{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T15:04:43Z","timestamp":1772809483732,"version":"3.50.1"},"reference-count":37,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AMC"],"published-print":{"date-parts":[[2019]]},"DOI":"10.3934\/amc.2019040","type":"journal-article","created":{"date-parts":[[2019,6,21]],"date-time":"2019-06-21T23:53:48Z","timestamp":1561161228000},"page":"645-688","source":"Crossref","is-referenced-by-count":2,"title":["Another look at success probability of linear cryptanalysis"],"prefix":"10.3934","volume":"13","author":[{"given":"Subhabrata","family":"Samajder","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Palash","family":"Sarkar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2019040-1","unstructured":"

T. Ashur, T. Beyne and V. Rijmen, Revisiting the wrong-key-randomization hypothesis, IACR Cryptology ePrint Archive<\/i>, 2016<\/b> (2016), 990, Available at http:\/\/eprint.iacr.org\/2016\/990<\/a>.<\/p>"},{"key":"key-10.3934\/amc.2019040-2","doi-asserted-by":"crossref","unstructured":"

T. Baign\u00e8res, P. Junod and S. Vaudenay, How far can we go beyond linear cryptanalysis?, In Pil Joong Lee, editor, Advances in Cryptology - ASIACRYPT 2004, 10th International Conference on the Theory and Application of Cryptology and Information Security, Jeju Island, Korea, December 5-9, 2004, Proceedings<\/i>, volume 3329 of Lecture Notes in Computer Science<\/i>, 432\u2013450. Springer, 2004. ISBN: 3-540-23975-8.<\/p>","DOI":"10.1007\/978-3-540-30539-2_31"},{"key":"key-10.3934\/amc.2019040-3","unstructured":"

T. Baign\u00e8res, P. Sepehrdad and S. Vaudenay, Distinguishing distributions using chernoff information, In Swee-Huay Heng and Kaoru Kurosawa, editors, Provable Security - 4th International Conference, ProvSec 2010, Malacca, Malaysia, October 13-15, 2010. Proceedings<\/i>, volume 6402 of Lecture Notes in Computer Science<\/i>, pages 144\u2013165. Springer, 2010. ISBN: 978-3-642-16279-4.<\/p>"},{"key":"key-10.3934\/amc.2019040-4","doi-asserted-by":"crossref","unstructured":"

A. Biryukov, C. De Canni\u00e8re and M. Quisquater, On multiple linear approximations, Advances in cryptology\u2013CRYPTO 2004, <\/i> Lecture Notes in Comput. Sci., Springer, Berlin, 3152<\/b> (2004), 1\u201322.<\/p>","DOI":"10.1007\/978-3-540-28628-8_1"},{"key":"key-10.3934\/amc.2019040-5","doi-asserted-by":"crossref","unstructured":"

C. Blondeau, B. G\u00e9rard and K. Nyberg, Multiple differential cryptanalysis using LLR and $\\chi^{2}$<\/tex-math><\/inline-formula> statistics, Security and Cryptography for Networks, <\/i> 343\u2013360, Lecture Notes in Comput. Sci., 7485, Springer, Heidelberg, 2012.<\/p>","DOI":"10.1007\/978-3-642-32928-9_19"},{"key":"key-10.3934\/amc.2019040-6","doi-asserted-by":"crossref","unstructured":"

C. Blondeau and M. Minier, Analysis of impossible, integral and zero-correlation attacks on type-ii generalized feistel networks using the matrix method, Fast Software Encryption - 22nd International Workshop, FSE 2015, Istanbul, Turkey, March 8-11, 2015, Revised Selected Papers<\/i>, Lecture Notes in Computer Science<\/i>, Springer, 9054<\/b> (2015), 92\u2013113.<\/p>","DOI":"10.1007\/978-3-662-48116-5_5"},{"key":"key-10.3934\/amc.2019040-7","doi-asserted-by":"crossref","unstructured":"

