{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T17:08:15Z","timestamp":1743008895984,"version":"3.40.3"},"publisher-location":"Cham","reference-count":42,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031803079"},{"type":"electronic","value":"9783031803086"}],"license":[{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-80308-6_1","type":"book-chapter","created":{"date-parts":[[2024,12,12]],"date-time":"2024-12-12T04:56:38Z","timestamp":1733979398000},"page":"3-27","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Efficient Noncommutative NTRU from\u00a0Semidirect Product"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1981-1984","authenticated-orcid":false,"given":"Vikas","family":"Kumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5576-7039","authenticated-orcid":false,"given":"Ali","family":"Raya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aditi Kar","family":"Gangopadhyay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sugata","family":"Gangopadhyay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Md Tarique","family":"Hussain","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,12,13]]},"reference":[{"key":"1_CR1","doi-asserted-by":"publisher","unstructured":"Albrecht, M., Bai, S., Ducas, L.: A subfield lattice attack on overstretched NTRU assumptions. In: Advances in Cryptology \u2013 CRYPTO 2016, pp. 153\u2013178. Springer Berlin Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53018-4_6","DOI":"10.1007\/978-3-662-53018-4_6"},{"key":"1_CR2","unstructured":"Alkim, E., Ducas, L., P\u00f6ppelmann, T., Schwabe, P.: Post-quantum key $$\\{$$Exchange-A$$\\}$$ new hope. In: 25th USENIX Security Symposium (USENIX Security 16), pp. 327\u2013343 (2016). https:\/\/www.usenix.org\/system\/files\/conference\/usenixsecurity16\/sec16_paper_alkim.pdf"},{"key":"1_CR3","doi-asserted-by":"publisher","unstructured":"Aono, Y., Wang, Y., Hayashi, T., Takagi, T.: Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 789\u2013819. Springer (2016).https:\/\/doi.org\/10.1007\/978-3-662-49890-3_30","DOI":"10.1007\/978-3-662-49890-3_30"},{"key":"1_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02579403","volume":"6","author":"L Babai","year":"1986","unstructured":"Babai, L.: On lov\u00e1sz\u2019 lattice reduction and the nearest lattice point problem. Combinatorica 6, 1\u201313 (1986). https:\/\/doi.org\/10.1007\/BF02579403","journal-title":"Combinatorica"},{"key":"1_CR5","doi-asserted-by":"publisher","unstructured":"Bagheri, K., Sadeghi, M.R., Panario, D.: A non-commutative cryptosystem based on quaternion algebras. Des. Codes Crypt. 86, 2345\u20132377 (2018). https:\/\/doi.org\/10.1007\/s10623-017-0451-4","DOI":"10.1007\/s10623-017-0451-4"},{"key":"1_CR6","doi-asserted-by":"publisher","unstructured":"Becker, A., Ducas, L., Gama, N., Laarhoven, T.: New directions in nearest neighbor searching with applications to lattice sieving. In: Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 10\u201324. SIAM (2016). https:\/\/doi.org\/10.1137\/1.9781611974331.ch2","DOI":"10.1137\/1.9781611974331.ch2"},{"key":"1_CR7","doi-asserted-by":"publisher","unstructured":"Bernstein, D.J., Chuengsatiansup, C., Lange, T., van Vredendaal, C.: NTRU Prime: reducing attack surface at low cost. In: Selected Areas in Cryptography \u2013 SAC 2017, pp. 235\u2013260. Springer International Publishing (2018). https:\/\/doi.org\/10.1007\/978-3-319-72565-9_12","DOI":"10.1007\/978-3-319-72565-9_12"},{"key":"1_CR8","doi-asserted-by":"publisher","unstructured":"Bernstein, D.J., Yang, B.Y.: Fast constant-time GCD computation and modular inversion. IACR Trans. Crypt. Hardw. Embed. Syst. 2019(3), 340\u2013398 (2019).https:\/\/doi.org\/10.13154\/tches.v2019.i3.340-398","DOI":"10.13154\/tches.v2019.i3.340-398"},{"key":"1_CR9","unstructured":"Chen, C., et al.: PQC round-3 candidate: NTRU. technical report. Tech. rep., NTRU Cryptosystems Technical Report No.11, Version 2, March 2001. Report (2019). https:\/\/ntru.org\/f\/ntru-20190330.pdf"},{"key":"1_CR10","unstructured":"Chen, C., Hoffstein, J., Whyte, W., Zhang, Z.: NIST PQ submission: NTRUEncrypt a lattice based encryption algorithm. NIST (2017). https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/post-quantum-cryptography-standardization\/round-1-submissions"},{"key":"1_CR11","unstructured":"Chen, Y.: R\u00e9duction de r\u00e9seau et s\u00e9curit\u00e9 concr\u00e8te du chiffrement compl\u00e8tement homomorphe. Ph. D. thesis, l\u2019Universit\u00e9 Paris Diderot (2013). http:\/\/www.theses.fr\/2013PA077242"},{"key":"1_CR12","doi-asserted-by":"publisher","unstructured":"Chen, Y., Nguyen, P.Q.: BKZ 2.0: better lattice security estimates. In: International Conference on the Theory and Application of Cryptology and Information Security, pp. 1\u201320. Springer (2011). https:\/\/doi.org\/10.1007\/978-3-642-25385-0_1","DOI":"10.1007\/978-3-642-25385-0_1"},{"key":"1_CR13","doi-asserted-by":"publisher","unstructured":"Coppersmith, D., Shamir, A.: Lattice attacks on NTRU. In: Advances in Cryptology \u2014 EUROCRYPT \u201997, pp. 52\u201361. Springer Berlin Heidelberg, Berlin, Heidelberg (1997). https:\/\/doi.org\/10.1007\/3-540-69053-0_5","DOI":"10.1007\/3-540-69053-0_5"},{"key":"1_CR14","doi-asserted-by":"publisher","unstructured":"Ducas, L., van Woerden, W.: NTRU fatigue: how stretched is overstretched? In: Advances in Cryptology \u2013 ASIACRYPT 2021, pp. 3\u201332. Springer International Publishing (2021). https:\/\/doi.org\/10.1007\/978-3-030-92068-5_1","DOI":"10.1007\/978-3-030-92068-5_1"},{"key":"1_CR15","unstructured":"Dummit, D.S., Foote, R.M.: Abstract Algebra, 3 edn. Wiley, Inc. (2003). https:\/\/www.wiley.com\/en-in\/Abstract+Algebra%2C+3rd+Edition-p-9780471433347"},{"key":"1_CR16","unstructured":"Fox, N.: Spectra of semidirect products of cyclic groups. Rose-Hulman Undergraduate Math. J. 11 (2010). https:\/\/scholar.rose-hulman.edu\/rhumj\/vol11\/iss2\/7"},{"key":"1_CR17","doi-asserted-by":"publisher","unstructured":"Gentry, C.: Key recovery and message attacks on NTRU-composite. In: Pfitzmann, B. (ed.) Advances in Cryptology \u2014 EUROCRYPT 2001, pp. 182\u2013194. Springer Berlin Heidelberg, Berlin, Heidelberg (2001). https:\/\/doi.org\/10.1007\/3-540-44987-6_12","DOI":"10.1007\/3-540-44987-6_12"},{"key":"1_CR18","volume-title":"An Introduction to Mathematical Cryptography","author":"J Hoffstein","year":"2008","unstructured":"Hoffstein, J., Pipher, J., Silverman, J.: An Introduction to Mathematical Cryptography, 1st edn. Springer Publishing Company, Incorporated, NY (2008)","edition":"1"},{"key":"1_CR19","doi-asserted-by":"publisher","unstructured":"Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: a ring-based public key cryptosystem. In: International Algorithmic Number Theory Symposium, pp. 267\u2013288. Springer, Berlin, Heidelberg (1998). https:\/\/doi.org\/10.1007\/BFb0054868","DOI":"10.1007\/BFb0054868"},{"key":"1_CR20","unstructured":"Hoffstein, J., Silverman, J.H., Whyte, W.: Meet-in-the-middle attack on an NTRU private key. Tech. rep., Technical report, NTRU Cryptosystems, July 2006. Report (2006). https:\/\/ntru.org\/f\/tr\/tr004v2.pdf"},{"key":"1_CR21","doi-asserted-by":"publisher","unstructured":"Howgrave-Graham, N.: A hybrid lattice-reduction and meet-in-the-middle attack against NTRU. In: Advances in Cryptology - CRYPTO 2007, pp. 150\u2013169. Springer