Enhancing the MILP/MIQCP-Based Automatic Search for Differential-Linear Distinguishers of IoT-Friendly Block Ciphers Simon and Simeck
<inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula> are two famous lightweight block cipher families,...
Uložené v:
| Vydané v: | IEEE internet of things journal Ročník 12; číslo 5; s. 5655 - 5671 |
|---|---|
| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Piscataway
IEEE
01.03.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Predmet: | |
| ISSN: | 2327-4662, 2327-4662 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | <inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula> are two famous lightweight block cipher families, both of which have good implementation performance benefiting from their extremely simple round functions. So, they are suitable and friendly in use for the Internet of Things devices that require high security but low-latency and low-energy. In this article, we aim to improve the mixed-integer linear programming/mixed-integer quadratic constraint programming (MILP/MIQCP)-based method, to find better differential-linear (DL) distinguishers for the above ciphers, which can be exploited to mount distinguishing or key-recovery attacks. In particular, first, we give the completely precise mixed-integer linear programming (MILP) model to describe the linear part, and utilize the general expressions of <inline-formula> <tex-math notation="LaTeX">\textsf {Gurobi} </tex-math></inline-formula> optimizer to model middle part in a quite easy way. Second, to explore DL trails in a reasonable time, we propose two heuristic strategies to speed up the searching process. Lastly, we introduce the transforming technique, which exploits the clustering effect on DL trails, to improve the estimated correlation of the DL approximation. By applying our enhanced method, we improve the DL distinguisher correlation from <inline-formula> <tex-math notation="LaTeX">2^{-59.75} </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">2^{-59.62} </tex-math></inline-formula> for 32-round <inline-formula> <tex-math notation="LaTeX">\textsf {Simon128} </tex-math></inline-formula>, and extend the number of longest rounds of valid DL distinguishers for <inline-formula> <tex-math notation="LaTeX">\textsf {Simon32/48/64/96} </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">11/16/16/25 </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">14/17/21/26 </tex-math></inline-formula>. For <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula>, we do not outperform the currently best work, but refresh Zhou et al.'s results (the first work to automate finding DL distinguishers for <inline-formula> <tex-math notation="LaTeX">\textsf {Simon/Simeck} </tex-math></inline-formula> using MILP/MIQCP). Our work not only provides a new insight on the automatic DL cryptanalysis, but also further confirms that <inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula> are sufficiently strong to resist the DL attacks. |
|---|---|
| AbstractList | <inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula> are two famous lightweight block cipher families, both of which have good implementation performance benefiting from their extremely simple round functions. So, they are suitable and friendly in use for the Internet of Things devices that require high security but low-latency and low-energy. In this article, we aim to improve the mixed-integer linear programming/mixed-integer quadratic constraint programming (MILP/MIQCP)-based method, to find better differential-linear (DL) distinguishers for the above ciphers, which can be exploited to mount distinguishing or key-recovery attacks. In particular, first, we give the completely precise mixed-integer linear programming (MILP) model to describe the linear