{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:40:20Z","timestamp":1764981620124,"version":"3.46.0"},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2020,12,20]],"date-time":"2020-12-20T00:00:00Z","timestamp":1608422400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,12,20]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>ElGamal cryptosystem has emerged as one of the most important construction in Public Key Cryptography (PKC) since Diffie-Hellman key exchange protocol was proposed. However, public key schemes which are based on number theoretic problems such as discrete logarithm problem (DLP) are at risk because of the evolution of quantum computers. As a result, other non-number theoretic alternatives are a dire need of entire cryptographic community.<\/jats:p>\n                  <jats:p>In 2016, Saba Inam and Rashid Ali proposed a ElGamal-like cryptosystem based on matrices over group rings in \u2018Neural Computing &amp; Applications\u2019. Using linear algebra approach, Jia et al. provided a cryptanalysis for the cryptosystem in 2019 and claimed that their attack could recover all the equivalent keys. However, this is not the case and we have improved their cryptanalysis approach and derived all equivalent key pairs that can be used to totally break the ElGamal-like cryptosystem proposed by Saba and Rashid. Using the decomposition of matrices over group rings to larger size matrices over rings, we have made the cryptanalysing algorithm more practical and efficient. We have also proved that the ElGamal cryptosystem proposed by Saba and Rashid does not achieve the security of IND-CPA and IND-CCA.<\/jats:p>","DOI":"10.1515\/jmc-2019-0054","type":"journal-article","created":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T09:48:59Z","timestamp":1608630539000},"page":"266-279","source":"Crossref","is-referenced-by-count":4,"title":["Improved cryptanalysis of a ElGamal Cryptosystem Based on Matrices Over Group Rings"],"prefix":"10.1515","volume":"15","author":[{"given":"Atul","family":"Pandey","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Delhi , Delhi - , India"}]},{"given":"Indivar","family":"Gupta","sequence":"additional","affiliation":[{"name":"SAG, Metcalfe House, DRDO Complex , Delhi - , India"}]},{"given":"Dhiraj","family":"Kumar Singh","sequence":"additional","affiliation":[{"name":"Zakir Husain College, University of Delhi , Delhi - , India"}]}],"member":"374","published-online":{"date-parts":[[2020,12,20]]},"reference":[{"unstructured":"P. J. Davis, Circulant matrices Chelsea (1994).","key":"2025120600333851232_j_jmc-2019-0054_ref_001"},{"doi-asserted-by":"crossref","unstructured":"T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms IEEE Trans Inf Theory 31, (1985), 469\u2013472.","key":"2025120600333851232_j_jmc-2019-0054_ref_002","DOI":"10.1109\/TIT.1985.1057074"},{"doi-asserted-by":"crossref","unstructured":"S. Inam and R. Ali, A new ElGamal-like cryptosystem based on matrices over group ring Neural Comput. Appl. 29(11), (2018), 1279\u20131283.","key":"2025120600333851232_j_jmc-2019-0054_ref_003","DOI":"10.1007\/s00521-016-2745-2"},{"doi-asserted-by":"crossref","unstructured":"J. Jia, J. Liu and H. Zhang, Cryptanalysis of cryptosystems based on general linear group China Commun. 13(6), (2016), 217\u2013224.","key":"2025120600333851232_j_jmc-2019-0054_ref_004","DOI":"10.1109\/CC.2016.7513216"},{"doi-asserted-by":"crossref","unstructured":"J. Jia, H. Wang, H. Zhang, S. Wang and J. Liu, Cryptanalysis of an ElGamal-Like Cryptosystem Based on Matrices Over Group Rings In: Zhang H., Zhao B., Yan F. (eds) Trusted Computing and Information Security. CTCIS 2018. Communications in Computer and Information Science, vol 960. Springer, Singapore (2019).","key":"2025120600333851232_j_jmc-2019-0054_ref_005","DOI":"10.1007\/978-981-13-5913-2_16"},{"doi-asserted-by":"crossref","unstructured":"M. Khan and T. Shah, A novel cryptosystem based on general linear group 3D Res. 6(1), (2015), 1\u20138.","key":"2025120600333851232_j_jmc-2019-0054_ref_006","DOI":"10.1007\/s13319-014-0035-2"},{"doi-asserted-by":"crossref","unstructured":"N. Koblitz, A course in Number Theory and Cryptography 2nd edn. springer, New York (1994).","key":"2025120600333851232_j_jmc-2019-0054_ref_007","DOI":"10.1007\/978-1-4419-8592-7"},{"doi-asserted-by":"crossref","unstructured":"M. Kreuzer, A. D. Myasnikov and A. Ushakov, A linear algebra attack to group-ring-based key exchange protocols Applied Cryptography and Network Security (ACNS 2014), Lecture Notes in Comput. Sci. 8479, Springer, Berlin, (2014), 37\u201343.","key":"2025120600333851232_j_jmc-2019-0054_ref_008","DOI":"10.1007\/978-3-319-07536-5_3"},{"doi-asserted-by":"crossref","unstructured":"A. D. Myasnikov and A. Ushakov: Quantum algorithm for the discrete logarithm problem for matrices over finite group rings Groups, Complexity, Cryptology 6, (2014), 31\u201336.","key":"2025120600333851232_j_jmc-2019-0054_ref_009","DOI":"10.1515\/gcc-2014-0003"},{"unstructured":"D. S. Passman, The Algebraic structure of Group Ring Wiley, New York (1977).","key":"2025120600333851232_j_jmc-2019-0054_ref_010"},{"doi-asserted-by":"crossref","unstructured":"A. Storjohann and T. Mulders, Fast algorithms for linear algebra modulo N Proceedings of Algorithms\u2014ESA\u201998. Springer Berlin Heidelberg, 1461, (1998), 139-150.","key":"2025120600333851232_j_jmc-2019-0054_ref_011","DOI":"10.1007\/3-540-68530-8_12"}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/jmc\/15\/1\/article-p266.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2019-0054\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2019-0054\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:35:19Z","timestamp":1764981319000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2019-0054\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,20]]},"references-count":11,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,4,20]]},"published-print":{"date-parts":[[2021,4,20]]}},"alternative-id":["10.1515\/jmc-2019-0054"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2019-0054","relation":{},"ISSN":["1862-2984"],"issn-type":[{"type":"electronic","value":"1862-2984"}],"subject":[],"published":{"date-parts":[[2020,12,20]]}}}