Berlin Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-74143-5_9","DOI":"10.1007\/978-3-540-74143-5_9"},{"key":"1_CR22","doi-asserted-by":"publisher","unstructured":"Howgrave-Graham, N., et al.: The impact of decryption failures on the security of NTRU encryption. In: Boneh, D. (ed.) Advances in Cryptology - CRYPTO 2003, pp. 226\u2013246. Springer Berlin Heidelberg, Berlin, Heidelberg (2003). https:\/\/doi.org\/10.1007\/978-3-540-45146-4_14","DOI":"10.1007\/978-3-540-45146-4_14"},{"key":"1_CR23","doi-asserted-by":"publisher","unstructured":"Howgrave-Graham, N., Silverman, J.H., Whyte, W.: Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3. In: Menezes, A. (ed.) Topics in Cryptology \u2013 CT-RSA 2005, pp. 118\u2013135 (2005). https:\/\/doi.org\/10.1007\/978-3-540-30574-3_10","DOI":"10.1007\/978-3-540-30574-3_10"},{"key":"1_CR24","unstructured":"Hurley, T.: Group rings and rings of matrices. Int. J. Pure Appl. Math. 31, 319\u2013335 (2006). https:\/\/www.researchgate.net\/publication\/228928727_Group_rings_and_rings_of_matrices"},{"key":"1_CR25","doi-asserted-by":"publisher","unstructured":"H\u00fclsing, A., Rijneveld, J., Schanck, J., Schwabe, P.: High-speed key encapsulation from NTRU. In: International Conference on Cryptographic Hardware and Embedded Systems, CHES 2017, pp. 232\u2013252 (2017). https:\/\/doi.org\/10.1007\/978-3-319-66787-4_12","DOI":"10.1007\/978-3-319-66787-4_12"},{"key":"1_CR26","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s10623-013-9850-3","volume":"74","author":"K Jarvis","year":"2015","unstructured":"Jarvis, K., Nevins, M.: ETRU: NTRU over the eisenstein integers. Des. Codes Cryptogr. 74, 219\u2013242 (2015). https:\/\/doi.org\/10.1007\/s10623-013-9850-3","journal-title":"Des. Codes Cryptogr."},{"key":"1_CR27","doi-asserted-by":"publisher","first-page":"2779","DOI":"10.1007\/s10623-023-01233-5","volume":"91","author":"J Kim","year":"2023","unstructured":"Kim, J., Lee, C.: A polynomial time algorithm for breaking NTRU encryption with multiple keys. Des. Codes Crypt. 91, 2779\u20132789 (2023). https:\/\/doi.org\/10.1007\/s10623-023-01233-5","journal-title":"Des. Codes Crypt."},{"key":"1_CR28","doi-asserted-by":"publisher","unstructured":"Kirchner, P., Fouque, P.A.: Revisiting lattice attacks on overstretched NTRU parameters. In: Advances in Cryptology \u2013 EUROCRYPT 2017, pp. 3\u201326. Springer International Publishing (2017). https:\/\/doi.org\/10.1007\/978-3-319-56620-7_1","DOI":"10.1007\/978-3-319-56620-7_1"},{"key":"1_CR29","doi-asserted-by":"publisher","unstructured":"Kirshanova, E., May, A., Nowakowski, J.: New NTRU records with improved lattice bases. In: Post-Quantum Cryptography, pp. 167\u2013195 (2023). https:\/\/doi.org\/10.1007\/978-3-031-40003-2_7","DOI":"10.1007\/978-3-031-40003-2_7"},{"key":"1_CR30","unstructured":"Kumar, V., Raya, A., Gangopadhyay, S., Gangopadhyay, A.K.: Lattice attack on group ring NTRU: the case of the dihedral group. arXiv:2309.08304 (2023)"},{"key":"1_CR31","unstructured":"Laarhoven, T.: Search problems in cryptography: from fingerprinting to lattice sieving. Ph. D. thesis, Eindhoven University of Technology (2015). https:\/\/research.tue.nl\/en\/publications\/search-problems-in-cryptography-from-fingerprinting-to-lattice-si"},{"key":"1_CR32","doi-asserted-by":"publisher","unstructured":"Lenstra, A.K., Lenstra, H.W., Lov\u00e1sz, L.: Factoring polynomials with rational coefficients. Mathematische annalen 261(ARTICLE), 515\u2013534 (1982). https:\/\/doi.org\/10.1007\/BF01457454","DOI":"10.1007\/BF01457454"},{"key":"1_CR33","doi-asserted-by":"publisher","unstructured":"Malekian, E., Zakerolhosseini, A.: OTRU: a non-associative and high speed public key cryptosystem. In: 2010 15th CSI International