{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:57:55Z","timestamp":1785434275889,"version":"3.56.0"},"reference-count":47,"publisher":"International Association for Cryptologic Research","issue":"3","license":[{"start":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T00:00:00Z","timestamp":1751846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IACR CiC"],"accepted":{"date-parts":[[2025,9,2]]},"abstract":"<jats:p>LightMAC is one of the ISO\/IEC standardized message authentication codes that provably achieves security roughly in the order of O(q^2\/2^n), where q is the total number of queries and n is the block size of the underlying block cipher. In a subsequent work, Naito proposed a beyond-birthday-bound variant of the LightMAC construction, dubbed LightMAC_Plus, and demonstrated that it achieves 2n\/3-bit PRF security. Later in EUROCRYPT'20, Kim et al. improved the security bound of LighMAC_Plus from 2n\/3 bits to 3n\/4 bits. However, all these security results have been proven in the single-user setting, where we assume that the adversary has access to a single instance of the construction. In this paper, we investigate, for the first time, the security of the LightMAC and the LightMAC_Plus constructions in the context of the multi-user setting, where we assume that the adversary has access to more than one instance of the construction. In particular, we have shown that LightMAC offers O(qq_maxl k\/2^n + up\/2^k) multi-user PRF security, where q denotes the total number of construction queries, p denotes the total number of offline primitive queries, q_max denotes the maximum number of queries per user, u denotes the total number of users and l denotes the maximum number of message blocks in a query. We have also shown that LightMAC_Plus maintains security up to approximately 2^2n\/3 construction queries and 2^2k\/3 ideal-cipher queries in the ideal-cipher model, where n denotes the block size and k denotes the key size of the block cipher.<\/jats:p>","DOI":"10.62056\/a0c3tx4e-","type":"journal-article","created":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T18:49:52Z","timestamp":1759776592000},"update-policy":"https:\/\/doi.org\/10.62056\/adfjwm02dj","source":"Crossref","is-referenced-by-count":0,"title":["Multi User Security of LightMAC and LightMAC_Plus"],"prefix":"10.62056","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9761-1192","authenticated-orcid":false,"given":"Nilanjan","family":"Datta","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05h2r8y34","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute for Advancing Intelligence, TCG CREST","place":["Bidhannagar, West Bengal, 700091, India"]},{"id":[{"id":"https:\/\/ror.org\/053rcsq61","id-type":"ROR","asserted-by":"publisher"}],"name":"Academy of Scientific and Innovative Research","place":["Ghaziabad, Uttar Pradesh, 201002, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-9686-0117","authenticated-orcid":false,"given":"Shreya","family":"Dey","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05h2r8y34","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute for Advancing Intelligence, TCG CREST","place":["Bidhannagar, West Bengal, 700091, India"]},{"id":[{"id":"https:\/\/ror.org\/03kp2qt98","id-type":"ROR","asserted-by":"publisher"}],"name":"Ramakrishna Mission Vivekananda Educational and Research Institute","place":["Howrah, West Bengal, 711202, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2672-7331","authenticated-orcid":false,"given":"Avijit","family":"Dutta","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05h2r8y34","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute for Advancing Intelligence, TCG CREST","place":["Bidhannagar, West Bengal, 700091, India"]},{"id":[{"id":"https:\/\/ror.org\/053rcsq61","id-type":"ROR","asserted-by":"publisher"}],"name":"Academy of Scientific and Innovative Research","place":["Ghaziabad, Uttar Pradesh, 201002, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Devdutta","family":"Kanungo","sequence":"additional","affiliation":[{"name":"Price Water Cooperhouse","place":["Bidhannagar, West Bengal, 700091, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"48349","published-online":{"date-parts":[[2025,10,6]]},"reference":[{"key":"ref1:caesar","volume-title":"CAESAR: Competition for Authenticated Encryption: Security,\n  Applicability, and Robustness","year":"2014"},{"key":"ref2:nist","volume-title":"Lightweight Cryptography","author":"NIST","year":"2018"},{"key":"ref3:iso\/iec","volume-title":"Information technology \u2014 lightweight cryptography \u2014 part\n  6: Message authentication codes (MACs). ISO\/IEC 29192-6, International\n  Organization for Standardization (2019)","author":"I.J.S 27","year":"2019"},{"key":"ref4:lyukx","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/978-3-662-52993-5_3","article-title":"A MAC Mode for Lightweight Block Ciphers","volume":"9783","author":"Atul Luykx","year":"2016"},{"key":"ref5:tsudik","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1145\/141809.141812","article-title":"Message authentication with one-way hash functions","volume":"22","author":"Gene Tsudik","year":"1992","journal-title":"Comput. Commun. Rev."