part, and utilize the general expressions of <inline-formula> <tex-math notation="LaTeX">\textsf {Gurobi} </tex-math></inline-formula> optimizer to model middle part in a quite easy way. Second, to explore DL trails in a reasonable time, we propose two heuristic strategies to speed up the searching process. Lastly, we introduce the transforming technique, which exploits the clustering effect on DL trails, to improve the estimated correlation of the DL approximation. By applying our enhanced method, we improve the DL distinguisher correlation from <inline-formula> <tex-math notation="LaTeX">2^{-59.75} </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">2^{-59.62} </tex-math></inline-formula> for 32-round <inline-formula> <tex-math notation="LaTeX">\textsf {Simon128} </tex-math></inline-formula>, and extend the number of longest rounds of valid DL distinguishers for <inline-formula> <tex-math notation="LaTeX">\textsf {Simon32/48/64/96} </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">11/16/16/25 </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">14/17/21/26 </tex-math></inline-formula>. For <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula>, we do not outperform the currently best work, but refresh Zhou et al.'s results (the first work to automate finding DL distinguishers for <inline-formula> <tex-math notation="LaTeX">\textsf {Simon/Simeck} </tex-math></inline-formula> using MILP/MIQCP). Our work not only provides a new insight on the automatic DL cryptanalysis, but also further confirms that <inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula> are sufficiently strong to resist the DL attacks. [Formula Omitted] and [Formula Omitted] are two famous lightweight block cipher families, both of which have good implementation performance benefiting from their extremely simple round functions. So, they are suitable and friendly in use for the Internet of Things devices that require high security but low-latency and low-energy. In this article, we aim to improve the mixed-integer linear programming/mixed-integer quadratic constraint programming (MILP/MIQCP)-based method, to find better differential-linear (DL) distinguishers for the above ciphers, which can be exploited to mount distinguishing or key-recovery attacks. In particular, first, we give the completely precise mixed-integer linear programming (MILP) model to describe the linear part, and utilize the general expressions of [Formula Omitted] optimizer to model middle part in a quite easy way. Second, to explore DL trails in a reasonable time, we propose two heuristic strategies to speed up the searching process. Lastly, we introduce the transforming technique, which exploits the clustering effect on DL trails, to improve the estimated correlation of the DL approximation. By applying our enhanced method, we improve the DL distinguisher correlation from [Formula Omitted] to [Formula Omitted] for 32-round [Formula Omitted], and extend the number of longest rounds of valid DL distinguishers for [Formula Omitted] from [Formula Omitted] to [Formula Omitted]. For [Formula Omitted], we do not outperform the currently best work, but refresh Zhou et al.’s results (the first work to automate finding DL distinguishers for [Formula Omitted] using MILP/MIQCP). Our work not only provides a new insight on the automatic DL cryptanalysis, but also further confirms that [Formula Omitted] and [Formula Omitted] are sufficiently strong to resist the DL attacks. |
| Author | Xiang, Zejun Chen, Siwei Qin, Guangxue Zeng, Xiangyong |
