka Z, Langendoerfer P (2005) Area efficient hardware implementation of elliptic curve cryptography by iteratively applying Karatsuba\u2019s method. In: Design, Automation and Test in Europe, Vol.3. p 70\u201375","DOI":"10.1109\/DATE.2005.67"},{"key":"5951_CR15","unstructured":"Alpirez Bock E (2015) SCA resistent implementation of the Montgomery kP-algorithm. Master thesis. https:\/\/opus4.kobv.de\/opus4-btu\/files\/3628\/Estuardo_AlpirezBock.pdf"},{"key":"5951_CR16","doi-asserted-by":"crossref","unstructured":"Kabin I, Kreiser D, Dyka Z, Langendoerfer P (2018) FPGA Implementation of ECC: Low-Cost Countermeasure against Horizontal Bus and Address-Bit SCA. In: 2018 International Conference on ReConFigurable Computing and FPGAs (ReConFig), p 1\u20137","DOI":"10.1109\/RECONFIG.2018.8641732"},{"key":"5951_CR17","doi-asserted-by":"publisher","unstructured":"Kabin I, Sosa A, Dyka Z, Klann D, Langendoerfer P (2019) On the Influence of the FPGA Compiler Optimization Options on the Success of the Horizontal Attack. In: 2019 International Conference on ReConFigurable Computing and FPGAs (ReConFig), p 1\u20135. https:\/\/doi.org\/10.1109\/ReConFig48160.2019.8994807","DOI":"10.1109\/ReConFig48160.2019.8994807"},{"key":"5951_CR18","unstructured":"IHP GmbH (2020) Low-Volume & Multi-Project Service. [Online]. Available: https:\/\/www.ihp-microelectronics.com\/de\/services\/mpw-prototyping\/sigec-bicmos-technologies.html. Accessed 17 Sep 2020"}],"container-title":["Journal of Electronic Testing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10836-021-05951-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10836-021-05951-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10836-021-05951-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:03:18Z","timestamp":1630368198000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10836-021-05951-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["5951"],"URL":"https:\/\/doi.org\/10.1007\/s10836-021-05951-3","relation":{},"ISSN":["0923-8174","1573-0727"],"issn-type":[{"value":"0923-8174","type":"print"},{"value":"1573-0727","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6]]},"assertion":[{"value":"30 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}