{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T07:42:42Z","timestamp":1770882162964,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,6,5]],"date-time":"2015-06-05T00:00:00Z","timestamp":1433462400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2016,8]]},"DOI":"10.1007\/s10623-015-0099-x","type":"journal-article","created":{"date-parts":[[2015,6,4]],"date-time":"2015-06-04T17:09:41Z","timestamp":1433437781000},"page":"359-377","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Squaring attacks on McEliece public-key cryptosystems using quasi-cyclic codes of even dimension"],"prefix":"10.1007","volume":"80","author":[{"given":"Carl","family":"L\u00f6ndahl","sequence":"first","affiliation":[]},{"given":"Thomas","family":"Johansson","sequence":"additional","affiliation":[]},{"given":"Masoumeh","family":"Koochak Shooshtari","sequence":"additional","affiliation":[]},{"given":"Mahmoud","family":"Ahmadian-Attari","sequence":"additional","affiliation":[]},{"given":"Mohammad Reza","family":"Aref","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,6,5]]},"reference":[{"key":"99_CR1","unstructured":"Baldi M.: LDPC codes in the McEliece cryptosystem: attacks and countermeasures. In: NATO Science for Peace and Security Series\u2014D: Information and Communication Security. LNCS, vol. 23 of , pp. 160\u2013174 (2009)."},{"key":"99_CR2","doi-asserted-by":"crossref","unstructured":"Baldi M., Bodrato M., Chiaraluce F.: A new analysis of the McEliece cryptosystem based on QC\u2013LDPC codes. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) 6th International Conference on Security and Cryptography for Networks (SCN 2008). LNCS, vol. 5229, pp. 246\u2013262. Springer, Berlin (2008).","DOI":"10.1007\/978-3-540-85855-3_17"},{"key":"99_CR3","doi-asserted-by":"crossref","unstructured":"Baldi M., Bambozzi F., Chiaraluce F.: On a family of circulant matrices for quasi-cyclic low-density generator matrix codes. IEEE Trans. Inf. Theory 57(9), 6052\u20136067 (2011).","DOI":"10.1109\/TIT.2011.2161953"},{"key":"99_CR4","doi-asserted-by":"crossref","unstructured":"Baldi M., Bianchi M., Chiaraluce F.: Security and complexity of the McEliece cryptosystem based on quasi-cyclic low-density parity-check codes. IET Inf. Secur. 7(3), 212\u2013220 (2013).","DOI":"10.1049\/iet-ifs.2012.0127"},{"key":"99_CR5","doi-asserted-by":"crossref","unstructured":"Baldi M., Bianchi M., Chiaraluce F.: Optimization of the parity-check matrix density in QC\u2013LDPC code-based McEliece cryptosystems. In: Workshop on Information Security Over Noisy and Lossy Communication Systems (IEEE ICC 2013) (2013).","DOI":"10.1109\/ICCW.2013.6649325"},{"key":"99_CR6","doi-asserted-by":"crossref","unstructured":"Baldi M., Chiaraluce F., Garello R., Mininni F.: Quasi-cyclic low-density parity-check codes in the McEliece cryptosystem. In: Proceedings of IEEE International Conference on Communications (ICC 2007), pp. 951\u2013956 (2007).","DOI":"10.1109\/ICC.2007.161"},{"key":"99_CR7","doi-asserted-by":"crossref","unstructured":"Becker A., Joux A., May A., Meurer A.: Decoding random binary linear codes in $$2^{n\/20}$$ 2 n \/ 20 : How 1 + 1 = 0 improves information set decoding. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 520\u2013536. Springer, Berlin (2012).","DOI":"10.1007\/978-3-642-29011-4_31"},{"key":"99_CR8","doi-asserted-by":"crossref","unstructured":"Bernstein D.J., Lange T., Peters C.: Attacking and defending the McEliece cryptosystem. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299. pp. 31\u201346. Springer, Berlin (2008).","DOI":"10.1007\/978-3-540-88403-3_3"},{"key":"99_CR9","doi-asserted-by":"crossref","unstructured":"Dumer I., Micciancio D., Sudan M.: Hardness of approximating the minimum distance of a linear code. IEEE Trans. Inf. Theory 49(1):22\u201337 (2007).","DOI":"10.1109\/TIT.2002.806118"},{"key":"99_CR10","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re J.C., Otmani A., Perret L., Tillich J-P.: Algebraic cryptanalysis of McEliece variants with compact keys. In: Gilbert, H. (eds.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 279\u2013298. Springer, Berlin (2010).","DOI":"10.1007\/978-3-642-13190-5_14"},{"key":"99_CR11","unstructured":"Gaborit P.: Shorter keys for code based cryptography. In: International Workshop on Coding and Cryptography. LNCS, vol. 6110, pp. 81\u201391 (2005)."