| Author_xml | – sequence: 1 givenname: Siwei orcidid: 0000-0003-3428-7647 surname: Chen fullname: Chen, Siwei organization: School of Cyber Science and Technology, Hubei University, Wuhan, Hubei, China – sequence: 2 givenname: Zejun orcidid: 0000-0002-5149-5133 surname: Xiang fullname: Xiang, Zejun email: xiangzejun@hubu.edu.cn organization: School of Cyber Science and Technology, Hubei University, Wuhan, Hubei, China – sequence: 3 givenname: Xiangyong orcidid: 0000-0002-8351-8766 surname: Zeng fullname: Zeng, Xiangyong organization: Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, Hubei, China – sequence: 4 givenname: Guangxue surname: Qin fullname: Qin, Guangxue organization: School of Cyber Science and Technology, Hubei University, Wuhan, Hubei, China |
| BookMark | eNpNUMtOAjEUbYwmovIBJi6auB7sazrMUhF0DASNuJ6Uzq1THVpshwUf4H87CAtW5-Sex03OBTp13gFC15QMKCX53UsxXwwYYWLAxVDmMj1BPcZZlggp2ekRP0f9GL8IIV0spbnsod-xq5XT1n3itgY8K6avd7PibfSaPKgIFb7ftH6lWqvxO6iga2x8wI_WGAjgWquaZGpdp3S32HYtGxtrCBF7gwu_SCbBgquaLX5ovP7GI7v-V9_tyjusXLVjoL-v0JlRTYT-AS_Rx2S8GD0n0_lTMbqfJpoJ2SaMck0hV7nmtAJtKsZyrSRZAhMq5UuiDR8yASwlwmREpLJDk9OlyhQMs4xfott97zr4nw3Etvzym-C6lyWnGRVZToToXHTv0sHHGMCU62BXKmxLSsrd4OVu8HI3eHkYvMvc7DMWAI78GZcpE_wPhz99_Q |
| CODEN | IITJAU |
| Cites_doi | 10.1007/978-3-662-53887-6_24 10.1007/978-3-642-04138-9_20 10.1007/s00145-016-9237-5 10.1007/978-3-662-47989-6_8 10.1007/978-3-319-78375-8_22 10.1007/978-3-642-15031-9_1 10.1007/978-3-319-16715-2_20 10.1109/ACCESS.2020.3005504 10.1007/978-3-662-48324-4_16 10.1007/978-3-642-23951-9_21 10.1007/978-3-030-84252-9_9 10.1007/978-1-4615-2694-0_23 10.1007/978-3-642-22792-9_13 10.1007/978-3-540-68351-3_14 10.1007/978-3-540-74619-5_12 10.1145/2744769.2747946 10.46586/tosc.v2020.i3.327-361 10.1007/978-3-031-30872-7_10 10.1049/2024/6164262 10.1007/978-3-540-68351-3_18 10.1007/978-3-319-66787-4_15 10.1007/978-3-662-53008-5_5 10.1007/s00145-021-09398-9 10.1007/3-540-48658-5_3 10.1007/3-540-36178-2_16 10.1007/978-3-662-45611-8_9 10.1007/978-3-030-92062-3_10 10.46586/tosc.v2017.i1.45-79 10.1007/978-3-030-17653-2_11 10.1007/3-540-46035-7_7 10.1007/3-540-60590-8_16 10.1007/978-3-662-48800-3_17 10.46586/tosc.v2021.i1.37-77 10.46586/tosc.v2022.i3.341-367 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2025 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2025 |
| DBID | 97E RIA RIE AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/JIOT.2024.3486965 |
| DatabaseName | IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Xplore url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 2327-4662 |
| EndPage | 5671 |
| ExternalDocumentID | 10_1109_JIOT_2024_3486965 10736524 |
| Genre | orig-research |
| GrantInformation_xml | – fundername: Innovation Group Project of the Natural Science Foundation of Hubei Province of China grantid: 2023AFA021 funderid: 10.13039/100017941 – fundername: National Natural Science Foundation of China grantid: 12401687 funderid: 10.13039/501100001809 – fundername: Science and Technology on Communication Security Laboratory Foundation grantid: 6142103012207 – fundername: National Natural Science Foundation of China grantid: 62272147 funderid: 10.13039/501100001809 – fundername: Research Foundation of Department of Education of Hubei Province grantid: D2020104 – fundername: Wuhan Science and Technology Bureau grantid: 2022010801020328 – fundername: National Natural Science Foundation of China grantid: 12471492; 62072161 funderid: 10.13039/501100001809 |
| GroupedDBID | 0R~ 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABJNI ABQJQ ABVLG AGQYO AHBIQ AKJIK AKQYR ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ EBS IFIPE IPLJI JAVBF M43 OCL PQQKQ RIA RIE AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c246t-213c1e9a9c31decfd229ca60be24a53b0cf3824e2504f7045604ff91ba7ae8773 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001432870800043&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2327-4662 |
