{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:48:01Z","timestamp":1740142081617,"version":"3.37.3"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T00:00:00Z","timestamp":1597104000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T00:00:00Z","timestamp":1597104000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Innovations Syst Softw Eng"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s11334-020-00371-6","type":"journal-article","created":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T09:34:30Z","timestamp":1597138470000},"page":"53-62","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Resisting HODPA attacks in modular exponentiation using inner product with differential evolution"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5568-1577","authenticated-orcid":false,"given":"Hridoy Jyoti","family":"Mahanta","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ajoy Kumar","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Somnath","family":"Mukhopadhyay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,8,11]]},"reference":[{"key":"371_CR1","doi-asserted-by":"crossref","unstructured":"Kocher P, Joshu J, Jun B (1999) Differential power analysis. In: CRYPTO 1999. LNCS . vol 1666. Springer Heidelberg, pp 388\u2013397","DOI":"10.1007\/3-540-48405-1_25"},{"key":"371_CR2","doi-asserted-by":"crossref","unstructured":"Messerges TS, Dabdish E A, Sloan RH (1999) Power analysis attacks of modular exponentiation in smartcards. In: Cryptographic hardware and embedded systems (CHES-99). Springer, Berlin, pp 144\u2013157","DOI":"10.1007\/3-540-48059-5_14"},{"key":"371_CR3","doi-asserted-by":"crossref","unstructured":"Fouque PA, Kunz-Jacques S et al (2006) Power attack on small RSA public exponent. In: Cryptographic hardware and embedded systems (CHES-06). Springer, Berlin, pp 339\u2013353","DOI":"10.1007\/11894063_27"},{"key":"371_CR4","doi-asserted-by":"crossref","unstructured":"Schindler W, Itoh K (2011) Exponent blinding does not always lift (partial) spa resistance to higher-level security. In: International conference on ACNS, pp 73\u201390","DOI":"10.1007\/978-3-642-21554-4_5"},{"issue":"4","key":"371_CR5","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/s13389-014-0081-y","volume":"4","author":"W Schindler","year":"2014","unstructured":"Schindler W, Wiemers A (2014) Power attacks in the presence of exponent blinding. J Cryptogr Eng 4(4):213\u2013236","journal-title":"J Cryptogr Eng"},{"key":"371_CR6","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s13389-016-0146-1","volume":"7","author":"W Schindler","year":"2017","unstructured":"Schindler W, Wiemers A (2017) Generic power attacks on RSA with CRT and exponent blinding: new results. J Cryptogr Eng 7:255\u2013272","journal-title":"J Cryptogr Eng"},{"key":"371_CR7","doi-asserted-by":"crossref","unstructured":"Witteman M F, Witteman J G, Menarini F (2011) Defeating RSA multiply-always and message blinding countermeasures. In: CT-RSA-2011, pp 77\u201388","DOI":"10.1007\/978-3-642-19074-2_6"},{"key":"371_CR8","doi-asserted-by":"crossref","unstructured":"Bauer S (2012) Attacking exponent blinding in RSA without CRT. In: International conference on COSADE, pp 82\u201388","DOI":"10.1007\/978-3-642-29912-4_7"},{"key":"371_CR9","doi-asserted-by":"crossref","unstructured":"Zhao B et al (2016) An improved power attack on small RSA public exponent. In: 12th IEEE international conference on CIS, pp 578\u2013581","DOI":"10.1109\/CIS.2016.0140"},{"key":"371_CR10","doi-asserted-by":"crossref","unstructured":"Bauer A, Jaulmes E (2013) Correlation analysis against protected SFM implementations of RSA. In: INDOCRYPT-2013. Springer, pp 98\u2013115","DOI":"10.1007\/978-3-319-03515-4_7"},{"key":"371_CR11","unstructured":"Kuzu EA et al (2013) New cross correlation attack methods on the montgomery ladder implementation of RSA. In: 3rd IEEE international advanced computing conference, pp 138\u2013142"},{"key":"371_CR12","unstructured":"Kuzu EA, Tangel A (2014) A new style CPA attack on the ML implementation of RSA. In: IEEE international computer science and engineering conference, pp 323\u2013328"},{"issue":"6","key":"371_CR13","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1109\/CC.2015.7122478","volume":"12","author":"W Wan","year":"2015","unstructured":"Wan