},{"key":"ref6:chaskey","first-page":"1182","article-title":"Chaskey: a MAC Algorithm for Microcontrollers - Status\n  Update and Proposal of Chaskey-12 -","author":"Nicky Mouha","year":"2015","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"ref7:pmac","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1007\/3-540-46035-7_25","article-title":"A Block-Cipher Mode of Operation for Parallelizable Message\n  Authentication","volume":"2332","author":"John Black","year":"2002"},{"key":"ref8:omac","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/978-3-540-39887-5_11","article-title":"OMAC: One-Key CBC MAC","volume":"2887","author":"Tetsu Iwata","year":"2003"},{"key":"ref9:cbc","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1006\/JCSS.1999.1694","article-title":"The Security of the Cipher Block Chaining Message\n  Authentication Code","volume":"61","author":"Mihir Bellare","year":"2000","journal-title":"J. Comput. Syst. Sci."},{"key":"ref10:xcbc","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/3-540-44598-6_12","article-title":"CBC MACs for Arbitrary-Length Messages: The Three-Key\n  Constructions","volume":"1880","author":"John Black","year":"2000"},{"key":"ref11:pmac-parity","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/978-3-642-27954-6_13","article-title":"PMAC with Parity: Minimizing the Query-Length Influence","volume":"7178","author":"Kan Yasuda","year":"2012"},{"key":"ref12:pmac3","doi-asserted-by":"publisher","first-page":"125","DOI":"10.13154\/TOSC.V2019.I2.125-145","article-title":"The Exact Security of PMAC with Two Powering-Up Masks","volume":"2019","author":"Yusuke Naito","year":"2019","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"ref13:shen","first-page":"1210","article-title":"LedMAC: More Efficient Variants of LightMAC","author":"Yaobin Shen","year":"2021","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"ref14:soumya","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1007\/978-3-030-92078-4_17","article-title":"Fine-Tuning the ISO\/IEC Standard LightMAC","volume":"13092","author":"Soumya Chattopadhyay","year":"2021"},{"key":"ref15:naito","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1007\/978-3-319-70700-6_16","article-title":"Blockcipher-Based MACs: Beyond the Birthday Bound Without\n  Message Length","volume":"10626","author":"Yusuke Naito","year":"2017"},{"key":"ref16:kim-eurocrypt","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/978-3-030-45721-1_16","article-title":"Tight Security Bounds for Double-Block Hash-then-Sum MACs","volume":"12105","author":"Seongkwang Kim","year":"2020"},{"key":"ref17:naito-ctrsa","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1007\/978-3-319-76953-0_16","article-title":"Improved Security Bound of LightMAC_Plus and Its\n  Single-Key Variant","volume":"10808","author":"Yusuke Naito","year":"2018"},{"key":"ref18:gaetan","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1007\/978-3-319-96884-1_11","article-title":"Generic Attacks Against Beyond-Birthday-Bound MACs","volume":"10991","author":"Ga\u00ebtan Leurent","year":"2018"},{"key":"ref19:dbhts","doi-asserted-by":"publisher","first-page":"36","DOI":"10.13154\/TOSC.V2018.I3.36-92","article-title":"Double-block Hash-then-Sum: A Paradigm for Constructing\n  BBB Secure PRF","volume":"2018","author":"Nilanjan Datta","year":"2018","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"ref20:datta-indocrypt","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1007\/978-3-031-56232-7_4","article-title":"Tight Security Bound of $\\textsf\n  {2k{\\text\n  {-}}LightMAC\\_Plus}$","volume":"14459","author":"Nilanjan Datta","year":"2023"},{"key":"ref21:song","doi-asserted-by":"publisher","first-page":"1818","DOI":"10.3390\/sym13101818","article-title":"A Single-Key Variant of LightMAC_Plus","volume":"13","author":"Haitao Song","year":"2021","journal-title":"Symmetry","ISSN":"https:\/\/id.crossref.org\/issn\/2073-8994","issn-type":"electronic"},{"key":"ref22:datta-amc","doi-asserted-by":"publisher","first-page":"1406","DOI":"10.3934\/AMC.2022100","article-title":"$\\textsf{LightMAC}$: Fork it and\n  make it faster","volume":"18","author":"Nilanjan Datta","year":"2024","journal-title":"Adv. Math. Commun."},{"key":"ref23:aes-gcm1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/978-3-540-30556-9_27","article-title":"The Security and Performance of the Galois\/Counter Mode\n  (GCM) of Operation","volume":"3348","author":"David A. McGrew","year":"2004"},{"key":"ref24:aes-gcm2","volume-title":"NIST Special Publication 800-38D, November 2007. 3, 5, 10","author":"M.Dworkin","year":"2007"},{"key":"ref25:biham","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/S0020-0190(02)00269-7","article-title":"How to decrypt or even substitute DES-encrypted messages in\n  2\\({}^{\\mbox{28}}\\) steps","volume":"84","author":"Eli Biham","year":"2002","journal-title":"Inf. Process. Lett."