| IngestDate | Mon Jun 30 07:47:58 EDT 2025 Sat Nov 29 08:03:31 EST 2025 Wed Aug 27 01:42:30 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c246t-213c1e9a9c31decfd229ca60be24a53b0cf3824e2504f7045604ff91ba7ae8773 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-5149-5133 0000-0003-3428-7647 0000-0002-8351-8766 |
| PQID | 3171479044 |
| PQPubID | 2040421 |
| PageCount | 17 |
| ParticipantIDs | crossref_primary_10_1109_JIOT_2024_3486965 ieee_primary_10736524 proquest_journals_3171479044 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-03-01 |
| PublicationDateYYYYMMDD | 2025-03-01 |
| PublicationDate_xml | – month: 03 year: 2025 text: 2025-03-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Piscataway |
| PublicationPlace_xml | – name: Piscataway |
| PublicationTitle | IEEE internet of things journal |
| PublicationTitleAbbrev | JIoT |
| PublicationYear | 2025 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 ref35 ref12 ref34 ref15 ref37 ref14 ref36 ref30 ref33 ref10 Biham (ref20); 537 ref1 ref17 ref39 ref16 ref19 ref18 Zhou (ref31) 2024; 2024 Mouha (ref38) 2011 Bogdanov (ref2) ref24 ref23 ref26 ref25 ref42 Matsui (ref21); 765 ref22 ref43 ref28 ref27 Todo (ref41) 2017 ref29 ref7 ref9 ref4 Hadipour (ref32) 2024 ref3 ref6 ref5 Shibutani (ref8) ref40 Borghoff (ref11) |
| References_xml | – volume: 537 start-page: 2 volume-title: Proc. CRYPTO ident: ref20 article-title: Differential cryptanalysis of DES-like cryptosystems – ident: ref40 doi: 10.1007/978-3-662-53887-6_24 – ident: ref6 doi: 10.1007/978-3-642-04138-9_20 – start-page: 57 volume-title: Information Security and Cryptology year: 2011 ident: ref38 article-title: Differential and linear cryptanalysis using mixed-integer linear programming – ident: ref36 doi: 10.1007/s00145-016-9237-5 – start-page: 450 volume-title: Proc. CHES ident: ref2 article-title: PRESENT: An ultralightweight block cipher – ident: ref34 doi: 10.1007/978-3-662-47989-6_8 – ident: ref29 doi: 10.1007/978-3-319-78375-8_22 – ident: ref7 doi: 10.1007/978-3-642-15031-9_1 – ident: ref27 doi: 10.1007/978-3-319-16715-2_20 – ident: ref37 doi: 10.1109/ACCESS.2020.3005504 – ident: ref13 doi: 10.1007/978-3-662-48324-4_16 – ident: ref10 doi: 10.1007/978-3-642-23951-9_21 – ident: ref25 doi: 10.1007/978-3-030-84252-9_9 – year: 2024 ident: ref32 article-title: Revisiting differentiallinear attacks via a boomerang perspective with application to AES, Ascon, CLEFIA, SKINNY, PRESENT, KNOT, TWINE, WARP, LBlock, Simeck, and SERPENT – ident: ref23 doi: 10.1007/978-1-4615-2694-0_23 – ident: ref9 doi: 10.1007/978-3-642-22792-9_13 – ident: ref5 doi: 10.1007/978-3-540-68351-3_14 – ident: ref3 doi: 10.1007/978-3-540-74619-5_12 – ident: ref12 doi: 10.1145/2744769.2747946 – ident: ref42 doi: 10.46586/tosc.v2020.i3.327-361 – ident: ref30 doi: 10.1007/978-3-031-30872-7_10 – volume: 2024 start-page: 1 year: 2024 ident: ref31 article-title: MILP/MIQCP-based fully automatic method of searching for differential-linear distinguishers for SIMONlike ciphers publication-title: IET Inf. Security – ident: ref33 doi: 10.1049/2024/6164262 – start-page: 208 volume-title: Proc. ASIACRYPT ident: ref11 article-title: PRINCE—A low-latency block cipher for pervasive computing applications—Extended abstract – ident: ref4 doi: 10.1007/978-3-540-68351-3_18 – ident: ref16 doi: 10.1007/978-3-319-66787-4_15 – ident: ref15 doi: 10.1007/978-3-662-53008-5_5 – ident: ref19 doi: 10.1007/s00145-021-09398-9 – ident: ref24 doi: 10.1007/3-540-48658-5_3 – ident: ref26 doi: 10.1007/3-540-36178-2_16 – ident: ref39 doi: 10.1007/978-3-662-45611-8_9 – ident: ref35 doi: 10.1007/978-3-030-92062-3_10 – volume: 765 start-page: 386 volume-title: Proc. EUROCRYPT ident: ref21 article-title: Linear cryptanalysis method for DES cipher – start-page: 342 volume-title: Proc. CHES ident: ref8 article-title: Piccolo: An ultralightweight blockcipher – ident: ref17 doi: 10.46586/tosc.v2017.i1.45-79 – ident: ref28 doi: 10.1007/978-3-030-17653-2_11 – start-page: 250 volume-title: Advances in Cryptology year: 2017 ident: ref41 article-title: Cube attacks on nonblackbox polynomials based on division property – ident: ref1 doi: 10.1007/3-540-46035-7_7 – ident: ref22 doi: 10.1007/3-540-60590-8_16 – ident: ref14 doi: 10.1007/978-3-662-48800-3_17 – ident: ref18 doi: 10.46586/tosc.v2021.i1.37-77 – ident: ref43 doi: 10.46586/tosc.v2022.i3.341-367 |