C. Blondeau and K. Nyberg, Improved parameter estimates for correlation and capacity deviates in linear cryptanalysis, IACR Transactions Symmetric Cryptology<\/i>, 2016<\/b> (2016), 162\u2013191. https:\/\/www.doi.org\/10.13154\/tosc.v2016.i2.162-191<\/a>.<\/p>","DOI":"10.46586\/tosc.v2016.i2.162-191"},{"key":"key-10.3934\/amc.2019040-8","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-016-0268-6"},{"key":"key-10.3934\/amc.2019040-9","unstructured":"

A. Bogdanov, H. Geng, M. Wang, L. Wen and B. Collard, Zero-correlation linear cryptanalysis with fft and improved attacks on iso standards camellia and CLEFIA, In Tanja Lange, Kristin E. Lauter, and Petr Lisonek, editors, Selected Areas in Cryptography - SAC 2013 - 20th International Conference, Burnaby, BC, Canada, August 14-16, 2013, Revised Selected Papers<\/i>, volume 8282 of Lecture Notes in Computer Science<\/i>, Springer, (2014), 306\u2013323. https:\/\/www.doi.org\/10.1007\/978-3-662-43414-7_16<\/a>, ISBN: 978-3-662-43413-0.<\/p>"},{"key":"key-10.3934\/amc.2019040-10","unstructured":"

A. Bogdanov, G. Leander, K. Nyberg and M. Wang, Integral and multidimensional linear distinguishers with correlation zero, In Xiaoyun Wang and Kazue Sako, editors, Advances in Cryptology - ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Beijing, China, December 2-6, 2012. Proceedings<\/i>, volume 7658 of Lecture Notes in Computer Science<\/i>, pages 244\u2013261. Springer, 2012. ISBN: 978-3-642-34960-7.<\/p>"},{"key":"key-10.3934\/amc.2019040-11","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-012-9697-z"},{"key":"key-10.3934\/amc.2019040-12","doi-asserted-by":"crossref","unstructured":"

A. Bogdanov and E. Tischhauser, On the wrong key randomisation and key equivalence hypotheses in matsui's algorithm 2, In Shiho Moriai, editor, Fast Software Encryption - 20th International Workshop, FSE 2013, Singapore, March 11-13, 2013. Revised Selected Papers<\/i>, volume 8424 of Lecture Notes in Computer Science<\/i>, pages 19\u201338. Springer, 2014. ISBN: 978-3-662-43932-6.<\/p>","DOI":"10.1007\/978-3-662-43933-3_2"},{"key":"key-10.3934\/amc.2019040-13","unstructured":"

A. Bogdanov and M. Wang, Zero correlation linear cryptanalysis with reduced data complexity, In Anne Canteaut, editor, Fast Software Encryption - 19th International Workshop, FSE 2012, Washington, DC, USA, March 19-21, 2012. Revised Selected Papers<\/i>, volume 7549 of Lecture Notes in Computer Science<\/i>, pages 29\u201348. Springer, 2012. ISBN: 978-3-642-34046-8.<\/p>"},{"key":"key-10.3934\/amc.2019040-14","unstructured":"

J. Daemen and V. Rijmen, Probability distributions of correlation and differentials in block ciphers, IACR Cryptology ePrint Archive<\/i>, 2005: 212, 2005. Available at http:\/\/eprint.iacr.org\/2005\/212<\/a>.<\/p>"},{"key":"key-10.3934\/amc.2019040-15","doi-asserted-by":"publisher","DOI":"10.1515\/JMC.2007.011"},{"key":"key-10.3934\/amc.2019040-16","unstructured":"

W. Feller, An Introduction to Probability Theory and Its Applications, Volume 1<\/i>, John Wiley & Sons, Inc., New York, N.Y., 1950.<\/p>"},{"key":"key-10.3934\/amc.2019040-17","doi-asserted-by":"crossref","unstructured":"