},{"key":"ref26:bbm","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/3-540-45539-6_18","article-title":"Public-Key Encryption in a Multi-user Setting: Security\n  Proofs and Improvements","volume":"1807","author":"Mihir Bellare","year":"2000"},{"key":"ref27:birukyov","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1007\/11693383_8","article-title":"Improved Time-Memory Trade-Offs with Multiple Data","volume":"3897","author":"Alex Biryukov","year":"2005"},{"key":"ref28:chatterjee","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/978-3-642-28496-0_18","article-title":"Another Look at Tightness","volume":"7118","author":"Sanjit Chatterjee","year":"2011"},{"key":"ref29:bt","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/978-3-662-53018-4_10","article-title":"The Multi-user Security of Authenticated Encryption:\n  AES-GCM in TLS 1.3","volume":"9814","author":"Mihir Bellare","year":"2016"},{"key":"ref30:bellare","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1007\/978-3-662-49890-3_22","article-title":"Hash-Function Based PRFs: AMAC and Its Multi-User\n  Security","volume":"9665","author":"Mihir Bellare","year":"2016"},{"key":"ref31:aes-gcm-siv","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"468","DOI":"10.1007\/978-3-319-78381-9_18","article-title":"Revisiting AES-GCM-SIV: Multi-user Security, Faster Key\n  Derivation, and Better Bounds","volume":"10820","author":"Priyanka Bose","year":"2018"},{"key":"ref32:expectation","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-662-53018-4_1","article-title":"Key-Alternating Ciphers and Key-Length Extension: Exact\n  Bounds and Multi-user Security","volume":"9814","author":"Viet Tung Hoang","year":"2016"},{"key":"ref33:double-enc","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/978-3-319-56614-6_13","article-title":"The Multi-user Security of Double Encryption","volume":"10211","author":"Viet Tung Hoang","year":"2017"},{"key":"ref34:luykx17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1007\/978-3-319-70697-9_20","article-title":"Analyzing Multi-key Security Degradation","volume":"10625","author":"Atul Luykx","year":"2017"},{"key":"ref35:luykx15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/978-3-662-47989-6_10","article-title":"Multi-key Security: The Even-Mansour Construction\n  Revisited","volume":"9215","author":"Nicky Mouha","year":"2015"},{"key":"ref36:andrew","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"724","DOI":"10.1007\/978-3-030-64837-4_24","article-title":"On the Adaptive Security of MACs and PRFs","volume":"12491","author":"Andrew Morgan","year":"2020"},{"key":"ref37:rgcm","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/978-3-662-53018-4_10","article-title":"The Multi-user Security of Authenticated Encryption:\n  AES-GCM in TLS 1.3","volume":"9814","author":"Mihir Bellare","year":"2016"},{"key":"ref38:yaobin","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/978-3-030-84252-9_11","article-title":"Revisiting the Security of DbHtS MACs: Beyond-Birthday-Bound\n  in the Multi-user Setting","volume":"12827","author":"Yaobin Shen","year":"2021"},{"key":"ref39:datta-tosc","doi-asserted-by":"publisher","first-page":"192","DOI":"10.46586\/TOSC.V2023.I1.192-223","article-title":"Tight Multi-User Security Bound of DbHtS","volume":"2023","author":"Nilanjan Datta","year":"2023","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"ref40:yasuda10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1007\/978-3-642-11925-5_25","article-title":"The Sum of CBC MACs Is a Secure PRF","volume":"5985","author":"Kan Yasuda","year":"2010"},{"key":"ref41:yasuda11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1007\/978-3-642-22792-9_34","article-title":"A New Variant of PMAC: Beyond the Birthday Bound","volume":"6841","author":"Kan Yasuda","year":"2011"},{"key":"ref42:zhang12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1007\/978-3-642-34961-4_19","article-title":"3kf9: Enhancing 3GPP-MAC beyond the Birthday Bound","volume":"7658","author":"Liting Zhang","year":"2012"},{"key":"ref43:naito-ctrsa24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/978-3-031-58868-6_3","article-title":"The Multi-user Security of MACs via Universal Hashing in the\n  Ideal Cipher Model","volume":"14643","author":"Yusuke Naito","year":"2024"},{"key":"ref44:duttaec","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/978-3-030-17653-2_15","article-title":"Beyond Birthday Bound Secure MAC in Faulty Nonce Model","volume":"11476","author":"Avijit Dutta","year":"2019"},{"key":"ref45:h-coeff","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1007\/978-3-642-04159-4_21","article-title":"The \"Coefficients H\" Technique","volume":"5381","author":"Jacques Patarin","year":"2008"},{"key":"ref46:nehtmp","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1007\/978-3-030-51938-4_9","article-title":"BBB Secure Nonce Based MAC Using Public Permutations","volume":"12174","author":"Avijit Dutta","year":"2020"},{"key":"ref47:chen22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/978-3-031-22963-3_13","article-title":"A Modular Approach to the Security Analysis of\n  Two-Permutation Constructions","volume":"13791","author":"Yu Long Chen","year":"2022"}],"container-title":["IACR Communications in Cryptology"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T20:23:21Z","timestamp":1759782201000},"score":1,"resource":{"primary":{"URL":"https:\/\/cic.iacr.org\/p\/2\/3\/29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,6]]},"references-count":47,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,10,6]]}},"URL":"https:\/\/doi.org\/10.62056\/a0c3tx4e-","archive":["Internet Archive","Internet Archive"],"relation":{},"ISSN":["3006-5496"],"issn-type":[{"value":"3006-5496","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,6]]},"assertion":[{"value":"2025-07-07","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-02","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"cc2-3-54"}}