W, Yang W, Chen J (2015) An optimized cross correlation power attack of message blinding exponentiation algorithms. China Commun 12(6):22\u201332","journal-title":"China Commun"},{"issue":"7","key":"371_CR14","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.1109\/TIFS.2015.2411213","volume":"10","author":"M Kaminaga","year":"2015","unstructured":"Kaminaga M, Yoshikawa H, Suzuki T (2015) Double counting in $$2^{t}$$-ary RSA precomputation reveals the secret exponent. IEEE Trans Inf Forensics Secur 10(7):1394\u20131401","journal-title":"IEEE Trans Inf Forensics Secur"},{"key":"371_CR15","doi-asserted-by":"crossref","unstructured":"Mamiya H, Miyaji A, Morimoto H (2004) Efficient countermeasures against RPA, DPA, and SPA. In: Cryptographic hardware and embedded systems (CHES-04). Springer, Berlin, pp 343\u2013356","DOI":"10.1007\/978-3-540-28632-5_25"},{"key":"371_CR16","doi-asserted-by":"crossref","unstructured":"Kim C et al (2004) A secure and practical CRT-based RSA to resist side channel attacks. In: International conference on computational science and its applications, pp 150\u2013158","DOI":"10.1007\/978-3-540-24707-4_19"},{"key":"371_CR17","unstructured":"Kim C et al (2005) An improved and efficient countermeasure against power analysis attacks. IACR Cryptol. ePrint Archive"},{"key":"371_CR18","unstructured":"Wang Y et al (2006) An efficient algorithm for DPA-resistant RSA. In: IEEE Asia Pacific conference on circuits and systems, pp 1659\u20131662"},{"key":"371_CR19","doi-asserted-by":"crossref","unstructured":"Yin X et al (2012) A randomized binary modular exponentiation based RSA algorithm against the comparative power analysis. In: IEEE international conference on intelligent control, automatic detection and high-end equipment, pp 160\u2013165","DOI":"10.1109\/ICADE.2012.6330119"},{"key":"371_CR20","unstructured":"Zhang Y et al (2008) A side-channel attack countermeasure based on segmented modular exponent randomizing in RSA cryptosystem. In: 11th IEEE Singapore international conference on communication systems, pp 148\u2013151"},{"key":"371_CR21","doi-asserted-by":"crossref","unstructured":"Jin J F, Lu E H, Gao XW (2009) Resistance DPA of RSA on smartcard. In: 5th IEEE international conference on information assurance and security, pp 406\u2013409","DOI":"10.1109\/IAS.2009.301"},{"issue":"4","key":"371_CR22","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1145\/2560020","volume":"13","author":"H Kim","year":"2014","unstructured":"Kim H et al (2014) Message blinding method requiring no multiplicative inversion for RSA. ACM Trans Embed Comput Syst 13(4):80\u201389","journal-title":"ACM Trans Embed Comput Syst"},{"key":"371_CR23","unstructured":"Fournaris AP, Koufopavlou O (2012) Protecting CRT RSA against fault and power side channel attacks. In: IEEE computer society annual symposium on VLSI, pp 159\u2013164"},{"issue":"3","key":"371_CR24","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1080\/10798587.2015.1118909","volume":"22","author":"Y Choi","year":"2016","unstructured":"Choi Y et al (2016) An improved square-always exponentiation resistant to side-channel attacks on RSA implementation. Intell Autom Soft Comput 22(3):353\u2013363","journal-title":"Intell Autom Soft Comput"},{"issue":"2","key":"371_CR25","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1080\/00207160.2014.935353","volume":"93","author":"H Kim","year":"2016","unstructured":"Kim H et al (2016) A secure exponentiation algorithm resistant to a combined attack on RSA implementation. Int J Comput Math 93(2):258\u2013272","journal-title":"Int J Comput Math"},{"key":"371_CR26","doi-asserted-by":"crossref","unstructured":"Chari S, Jutla C, Rao J R, Rohatgi P (1999) Towards sound approaches to counteract power-analysis attacks. In: CRYPTO-1999. Springer, Berlin, p 791","DOI":"10.1007\/3-540-48405-1_26"},{"key":"371_CR27","doi-asserted-by":"crossref","unstructured":"Dziembowski S, Faust S (2012) Leakage-resilient circuits without computational assumptions. In: Theory of cryptography conference, pp 230\u2013247","DOI":"10.1007\/978-3-642-28914-9_13"},{"key":"371_CR28","doi-asserted-by":"crossref","unstructured":"Balasch J et al (2012) Theory and practice of a leakage resilient masking scheme. In: ASIACRYPT-2012. Springer, pp 