{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T09:06:12Z","timestamp":1722589572493},"reference-count":46,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T00:00:00Z","timestamp":1648166400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"The advent of the Internet of Things (IoT) has enabled millions of potential new uses for consumers and businesses. However, with these new uses emerge some of the more pronounced risks in the connected object domain. Finite fields play a crucial role in many public-key cryptographic algorithms (PKCs), which are used extensively for the security and privacy of IoT devices, consumer electronic equipment, and software systems. Given that inversion is the most sensitive and costly finite field arithmetic operation in PKCs, this paper proposes a new, fast, constant-time inverter over prime fields Fp based on the traditional Binary Extended Euclidean (BEE) algorithm. A modified BEE algorithm (MBEEA) resistant to simple power analysis attacks (SPA) is presented, and the design performance area-delay over Fp is explored. Furthermore, the BEE algorithm, modular addition, and subtraction are revisited to optimize and balance the MBEEA signal flow and resource utilization efficiency. The proposed MBEEA architecture was implemented and tested on Xilinx FPGA Virtex #5, #6, and #7 devices. Our implementation over Fp (length of p = 256 bits) with 2035 slices achieved one modular inversion in only 1.12 \u03bcs on Virtex-7. Finally, we conducted a thorough comparison and performance analysis to demonstrate that the proposed design outperforms the competing designs, i.e., has a lower area-delay product (ADP) than the reported inverters.<\/jats:p>","DOI":"10.3390\/s22072535","type":"journal-article","created":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T01:31:25Z","timestamp":1648431085000},"page":"2535","source":"Crossref","is-referenced-by-count":2,"title":["Fast Constant-Time Modular Inversion over Fp Resistant to Simple Power Analysis Attacks for IoT Applications"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-4578-7308","authenticated-orcid":false,"given":"Anissa","family":"Sghaier","sequence":"first","affiliation":[{"name":"Electronics and Micro-Electronics Laboratory, Faculty of Sciences, University of Monastir, Monastir 5000, Tunisia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-8217-3455","authenticated-orcid":false,"given":"Medien","family":"Zeghid","sequence":"additional","affiliation":[{"name":"Electronics and Micro-Electronics Laboratory, Faculty of Sciences, University of Monastir, Monastir 5000, Tunisia"},{"name":"Electrical Engineering Department, College of Engineering at Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia"}]},{"given":"Chiraz","family":"Massoud","sequence":"additional","affiliation":[{"name":"Electronics and Micro-Electronics Laboratory, Faculty of Sciences, University of Monastir, Monastir 5000, Tunisia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-0452-2271","authenticated-orcid":false,"given":"Hassan Yousif","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, College of Engineering at Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-4193-6062","authenticated-orcid":false,"given":"Abdellah","family":"Chehri","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences, University of Quebec in Chicoutimi (UQAC), Chicoutimi, QC G7H 2B1, Canada"}]},{"given":"Mohsen","family":"Machhout","sequence":"additional","affiliation":[{"name":"Electronics and Micro-Electronics Laboratory, Faculty of Sciences, University of Monastir, Monastir 5000, Tunisia"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4267","DOI":"10.1007\/s11227-018-2440-4","article-title":"An effective security measures for nuclear power plant using big data analysis approach","volume":"75","author":"Lee","year":"2019","journal-title":"J. Supercomput."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kim, S.-K., Kim, U.-M., and Huh, J.-H. (2019). A Study on Improvement of Blockchain Application to Overcome Vulnerability of IoT Multiplatform Security. Energies, 12.","DOI":"10.3390\/en12030402"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Miller, V.-S. (1986). Use of elliptic curves in cryptography. Advances in Cryptology\u2014CRYPTO \u201985 Proceedings. CRYPTO 1985, Springer, Inc.. Lecture Notes in Computer Science.","DOI":"10.1007\/3-540-39799-X_31"},{"key":"ref_4","unstructured":"Arefin, M.S., Kaiser, M.S., Bandyopadhyay, A., Ahad, M.A.R., and Ray, K. (2022). An ECC Based Secure Communication Protocol for Resource Constraints IoT Devices in Smart Home. Proceedings of the International Conference on Big Data, IoT, and Machine Learning, Springer. Lecture Notes on Data Engineering and Communications Technologies."},{"key":"ref_5","first-page":"1","article-title":"ECC based inter-device authentication and authorization scheme using MQTT for IoT networks","volume":"46","author":"Lohachab","year":"2019","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"21478","DOI":"10.3390\/s150921478","article-title":"Optimized ECC Implementation for Secure Communication between Heterogeneous IoT Devices","volume":"15","author":"Marin","year":"2015","journal-title":"Sensors"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Varchola, M., Drutarovsky, M., Repka, M., and Zajac, P. (2015, January 7\u20139). Side-channel attack on multi-precision multiplier used in protected ecdsa implementation. Proceedings of the 2015 International Conference on ReConFigurable Computing and FPGAs (ReConFig), Riviera Maya, Mexico.","DOI":"10.1109\/ReConFig.2015.7393359"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Fan, J., and Verbauwhede, I. (2012). An updated survey on secure ECC implementations: Attacks, countermeasures and cost. Cryptography and Security: From Theory to Applications, Springer.","DOI":"10.1007\/978-3-642-28368-0_18"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Rafik, M.