Symposium on Computer Architecture and Digital Systems, pp. 83\u201390 (2010). https:\/\/doi.org\/10.1109\/CADS.2010.5623536","DOI":"10.1109\/CADS.2010.5623536"},{"key":"1_CR34","unstructured":"Malekian, E., Zakerolhosseini, A., Mashatan, A.: QTRU : a lattice attack resistant version of NTRU PKCS based on quaternion algebra. IACR Cryptol. ePrint Archive 386 (2009). https:\/\/eprint.iacr.org\/2009\/386"},{"key":"1_CR35","doi-asserted-by":"publisher","unstructured":"Raya, A., Kumar, V., Gangopadhyay, S.: DiTRU: a resurrection of NTRU over dihedral group. In: Vaudenay, S., Petit, C. (eds.) Progress in Cryptology - AFRICACRYPT 2024, pp. 349\u2013375. Springer Nature Switzerland, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-64381-1_16","DOI":"10.1007\/978-3-031-64381-1_16"},{"issue":"2","key":"1_CR36","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/0304-3975(87)90064-8","volume":"53","author":"C Schnorr","year":"1987","unstructured":"Schnorr, C.: A hierarchy of polynomial time lattice basis reduction algorithms. Theoret. Comput. Sci. 53(2), 201\u2013224 (1987). https:\/\/doi.org\/10.1016\/0304-3975(87)90064-8","journal-title":"Theoret. Comput. Sci."},{"key":"1_CR37","unstructured":"Silverman, J.H.: Almost inverses and fast NTRU key creation. NTRU Cryptosystems Technical Report #14 (1999). https:\/\/ntru.org\/f\/tr\/tr014v1.pdf"},{"key":"1_CR38","doi-asserted-by":"publisher","unstructured":"Stinson, D., Paterson, M.: Cryptography: Theory and Practice, 4 edn. CRC Press, Chapman and Hall Book, Taylor & Francis (2017). https:\/\/doi.org\/10.1201\/9781315282497","DOI":"10.1201\/9781315282497"},{"key":"1_CR39","unstructured":"Thakur, K.: A variant of NTRU with split quaternions algebra. Palestine J. Math. 6(2), 598\u2013610 (2017). https:\/\/pjm.ppu.edu\/sites\/default\/files\/papers\/PJM_April_2017_28.pdf"},{"key":"1_CR40","unstructured":"Truman, K.R.: Analysis and extension of non-commutative NTRU. Ph. D. dissertation, University of Maryland (2007). https:\/\/drum.lib.umd.edu\/handle\/1903\/7344"},{"key":"1_CR41","doi-asserted-by":"publisher","unstructured":"Venier, D., Cheung, R.C.: A highly parallel constant-time almost-inverse algorithm. In: 2020 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), pp.\u00a01\u20136 (2020). https:\/\/doi.org\/10.1109\/ICSPCC50002.2020.9259505","DOI":"10.1109\/ICSPCC50002.2020.9259505"},{"key":"1_CR42","unstructured":"Yasuda, T., Dahan, X., Sakurai, K.: Characterizing NTRU-variants using group ring and evaluating their lattice security. IACR Cryptol. ePrint Arch. 1170 (2015). http:\/\/eprint.iacr.org\/2015\/1170"}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology \u2013 INDOCRYPT 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-80308-6_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,12]],"date-time":"2024-12-12T05:02:44Z","timestamp":1733979764000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-80308-6_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,13]]},"ISBN":["9783031803079","9783031803086"],"references-count":42,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-80308-6_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024,12,13]]},"assertion":[{"value":"13 December 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"INDOCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Cryptology in India","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Chennai","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"India","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 December 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 December 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"indocrypt2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}