B. G\u00e9rard and J.-P. Tillich, On linear cryptanalysis with many linear approximations, In Matthew G. Parker, editor, Cryptography and Coding, 12th IMA International Conference, Cryptography and Coding 2009, Cirencester, UK, December 15-17, 2009. Proceedings<\/i>, volume 5921 of Lecture Notes in Computer Science<\/i>, 112\u2013132. Springer, 2009.<\/p>","DOI":"10.1007\/978-3-642-10868-6_8"},{"key":"key-10.3934\/amc.2019040-18","unstructured":"

C. Harpes, G. G. Kramer and J. L. Massey, A generalization of linear cryptanalysis and the applicability of matsui's piling-up lemma, In Louis C. Guillou and Jean-Jacques Quisquater, editors, Advances in Cryptology - EUROCRYPT '95, International Conference on the Theory and Application of Cryptographic Techniques, Saint-Malo, France, May 21-25, 1995, Proceeding<\/i>, volume 921 of Lecture Notes in Computer Science<\/i>, 24\u201338. Springer, 1995. https:\/\/www.doi.org\/10.1007\/3-540-49264-X_3<\/a>.<\/p>"},{"key":"key-10.3934\/amc.2019040-19","unstructured":"

M. Hermelin, J. Y. Cho and K. Nyberg, Multidimensional extension of matsui's algorithm 2, In Fast Software Encryption, 16th International Workshop, FSE 2009, Leuven, Belgium, February 22-25, 2009, Revised Selected Papers<\/i>, volume 5665 of Lecture Notes in Computer Science<\/i>, 209\u2013227. Springer, 2009.<\/p>"},{"key":"key-10.3934\/amc.2019040-20","doi-asserted-by":"crossref","unstructured":"

J. Huang, S. Vaudenay, X. Lai and K. Nyberg, Capacity and data complexity in multidimensional linear attack, In Rosario Gennaro and Matthew Robshaw, editors, Advances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part I<\/i>, volume 9215 of Lecture Notes in Computer Science<\/i>, 141\u2013160, Springer, 2015.<\/p>","DOI":"10.1007\/978-3-662-47989-6_7"},{"key":"key-10.3934\/amc.2019040-21","doi-asserted-by":"crossref","unstructured":"

B. S. Kaliski Jr. and M. J. B. Robshaw, Linear cryptanalysis using multiple approximations, In Yvo Desmedt, editor, Advances in Cryptology - CRYPTO '94, 14th Annual International Cryptology Conference, Santa Barbara, California, USA, August 21-25, 1994, Proceedings<\/i>, volume 839 of Lecture Notes in Computer Science<\/i>, 26\u201339, Springer, 1994.<\/p>","DOI":"10.1007\/3-540-48658-5_4"},{"key":"key-10.3934\/amc.2019040-22","unstructured":"

P. Junod, On the complexity of matsui's attack, In Serge Vaudenay and Amr M. Youssef, editors, Selected Areas in Cryptography, 8th Annual International Workshop, SAC 2001 Toronto, Ontario, Canada, August 16-17, 2001, Revised Papers<\/i>, volume 2259 of Lecture Notes in Computer Science<\/i>, 199\u2013211, Springer, 2001.<\/p>"},{"key":"key-10.3934\/amc.2019040-23","doi-asserted-by":"crossref","unstructured":"

P. Junod, On the optimality of linear, differential, and sequential distinguishers, In Eli Biham, editor, Advances in Cryptology - EUROCRYPT 2003, International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, May 4-8, 2003, Proceedings<\/i>, volume 2656 of Lecture Notes in Computer Science<\/i>, 17\u201332, Springer, 2003.<\/p>","DOI":"10.1007\/3-540-39200-9_2"},{"key":"key-10.3934\/amc.2019040-24","doi-asserted-by":"crossref","unstructured":"

