[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81560-en":3,"doc-seo-81560-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},81560,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Security Index from Input Output Data Theory and Computation","Security index quantifies the minimum number of components that must be compromised to execute a stealth attack while remaining undetected. The proposed data-driven security index evaluates component risk using only input/output data, even when the system model is unknown. A sufficient condition is derived under which the data-driven index matches the model-based security index, enabling exact component risk identification from data. An accompanying algorithm computes the data-driven index efficiently.","Security Index from Input/Output Data: Theory and Computation ⋆  \nTakumi Shinohara ∗ Karl Henrik Johansson ∗ Henrik Sandberg ∗  \n∗ Department of Decision and Control Systems, KTH Royal Institute of Technology, and Digital Futures, 100 44 Stockholm, Sweden.  \n(E-mail: [tashin@kth.se](tashin@kth.se), [kallej@kth.se](kallej@kth.se), [hsan@kth.se](hsan@kth.se))  \n2026  \nAbstract: The concept of a security index quantifies the minimum number of components that must be compromised to carry out a stealth attack. This metric enables system operators to assess the security risk of each component and implement countermeasures accordingly. In this paper, we introduce a data-driven security index that can be computed solely from input/output data when the system model is unknown. We show a sufficient condition under which the datadriven security index coincides with the model-based security index, which implies that the exact risk level of each component can be identified solely from data. We also provide an algorithm for computing the data-driven security index.  \nKeywords: Security index, data-driven method, linear systems, security analysis, system security  \n10 Jul  \n1. INTRODUCTION  \nA key strategy for enhancing cybersecurity and resilience of control systems is the risk-based approach, which en-  \narXiv :25 1 1 .09524v2  \nof sensors that must be compromised while remaining undetected (Sandberg et al., 2010; Hendrickx et al., 2014) . While this index was initially proposed for static systems, subsequent studies (Sandberg and Teixeira, 2016; Tanget al., 2019) extended this concept to dynamical systems. In addition, the authors of (Milosevic et al., 2020; Gracyet al., 2021) formulated the security index for dynamical systems based on the notion of perfectly undetectable attacks. For a given component i 1 , the security index is defined as the minimum number of sensors and actuators that must be compromised to carry out a perfectly undetectable attack involving component i. Thus, components with a smaller security index are more vulnerable to stealthy attacks than other components. System operators can assess the risk level of each component based on the security index.  \n(Milosevic et al., 2020; Gracy et al., 2021) introduced security indices for structured systems, addressing cases  \n⋆ This work was supported in part by the Knut and Alice Wallenberg Foundation Wallenberg Scholar, Swedish Research Council (Project 2023-04770), and VINNOVA project “Control-computingcommunication co-design for autonomous industry (3C4AI)” (No. 2025-01119) .  \n1 An actuator or a sensor.  \nwhere system operators possess only incomplete knowledge of the system model. Yet, as emphasized in the datadriven control literature (De Persis and Tesi, 2020; van Waarde et al., 2025), it is often challenging to obtain even the system’s structure; instead, often only input/output data (I/O data) are available. This motivates our central question: Given only I/O data, how can we assess the risk level of control systems via a security index?  \nIn answering this question, our primary contributions can be summarized as follows:  \n(1) We develop a data-driven security index which can be computed solely from I/O data, without any model parameters.  \n(2) We establish a sufficient condition under which the data-driven security index coincides with the modelbased security index.  \n(3) We present an algorithm to compute the data-driven security index.  \nSeveral studies (e.g., (Krishnan and Pasqualetti, 2021)) have examined data-driven security issues, but most existing research focuses on detecting and identifying attacks. While our recent work (Shinohara et al., 2026) proposed data-driven resilience assessment metrics for sparse sensor attacks, this paper considers a more general problem by incorporating actuator attacks alongside sensor attacks.  \nThe remainder of this paper is organized as follows. Section 2 presents preliminary descriptions of the system model, data model, a","cbCaivL1zlm1v24F","https://ap.wps.com/l/cbCaivL1zlm1v24F","pdf",385733,1,6,"English","en",105,"# Introduction\n## Problem\n## Notation","[{\"question\":\"What is the security index and how is it used?\",\"answer\":\"The security index measures the minimum number of sensors and actuators that must be compromised to perform a perfectly undetectable stealth attack involving a specific component. Components with smaller indices are more vulnerable, allowing operators to assess component risk and plan countermeasures.\"},{\"question\":\"How does the paper compute a security index when the system model is unknown?\",\"answer\":\"It introduces a data-driven security index that can be computed solely from input/output data, without using any model parameters. This addresses situations where system structure is unavailable and only I/O data can be collected.\"},{\"question\":\"When does the data-driven security index equal the model-based security index?\",\"answer\":\"The paper provides a sufficient condition under which the data-driven security index coincides with the model-based security index. Under this condition, the exact risk level of each component can be identified from data alone.\"}]",1784174329,15,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"security-index-from-input-output-data-theory-and-computation","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/security-index-from-input-output-data-theory-and-computation/81560/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What is the security index and how is it used?","Question",{"text":74,"@type":75},"The security index measures the minimum number of sensors and actuators that must be compromised to perform a perfectly undetectable stealth attack involving a specific component. Components with smaller indices are more vulnerable, allowing operators to assess component risk and plan countermeasures.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the paper compute a security index when the system model is unknown?",{"text":79,"@type":75},"It introduces a data-driven security index that can be computed solely from input/output data, without using any model parameters. This addresses situations where system structure is unavailable and only I/O data can be collected.",{"name":81,"@type":72,"acceptedAnswer":82},"When does the data-driven security index equal the model-based security index?",{"text":83,"@type":75},"The paper provides a sufficient condition under which the data-driven security index coincides with the model-based security index. 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