758\u2013775","DOI":"10.1007\/978-3-642-34961-4_45"},{"key":"371_CR29","doi-asserted-by":"crossref","unstructured":"Balasch J, Faust S, Gierlichs B (2015) Inner product masking revisited. ICAR Cryptol. e-Print Archive 105","DOI":"10.1007\/978-3-662-46800-5_19"},{"issue":"1","key":"371_CR30","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s11334-019-00346-2","volume":"16","author":"HJ Mahanta","year":"2020","unstructured":"Mahanta HJ, Khan AK, Mukhopadhyay S (2020) Modular exponentiation with inner product to resist higher-order DPA attacks. Innov Syst Softw Eng 16(1):87\u201397","journal-title":"Innov Syst Softw Eng"},{"key":"371_CR31","doi-asserted-by":"crossref","unstructured":"Storn R (1996) On the usage of differential evolution for function optimization. In: IEEE biennial conference of the North American of fuzzy information processing society, pp 519\u2013523","DOI":"10.1109\/NAFIPS.1996.534789"},{"issue":"4","key":"371_CR32","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341\u2013359","journal-title":"J Glob Optim"},{"key":"371_CR33","volume-title":"Differential evolution: a practical approach to global optimization","author":"K Price","year":"2006","unstructured":"Price K, Storn RM, Lampinen JA (2006) Differential evolution: a practical approach to global optimization. Springer, Berlin"},{"key":"371_CR34","doi-asserted-by":"crossref","unstructured":"Walter C D (2001) Sliding windows succumbs to Big Mac attack. In: Cryptographic hardware and embedded systems (CHES-2001). Springer, Berlin, pp 286\u2013299","DOI":"10.1007\/3-540-44709-1_24"},{"key":"371_CR35","doi-asserted-by":"crossref","unstructured":"Bauer A, Jaulmes E, Prouff E, Wild J (2013) Horizontal and vertical side-channel attacks against secure RSA implementations. In: CT-RSA-2013. Springer, Berlin, pp 1\u201317","DOI":"10.1007\/978-3-642-36095-4_1"},{"key":"371_CR36","doi-asserted-by":"crossref","unstructured":"Clavier C et al (2010) Horizontal correlation analysis on exponentiation. In: Lecture notes on computer science, vol 6476, pp 46\u201361","DOI":"10.1007\/978-3-642-17650-0_5"},{"key":"371_CR37","doi-asserted-by":"crossref","unstructured":"Gierlichs B et al (2008) Mutual information analysis. In: Cryptographic hardware and embedded systems (CHES-2008), pp 426\u2013442","DOI":"10.1007\/978-3-540-85053-3_27"},{"key":"371_CR38","unstructured":"Veyrat-Charvillon N, Standaert F (2009) Mutual information analysis: how, when and why? In: Cryptographic hardware and embedded systems (CHES-2009). Springer, Berlin, pp 429\u2013443"},{"issue":"1","key":"371_CR39","doi-asserted-by":"publisher","first-page":"102","DOI":"10.4218\/etrij.10.0109.0249","volume":"32","author":"H Kim","year":"2010","unstructured":"Kim H, Kim TH, Yoon JC, Hong S (2010) Practical second-order correlation power analysis on the message blinding method and its novel countermeasure for RSA. ETRI J 32(1):102\u2013111","journal-title":"ETRI J"},{"key":"371_CR40","doi-asserted-by":"crossref","unstructured":"Okeya K, Sakurai K (2000) Power analysis breaks elliptic curve cryptosystems even secure against the timing attack. In: INDOCRYPT-2000, LNCS, vol 1977. Springer, Berlin, pp 178\u2013190","DOI":"10.1007\/3-540-44495-5_16"}],"container-title":["Innovations in Systems and Software Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11334-020-00371-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11334-020-00371-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11334-020-00371-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T23:25:49Z","timestamp":1628637949000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11334-020-00371-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,11]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["371"],"URL":"https:\/\/doi.org\/10.1007\/s11334-020-00371-6","relation":{},"ISSN":["1614-5046","1614-5054"],"issn-type":[{"type":"print","value":"1614-5046"},{"type":"electronic","value":"1614-5054"}],"subject":[],"published":{"date-parts":[[2020,8,11]]},"assertion":[{"value":"20 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declares that they have no conflict of interests. The article does not have financial or technical support from any other institution or organization.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}