{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T14:10:40Z","timestamp":1788876640290,"version":"build-2803163510"},"reference-count":23,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T00:00:00Z","timestamp":1788825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Fund for Young Talents of Guangxi","award":["DT2500002644"],"award-info":[{"award-number":["DT2500002644"]}]},{"DOI":"10.13039\/501100003457","name":"Guilin University of Technology","doi-asserted-by":"publisher","award":["GUTQDJJ2024016"],"award-info":[{"award-number":["GUTQDJJ2024016"]}],"id":[{"id":"10.13039\/501100003457","id-type":"DOI","asserted-by":"publisher"}]},{"award":["GUTQDJJ2024016"],"award-info":[{"award-number":["GUTQDJJ2024016"]}],"id":[{"id":"https:\/\/ror.org\/03z391397","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Secrecy and Cryptography Technology Laboratory of Jiangxi Province","award":["JXWAYKT202501"],"award-info":[{"award-number":["JXWAYKT202501"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>PICO is an ultra-lightweight substitution\u2013permutation network block cipher designed for resource-constrained devices such as Internet of Things terminals and edge agents. For fixed endpoints, summing the characteristic probabilities over an enumerated finite weight window gives a verifiable lower bound on the differential probability. We use a PICO-specific workflow that combines mixed-integer linear programming bounds on active substitution boxes, exact-weight Boolean satisfiability search, optional Matsui pruning, and fixed-endpoint enumeration. For the selected endpoints, enumeration over W=63,\u2026,76 and W=66,\u2026,79 gives finite-window lower bounds of 2\u221259.95 and 2\u221261.95 for 21 and 22 rounds, respectively. We prepend two rounds and append three rounds to the 21-round differential distinguisher. The resulting 26-round analysis is an analytical equivalent-round-key filtering-and-ranking procedure for a 108-bit tuple. The verified 21-round finite-window probability input is a factor of 20.8032\u22481.745 larger than the previously reported input, increasing the expected right-tuple support at fixed S under the analytical accounting. For the illustrative choice S=242, the analytical resources are D=262 chosen plaintexts, a normalized substitution-box filtering workload of T=2100.11 equivalent 26-round encryptions, and M=262 stored plaintext\u2013ciphertext records. This setting is not tied to a demonstrated success probability and does not establish an equal-success complexity advantage over prior work.<\/jats:p>","DOI":"10.3390\/e28091006","type":"journal-article","created":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T13:46:33Z","timestamp":1788875193000},"page":"1006","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improved Differential Cryptanalysis of the Ultra-Lightweight Block Cipher PICO"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1158-4641","authenticated-orcid":false,"given":"Yu","family":"Wang","sequence":"first","affiliation":[{"name":"College of Computer Science and Engineering, Guilin University of Technology, Guilin 541006, China"},{"name":"Guangxi Key Laboratory of Embedded Technology and Intelligent System, Guilin 541006, 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ultra-lightweight block cipher","volume":"Volume 4727","author":"Paillier","year":"2007","journal-title":"Cryptographic Hardware and Embedded Systems\u2014CHES 2007"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/978-3-319-66787-4_16","article-title":"GIFT: A small present\u2014Towards reaching the limit of lightweight encryption","volume":"Volume 10529","author":"Fischer","year":"2017","journal-title":"Cryptographic Hardware and Embedded Systems\u2014CHES 2017"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/978-3-662-53008-5_5","article-title":"The SKINNY family of block ciphers and its low-latency variant MANTIS","volume":"Volume 9815","author":"Robshaw","year":"2016","journal-title":"Advances in Cryptology\u2014CRYPTO 2016"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/978-3-642-21554-4_19","article-title":"LBlock: A lightweight block cipher","volume":"Volume 6715","author":"Lopez","year":"2011","journal-title":"Applied Cryptography and Network Security"},{"key":"ref_5","first-page":"45583","article-title":"LLBC: A novel Feistel-based low-latency block cipher for IoT applications","volume":"12","author":"Li","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"259","DOI":"10.14429\/dsj.66.9276","article-title":"PICO: An ultra lightweight and low power encryption design for ubiquitous computing","volume":"66","author":"Bansod","year":"2016","journal-title":"Def. Sci. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF00630563","article-title":"Differential cryptanalysis of DES-like cryptosystems","volume":"4","author":"Biham","year":"1991","journal-title":"J. Cryptol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/3-540-46416-6_2","article-title":"Markov ciphers and differential cryptanalysis","volume":"Volume 547","author":"Davies","year":"1991","journal-title":"Advances in Cryptology\u2014EUROCRYPT \u201991"},{"key":"ref_9","first-page":"272","article-title":"Clustering effect in Simon and Simeck","volume":"Volume 13090","author":"Tibouchi","year":"2021","journal-title":"Advances in Cryptology\u2014ASIACRYPT 2021"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/978-3-642-34704-7_5","article-title":"Differential and linear cryptanalysis using mixed-integer linear programming","volume":"Volume 7537","author":"Wu","year":"2012","journal-title":"Information Security and Cryptology"},{"key":"ref_11","first-page":"158","article-title":"Automatic security evaluation and (related-key) differential characteristic search: Application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers","volume":"Volume 8873","author":"Sarkar","year":"2014","journal-title":"Advances in Cryptology\u2014ASIACRYPT 2014"},{"key":"ref_12","unstructured":"Mouha, N., and Preneel, B. (2026, July 18). Towards Finding Optimal Differential Characteristics for ARX: Application to Salsa20. Cryptology ePrint Archive. Available online: https:\/\/eprint.iacr.org\/2013\/328."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/978-3-662-47989-6_8","article-title":"Observations on the SIMON block cipher family","volume":"Volume 9215","author":"Gennaro","year":"2015","journal-title":"Advances in Cryptology\u2014CRYPTO 2015"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"269","DOI":"10.46586\/tosc.v2021.i1.269-315","article-title":"Accelerating the search of differential and linear characteristics with the SAT method","volume":"2021","author":"Sun","year":"2021","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"516","DOI":"10.46586\/tosc.v2025.i3.516-576","article-title":"Divide-and-conquer SAT for exploring optimal differential and linear characteristics and its applications","volume":"2025","author":"Taka","year":"2025","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"ref_16","unstructured":"Kim, I., Kim, S., Kim, S., Kwon, D., Shin, H., Lee, D., Hong, D., Sung, J., and Hong, S. (2026, July 18). Towards Optimal Differential Attacks on FLY and PIPO. Cryptology ePrint Archive. Available online: https:\/\/eprint.iacr.org\/2025\/837."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1080\/01611194.2019.1650844","article-title":"Optimal differential trails in lightweight block ciphers ANU and PICO","volume":"44","author":"Kumar","year":"2020","journal-title":"Cryptologia"},{"key":"ref_18","first-page":"413","article-title":"Zero-correlation linear cryptanalysis on PICO and RECTANGLE","volume":"4","author":"Ma","year":"2017","journal-title":"J. Cryptologic Res."},{"key":"ref_19","first-page":"910","article-title":"MILP-based search for differential and linear distinguishers of PICO algorithm","volume":"10","author":"Shi","year":"2023","journal-title":"J. Cryptologic Res."},{"key":"ref_20","first-page":"685","article-title":"Differential cryptanalysis on ultra lightweight block cipher PICO","volume":"10","author":"Wang","year":"2023","journal-title":"J. Cryptologic Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/978-3-319-69284-5_11","article-title":"New algorithm for modeling S-box in MILP based differential and division trail search","volume":"Volume 10543","author":"Farshim","year":"2017","journal-title":"Innovative Security Solutions for Information Technology and Communications"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1007\/11564751_73","article-title":"Towards an optimal CNF encoding of Boolean cardinality constraints","volume":"Volume 3709","year":"2005","journal-title":"Principles and Practice of Constraint Programming\u2014CP 2005"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s00145-007-9013-7","article-title":"On probability of success in linear and differential cryptanalysis","volume":"21","year":"2008","journal-title":"J. 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