{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,28]],"date-time":"2026-06-28T05:08:10Z","timestamp":1782623290953,"version":"3.54.5"},"reference-count":26,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T00:00:00Z","timestamp":1589760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100010418","name":"Institute for Information and Communications Technology Promotion","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100010418","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Research on Blockchain Security Technology for IoT Services","award":["2018-0-00264"],"award-info":[{"award-number":["2018-0-00264"]}]},{"DOI":"10.13039\/501100003626","name":"Defense Acquisition Program Administration","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003626","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100005073","name":"Agency for Defense Development","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005073","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Korean government"},{"DOI":"10.13039\/100017354","name":"Military Crypto Research Center","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100017354","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Korean governmen","award":["NRF-2017R1C1B5075742"],"award-info":[{"award-number":["NRF-2017R1C1B5075742"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Embed. Comput. Syst."],"published-print":{"date-parts":[[2020,5,31]]},"abstract":"<jats:p>For traditional public key cryptography and post-quantum cryptography, such as elliptic curve cryptography and supersingular isogeny key encapsulation, modular multiplication is the most performance-critical operation among basic arithmetic of these cryptographic schemes. For this reason, the execution timing of such cryptographic schemes, which may highly determine that the service availability for low-end microprocessors (e.g., 8-bit AVR, 16-bit MSP430X, and 32-bit ARM Cortex-M), mainly relies on the efficiency of modular multiplication on target embedded processors.<\/jats:p>\n          <jats:p>In this article, we present new optimal modular multiplication techniques based on the interleaved Montgomery multiplication on 16-bit MSP430X microprocessors, where the multiplication part is performed in a hardware multiplier and the reduction part is performed in a basic arithmetic logic unit (ALU) with the optimal modular multiplication routine, respectively. This two-step approach is effective for the special modulus of NIST curves, SM2 curves, and supersingular isogeny key encapsulation. We further optimized the Montgomery reduction by using techniques for \u201cMontgomery-friendly\u201d prime. This technique significantly reduces the number of partial products. To demonstrate the superiority of the proposed implementation of Montgomery multiplication, we applied the proposed method to the NIST P-256 curve, of which the implementation improves the previous modular multiplication operation by 23.6% on 16-bit MSP430X microprocessors and to the SM2 curve as well (first implementation on 16-bit MSP430X microcontrollers).<\/jats:p>\n          <jats:p>Moreover, secure countermeasures against timing attack and simple power analysis are also applied to the scalar multiplication of NIST P-256 and SM2 curves, which achieve the 8,582,338 clock cycles (0.53 seconds@16 MHz) and 10,027,086 clock cycles (0.62 seconds@16 MHz), respectively. The proposed Montgomery multiplication is a generic method that can be applied to other cryptographic schemes and microprocessors with minor modifications.<\/jats:p>","DOI":"10.1145\/3387919","type":"journal-article","created":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T18:00:15Z","timestamp":1590429615000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Montgomery Multiplication for Public Key Cryptography on MSP430X"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0069-9061","authenticated-orcid":false,"given":"Hwajeong","family":"Seo","sequence":"first","affiliation":[{"name":"Hansung University, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kyuhwang","family":"An","sequence":"additional","affiliation":[{"name":"Hansung University, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyeokdong","family":"Kwon","sequence":"additional","affiliation":[{"name":"Hansung University, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhi","family":"Hu","sequence":"additional","affiliation":[{"name":"Central South University, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2020,5,18]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the Workshop on Elliptic Curve Cryptography Sta","author":"Adalier Mehmet","year":"2015","unstructured":"Mehmet Adalier . 2015 . Efficient and secure elliptic curve cryptography implementation of Curve P-256 . In Proceedings of the Workshop on Elliptic Curve Cryptography Sta Mehmet Adalier. 2015. Efficient and secure elliptic curve cryptography implementation of Curve P-256. In Proceedings of the Workshop on Elliptic Curve Cryptography Sta"},{"key":"e_1_2_1_2_1","volume-title":"Retrieved","author":"Azarderakhsh Reza","year":"2017","unstructured":"Reza Azarderakhsh , Matthew Campagna , Craig Costello , Luca De Feo , Basil Hess , Amir Jalali , David Jao , 2017 . Supersingular Isogeny Key Encapsulation\u2014Submission to the NIST\u2019s Post-Quantum Cryptography Standardization Process . Retrieved April 19, 2020 from https:\/\/csrc.nist.gov\/CSRC\/media\/Projects\/Post-Quantum-Cryptography\/documents\/round-1\/submissions\/SIKE.zip. Reza Azarderakhsh, Matthew Campagna, Craig Costello, Luca De Feo, Basil Hess, Amir Jalali, David Jao, et al. 2017. Supersingular Isogeny Key Encapsulation\u2014Submission to the NIST\u2019s Post-Quantum Cryptography Standardization Process. Retrieved April 19, 2020 from https:\/\/csrc.nist.gov\/CSRC\/media\/Projects\/Post-Quantum-Cryptography\/documents\/round-1\/submissions\/SIKE.zip."},{"key":"e_1_2_1_3_1","volume-title":"Retrieved","author":"Azarderakhsh Reza","year":"2019","unstructured":"Reza Azarderakhsh , Matthew Campagna , Craig Costello , Luca De Feo , Basil Hess , Amir Jalali , David Jao , 2019 . Supersingular Isogeny Key Encapsulation\u2014Submission to the NIST\u2019s Post-Quantum Cryptography Standardization Process, Round 2 . Retrieved April 19, 2020 from https:\/\/csrc.nist.gov\/CSRC\/media\/Projects\/Post-Quantum-Cryptography\/documents\/round-2\/submissions\/SIKE-Round2.zip. Reza Azarderakhsh, Matthew Campagna, Craig Costello, Luca De Feo, Basil Hess, Amir Jalali, David Jao, et al. 2019. Supersingular Isogeny Key Encapsulation\u2014Submission to the NIST\u2019s Post-Quantum Cryptography Standardization Process, Round 2. Retrieved April 19, 2020 from https:\/\/csrc.nist.gov\/CSRC\/media\/Projects\/Post-Quantum-Cryptography\/documents\/round-2\/submissions\/SIKE-Round2.zip."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-53018-4_21"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-015-0087-1"},{"key":"e_1_2_1_6_1","first-page":"186","article-title":"Digital Signature Standard (DSS)","author":"FIPS","year":"2000","unstructured":"FIPS 186-2. 2000 . Digital Signature Standard (DSS) . Federal Information Processing Standards Publication 186 - 182 . National Institute of Standards and Technology. FIPS 186-2. 2000. Digital Signature Standard (DSS). Federal Information Processing Standards Publication 186-2. 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Full-size high-security ECC implementation on MSP430 microcontrollers. In Proceedings of the International Conference on Cryptology and Information Security in Latin America. 31--47."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/TDSC.2017.2723891"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48965-0_6"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TDSC.2018.2825449"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIFS.2015.2491261"},{"key":"e_1_2_1_15_1","first-page":"8","article-title":"An energy efficient parallel embedded system for small satellite applications","volume":"1","author":"Peters Daniel","year":"2009","unstructured":"Daniel Peters , Dejan Raskovic , and Denise Thorsen . 2009 . An energy efficient parallel embedded system for small satellite applications . ISAST Transactions on Computers and Intelligent Systems 1 , 2 (2009), 8 -- 16 . 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