},{"key":"99_CR12","doi-asserted-by":"crossref","unstructured":"Heyse S., von Maurich I., G\u00fcneysu T.: Smaller keys for code-based cryptography: QC-MDPC McEliece implementations on embedded devices. In: Bertoni, G., Coron, J. (eds.) CHES 2013. LNCS, vol. 8086, pp. 273\u2013292. Springer, Berlin (2013).","DOI":"10.1007\/978-3-642-40349-1_16"},{"key":"99_CR13","unstructured":"Johansson T., L\u00f6ndahl C.: An improvement to Stern\u2019s algorithm, internal report. http:\/\/lup.lub.lu.se\/record\/2204753 (2011)."},{"key":"99_CR14","unstructured":"Koochak Shooshtari M., Ahmadian M., Payandeh A.: Improving the security of McEliece-like public key cryptosystem based on LDPC codes. In: Proceedings of the 11th International Conference on Advanced Communication Technology (ICACT\u201909), pp. 1050\u20131053. IEEE Press, New York (2009)."},{"key":"99_CR15","unstructured":"L\u00f6ndahl C.: Some notes on code-based cryptography, PhD thesis, Lund University. http:\/\/lup.lub.lu.se\/record\/4934002 (2014)."},{"key":"99_CR16","doi-asserted-by":"crossref","unstructured":"L\u00f6ndahl C., Johansson T.: A new version of McEliece PKC based on convolutional codes. In: Information and Communications Security. LNCS, vol. 7618, pp. 461\u2013470. Springer, Berlin (2012).","DOI":"10.1007\/978-3-642-34129-8_45"},{"key":"99_CR17","doi-asserted-by":"crossref","unstructured":"L\u00f6ndahl C., Johansson T.: Improved algorithms for finding low-weight polynomial multiples in $${\\mathbb{F}}_{2}^{}[x]$$ F 2 [ x ] and some cryptographic applications. Des. Codes Cryptogr. 73(2), 625\u2013640 (2014).","DOI":"10.1007\/s10623-014-9960-6"},{"key":"99_CR18","doi-asserted-by":"crossref","unstructured":"May A., Meurer A., Thomae E.: Decoding random linear codes in $$\\tilde{O}({2^{0.054n}})$$ O ~ ( 2 0.054 n ) . In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 107\u2013124. Springer, Berlin (2011).","DOI":"10.1007\/978-3-642-25385-0_6"},{"key":"99_CR19","unstructured":"McEliece R.J.: A public-key cryptosystem based on algebraic coding theory. DSN Prog. Rep. 42(44), 114\u2013116 (1978)."},{"key":"99_CR20","doi-asserted-by":"crossref","unstructured":"Misoczki R., Tillich J-P., Sendrier N., Barreto P.S.L.M.: MDPC-McEliece: new McEliece variants from moderate density parity-check codes ePrint archive 2012\/409 (2013).","DOI":"10.1109\/ISIT.2013.6620590"},{"key":"99_CR21","doi-asserted-by":"crossref","unstructured":"Misoczki R., Tillich J-P., Sendrier N., Barreto P.S.L.M.: MDPC-McEliece: new McEliece variants from moderate density parity-check codes. In: IEEE International Symposium on Information Theory (ISIT\u20192013), pp. 2069\u20132073 (2013).","DOI":"10.1109\/ISIT.2013.6620590"},{"key":"99_CR22","doi-asserted-by":"crossref","unstructured":"Monico C., Rosenthal J., Shokrollahi A.: Using low density parity check codes in the McEliece cryptosystem. In: IEEE International Symposium on Information Theory (ISIT\u20192000), p. 215 (2000).","DOI":"10.1109\/ISIT.2000.866513"},{"key":"99_CR23","doi-asserted-by":"crossref","unstructured":"Sendrier N.: Decoding one out of many. In Yang, B. (eds.) Post-Quantum Cryptography. LNCS, vol. 7071, pp. 51\u201367. Springer, Berlin (2011).","DOI":"10.1007\/978-3-642-25405-5_4"},{"key":"99_CR24","doi-asserted-by":"crossref","unstructured":"Shor P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 35th Annual Symposium on Foundations of Computer Science, 20\u201322 Nov 1994, Santa Fe, pp. 124\u2013134. IEEE Press, New York (1994).","DOI":"10.1109\/SFCS.1994.365700"},{"key":"99_CR25","doi-asserted-by":"crossref","unstructured":"Sidelnikov V.M., Shestakov S.O.: On the insecurity of cryptosystems based on generalized Reed\u2013Solomon codes. Discret. Math. Appl. 2(4), 439\u2013444 (1992).","DOI":"10.1515\/dma.1992.2.4.439"},{"key":"99_CR26","doi-asserted-by":"crossref","unstructured":"Stern J.: A method for finding codewords of small weight. In: Wolfmann, J., Cohen, G.D. (eds.) Coding Theory and Applications. LNCS, vol. 388, pp. 106\u2013113. Springer, Berlin (1989).","DOI":"10.1007\/BFb0019850"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-015-0099-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-015-0099-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-015-0099-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T04:35:51Z","timestamp":1566794151000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-015-0099-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,5]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["99"],"URL":"https:\/\/doi.org\/10.1007\/s10623-015-0099-x","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,5]]}}}