| SSID | ssj0001105196 |
| Score | 2.3337097 |
| Snippet | <inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck}... [Formula Omitted] and [Formula Omitted] are two famous lightweight block cipher families, both of which have good implementation performance benefiting from... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 5655 |
| SubjectTerms | Automatic tool Automation Ciphers Clustering Computational modeling Correlation differential-linear (DL) cryptanalysis Genetic expression Integer programming Internet of Things lightweight cryptography Linear approximation Linear programming Merging Mixed integer mixed-integer linear programming/mixed-integer quadratic constraint programming (MILP/MIQCP) Search problems Security Simeck Simon Wireless communication |
| Title | Enhancing the MILP/MIQCP-Based Automatic Search for Differential-Linear Distinguishers of IoT-Friendly Block Ciphers Simon and Simeck |
| URI | https://ieeexplore.ieee.org/document/10736524 https://www.proquest.com/docview/3171479044 |
| Volume | 12 |
| WOSCitedRecordID | wos001432870800043&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Xplore customDbUrl: eissn: 2327-4662 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001105196 issn: 2327-4662 databaseCode: RIE dateStart: 20140101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1bS8MwFA4qPvjideK8kQefhGibdE3z6KbDiZeJE_ZW0iTVMWnFbYI_wP_tOWmHgvjgU0OTlpKvJ-d8ybkQcgSQ2lCKjIHu40BQnGWZkJZxjGrUUsZW-EDha3l7mwyHql8Hq_tYGOecdz5zJ9j0Z_m2NDPcKgMJlyJu8WiRLMJbqmCt7w2VEK2RuD65DAN1etW7GwAD5NGJiJJYof74oXt8MZVfK7BXK921f37QOlmt7Ud6VgG-QRZcsUnW5rUZaC2qW-TzonjGVBrFEwUTj970rvunN737Tp-1QW9Zejablj5bK60cjikYr_S8rpYCUv_CgKVCD9yboGf0rPKdp2VOe-WAdTE9sn35oG1QhmPaGb363gdAvqC6sNhyZtwgj92LQeeS1SUXmOFRPGU8FCZ0SisjQutMbjlXRsdB5nikWyILTC4SHjlMfJZLNAfhmqsw01K7REqxTZaKsnA7hGZAeJ3OgY5YsNIwDzxvAY1PtApcmNmkSY7nYKSvVWaN1DOSQKWIXIrIpTVyTdLA2f8xsJr4Jtmf45fWwjdJBRZ1lyqIot0_HtsjKxzr-Hpfsn2yNH2buQOybN6no8nbof-vvgAcBsxT |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Nb9QwEB1BQYIL5aMVSwv4wAnJbWJ74_jYbrtqYHdZxCL1Fjm201atkqq7i8QP4H8z42RFJcSBU6I4kSK_TOY9ez4APiCkPtWy4uj7BAqU4HklteeCshqt1pmXMVF4omez_PzczPtk9ZgLE0KIwWfhgE7jXr5v3ZqWytDCtcyGQj2ER0OlRNKla_1ZUkmJj2T93mWamMNPxZcFakChDqTKM0Me5J73ie1U_voHR8cy3v7PV3oOz3oGyY46yF_Ag9C8hO1NdwbWG-sr-HXaXFIxjeaCIclj02IyP5wWX0dzfoyey7Oj9aqN9VpZF3LMkL6yk75fCtr9DUediiN4bUmx0esuep61NSvaBR9TgWR_85Mdozu8ZqOr2zj6DbFvmG08nQV3vQPfx6eL0Rnvmy5wJ1S24iKVLg3GGidTH1zthTDOZkkVhLJDWSWulrlQgUqf1ZoIIR5rk1ZW25BrLXdhq2mb8BpYhZI32BoFiUeeRpXgxRCFfG5NEtLK5wP4uAGjvO1qa5RRkySmJORKQq7skRvADs3-vRu7iR_A_ga_sje_ZSmprbs2iVJv_vHYe3hytphOykkx-7wHTwV19Y2RZfuwtbpbh7fw2P1YXS3v3sVv7DfkBM-a |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Enhancing+the+MILP%2FMIQCP-Based+Automatic+Search+for+Differential-Linear+Distinguishers+of+IoT-Friendly+Block+Ciphers+Simon+and+Simeck&rft.jtitle=IEEE+internet+of+things+journal&rft.au=Chen%2C+Siwei&rft.au=Xiang%2C+Zejun&rft.au=Zeng%2C+Xiangyong&rft.au=Qin%2C+Guangxue&rft.date=2025-03-01&rft.pub=IEEE&rft.eissn=2327-4662&rft.volume=12&rft.issue=5&rft.spage=5655&rft.epage=5671&rft_id=info:doi/10.1109%2FJIOT.2024.3486965&rft.externalDocID=10736524 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2327-4662&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2327-4662&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2327-4662&client=summon |