-B.-O., and Mohammed, F. (2013, January 22\u201324). The impact of ecc\u2019s scalar multiplication on wireless sensor networks. Proceedings of the 2013 11th International Symposium on Programming and Systems (ISPS), Algiers, Algeria.","DOI":"10.1109\/ISPS.2013.6581488"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1798","DOI":"10.1109\/TCSI.2010.2103190","article-title":"Petrel: Power and timing attack resistant elliptic curve scalar multiplier based on programmable GF(p) arithmetic unit","volume":"58","author":"Ghosh","year":"2011","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Koblitz, N. (1996). Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems. Advances in Cryptology\u2014CRYPTO\u201996, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/3-540-68697-5"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1049\/iet-wss.2018.5157","article-title":"Survey on power analysis attacks and its impact on intelligent sensor networks","volume":"8","author":"Shanmugham","year":"2018","journal-title":"IET Wirel. Sens. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.compeleceng.2018.02.030","article-title":"IoT application protection against power analysis attack","volume":"67","author":"Moon","year":"2018","journal-title":"Comput. Electr. Eng."},{"key":"ref_14","first-page":"1","article-title":"Reproducibility Enhancement by Optimized Power Analysis Attacks in Vulnerability Assessment of IoT Transducers","volume":"70","author":"Arpaia","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"24768","DOI":"10.1109\/ACCESS.2021.3057369","article-title":"Exploiting the Back-Gate Biasing Technique as a Countermeasure Against Power Analysis Attacks","volume":"9","author":"Dao","year":"2021","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2820611","article-title":"ECDSA Passive Attacks, Leakage Sources, and Common Design Mistakes","volume":"21","author":"Dubeuf","year":"2016","journal-title":"ACM Trans. Des. Autom. Electron. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Genkin, D., Pachmanov, L., Pipman, I., Tromer, E., and Yarom, Y. (2016, January 24\u201328). ECDSA Key Extraction from Mobile Devices via Nonintrusive Physical Side Channels. Proceedings of the ACM SIGSAC Conference on Computer and Communications Security, Vienna, Austria.","DOI":"10.1145\/2976749.2978353"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhang, K., Xu, S., Gu, D., Gu, H., Liu, J., Guo, Z., Liu, R., Liu, L., and Hu, X. (2017, January 15\u201318). Practical Partial-Nonce-Exposure Attack on ECC Algorithm. Proceedings of the 13th International Conference on Computational Intelligence and Security (CIS), Hong Kong, China.","DOI":"10.1109\/CIS.2017.00061"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wunan, W., Hao, C., and Jun, C. (2019). The Attack Case of ECDSA on Blockchain Based on Improved Simple Power Analysis. Artificial Intelligence and Security. ICAIS 2019, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-030-24268-8_12"},{"key":"ref_20","unstructured":"Thibault, J.-P., O\u2019Flynn, C., and Dewar, A. (2022, January 25). Ark of the ECC: An Open-Source ECDSA Power Analysis Attack on an FPGA Based Curve P-256 Implementation. Cryptology ePrint Archive: Report 2021\/1520. Available online: https:\/\/eprint.iacr.org\/2021\/1520."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sghaier, A., Zeghid, M., Massoud, C., and Mahchout, M. (2017). Design and Implementation of Low Area\/Power Elliptic Curve Digital Signature Hardware Core. Electronics, 6.","DOI":"10.3390\/electronics6020046"},{"key":"ref_22","first-page":"425","article-title":"Efficient Design and Performance Analysis of a Hardware Right-shift Binary Modular Inversion Algorithm in GF(p)","volume":"17","author":"Choi","year":"2017","journal-title":"J. Semicond. Technol. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"58704","DOI":"10.1109\/ACCESS.2019.2914641","article-title":"Fast Large Integer Modular Addition in GF(p) Using Novel Attribute-Based Representation","volume":"7","author":"Alhazmi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_24","unstructured":"Patel, Z., Gupta, S., and Kumar, Y.B.N. (2020). Qualitative and Quantitative Analysis of Parallel-Prefix Adders. Advances in VLSI and Embedded Systems, Springer. Lecture Notes in Electrical Engineering."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s13389-014-0084-8","article-title":"Constant time modular inversion","volume":"4","author":"Bos","year":"2014","journal-title":"J. Cryptogr. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1007\/978-3-319-40253-6_6","article-title":"Energy-efficient elliptic curve cryptography for MSP430-based wireless sensor nodes","volume":"Volume 9722","author":"Liu","year":"2016","journal-title":"Proceedings of the 21st Australasian Conference on Information Security and Privacy"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Xu, S., Gu, H., Wang, L., Guo, Z., Liu, J., Lu, X., and Gu, D. (2017, January 15\u201318). Efficient and Constant Time Modular Inversions Over Prime Fields. Proceedings of the 13th International Conference on Computational Intelligence and Security (CIS), Hong Kong, China.","DOI":"10.1109\/CIS.2017.00122"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1002\/cta.2283","article-title":"Side-channel analysis of the modular inversion step in the RSA key generation algorithm","volume":"45","author":"Aldaya","year":"2017","journal-title":"Int. J. Circuit Theory Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s13389-017-0161-x","article-title":"Montgomery inversion","volume":"8","year":"2018","journal-title":"J. Cryptogr. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Bernstein, D.-J., and Yang, B.-Y. (2019). Fast constant-time gcd computation and modular inversion. IACR Trans. Cryptogr. Hardw. Embed. Syst., 340\u2013398.","DOI":"10.46586\/tches.v2019.i3.340-398"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Awaludin, A.-M., Larasati, H.-T., and Kim, H. (2021). High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA. Sensors, 21.","DOI":"10.20944\/preprints202101.0250.v1"},{"key":"ref_32","unstructured":"Sarna, S., and Czerwinski, R. (May, January 29). RSA and ECC universal, constant time modular inversion. Proceedings of the AIP Conference Proceedings, Crete, Greece."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s13389-016-0135-4","article-title":"Spa vulnerabilities of the binary extended Euclidean algorithm","volume":"7","author":"Aldaya","year":"2017","journal-title":"J. Cryptogr. Eng."},{"key":"ref_34","first-page":"21","article-title":"An Efficient Processing by using Kogge-Stone High-Speed Addition Technique","volume":"131","author":"Rajnish","year":"2015","journal-title":"Int. J. Comput. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Vitoroulis, K., and Al-Khalili, A.-J. (2007, January 5\u20138). Performance of Parallel Prefix Adders implemented with FPGA technology. Proceedings of the 2007 IEEE Northeast Workshop on Circuits and Systems, Montreal, QC, Canada.","DOI":"10.1109\/NEWCAS.2007.4487969"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Hossain, M.-S., and Kong, Y. (2015, January 11\u201313). High-Performance FPGA Implementation of Modular Inversion over F256 for Elliptic Curve Cryptography. Proceedings of the 2015 IEEE international conference on Data Science and Data Intensive Systems, Sydney, NSW, Australia.","DOI":"10.1109\/DSDIS.2015.47"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1049\/iet-cdt.2016.0033","article-title":"High-performance elliptic curve cryptography processor over NIST prime fields","volume":"11","author":"Hossain","year":"2016","journal-title":"IET Comput. Digit. Tech."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1002\/cta.2295","article-title":"Low latency flexible FPGA implementation of point multiplication on elliptic curves over GF (p)","volume":"45","author":"Javeed","year":"2017","journal-title":"Int. J. Circuit Theory Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.micpro.2016.12.005","article-title":"High-performance hardware support for elliptic curve cryptography over general prime field","volume":"51","author":"Javeed","year":"2017","journal-title":"Microprocess. Microsyst."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Mrabet, A., El-Mrabet, N., Bouallegue, B., Mesnager, S., and Machhout, M. (2017, January 8\u201310). An efficient and scalable modular inversion\/division for public-key cryptosystems. Proceedings of the 2017 International Conference on Engineering & MIS (ICEMIS), Monastir, Tunisia.","DOI":"10.1109\/ICEMIS.2017.8272995"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/s11227-018-02740-2","article-title":"High-performance ECC processor architecture design for IoT security applications","volume":"75","author":"Kudithi","year":"2019","journal-title":"J. Supercomput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1109\/TIE.2016.2625241","article-title":"An efficient and flexible hardware implementation of the dual field elliptic curve cryptographic processor","volume":"64","author":"Liu","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/TVLSI.2013.2237930","article-title":"Efficient power analysis resistant dual field elliptic curve cryptographic processor using heterogeneous dual processing element architecture","volume":"22","author":"Lee","year":"2014","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI)"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Vliegen, J., Mentens, N., Genoe, J., Braeken, A., Kubera, S., Touha, A., and Verbauwhede, I. (2010, January 7\u20139). A compact FPGA based architecture for elliptic curve cryptography over prime fields. Proceedings of the ASAP 2010\u201421st IEEE International Conference on Application-Specific Systems, Architectures and Processors, Rennes, France.","DOI":"10.1109\/ASAP.2010.5540977"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1946","DOI":"10.1109\/TCSI.2006.880184","article-title":"Hardware elliptic curve cryptographic processor over GF(p)","volume":"53","author":"McIvor","year":"2006","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.micpro.2004.03.006","article-title":"An FPGA Implementation of a GF(p) ALU for encryption processors","volume":"28","author":"Daly","year":"2004","journal-title":"Microprocess. Microsyst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/7\/2535\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,27]],"date-time":"2024-07-27T20:46:21Z","timestamp":1722113181000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/7\/2535"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,25]]},"references-count":46,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["s22072535"],"URL":"http:\/\/dx.doi.org\/10.3390\/s22072535","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,25]]}}}