P. Junod and S. Vaudenay, Optimal key ranking procedures in a statistical cryptanalysis, In Thomas Johansson, editor, Fast Software Encryption, 10th International Workshop, FSE 2003, Lund, Sweden, February 24-26, 2003, Revised Papers<\/i>, volume 2887 of Lecture Notes in Computer Science<\/i>, 235\u2013246, Springer, 2003.<\/p>","DOI":"10.1007\/978-3-540-39887-5_18"},{"key":"key-10.3934\/amc.2019040-25","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-07-08676-5"},{"key":"key-10.3934\/amc.2019040-26","unstructured":"

M. Matsui, Linear cryptanalysis method for des cipher, In Tor Helleseth, editor, Advances in Cryptology - EUROCRYPT '93, Workshop on the Theory and Application of of Cryptographic Techniques, Lofthus, Norway, May 23-27, 1993, Proceedings<\/i>, volume 765 of Lecture Notes in Computer Science<\/i>, 386\u2013397, Springer, 1994. https:\/\/www.doi.org\/10.1007\/3-540-48285-7_33<\/a>.<\/p>"},{"key":"key-10.3934\/amc.2019040-27","unstructured":"

M. Matsui, The first experimental cryptanalysis of the data encryption standard, In Yvo Desmedt, editor, Advances in Cryptology - CRYPTO '94, 14th Annual International Cryptology Conference, Santa Barbara, California, USA, August 21-25, 1994, Proceedings<\/i>, volume 839 of Lecture Notes in Computer Science<\/i>, 1\u201311, Springer, 1994. https:\/\/www.doi.org\/10.1007\/3-540-48658-5_1<\/a>.<\/p>"},{"key":"key-10.3934\/amc.2019040-28","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.885528"},{"key":"key-10.3934\/amc.2019040-29","doi-asserted-by":"publisher","DOI":"10.1515\/jmc-2016-0006"},{"key":"key-10.3934\/amc.2019040-30","unstructured":"

S. Samajder and P. Sarkar, A new test statistic for key recovery attacks using multiple linear approximations, In Raphael C.-W. Phan and Moti Yung, editors, Paradigms in Cryptology - Mycrypt 2016. Malicious and Exploratory Cryptology - Second International Conference, Mycrypt 2016, Kuala Lumpur, Malaysia, December 1-2, 2016, Revised Selected Papers<\/i>, volume 10311 of Lecture Notes in Computer Science<\/i>, 277\u2013293, Springer, 2017, https:\/\/www.doi.org\/10.1007\/978-3-319-61273-7_14<\/a>.<\/p>"},{"key":"key-10.3934\/amc.2019040-31","doi-asserted-by":"publisher","DOI":"10.1515\/jmc-2016-0026"},{"key":"key-10.3934\/amc.2019040-32","doi-asserted-by":"publisher","DOI":"10.1007\/s12095-017-0257-2"},{"key":"key-10.3934\/amc.2019040-33","doi-asserted-by":"publisher","DOI":"10.1007\/s00145-007-9013-7"},{"key":"key-10.3934\/amc.2019040-34","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-014-9976-y"},{"key":"key-10.3934\/amc.2019040-35","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-017-0430-9"},{"key":"key-10.3934\/amc.2019040-36","unstructured":"

E. W. Tischhauser, Mathematical Aspects of Symmetric-Key Cryptography<\/i>, PhD thesis, Katholieke Universiteit Leuven, 2012.<\/p>"},{"key":"key-10.3934\/amc.2019040-37","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1968.tb00757.x"}],"container-title":["Advances in Mathematics of Communications"],"original-title":[],"deposited":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T10:08:20Z","timestamp":1772791700000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.aimsciences.org\/\/article\/doi\/10.3934\/amc.2019040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019]]}},"URL":"https:\/\/doi.org\/10.3934\/amc.2019040","relation":{},"ISSN":["1930-5346","1930-5338"],"issn-type":[{"value":"1930-5346","type":"print"},{"value":"1930-5338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]}}}