[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82755-en":3,"doc-seo-82755-105":30,"detail-sidebar-cat-0-en-105":91},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82755,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Observer-Quotient Security: Composable Leakage Bounds for Hidden State Continuations","Observer-quotient security studies cryptographic executions through the distributions visible to an explicit observer class, capturing how hidden internal protocol evolution may occur while the public transcript stays unchanged. The paper formalizes interactive observer-quotient security games using session identifiers, oracle forwarding, adaptive observer schedulers, and ideal quotient functionalities. A real/ideal theorem bounds leakage under time evolution via indexed hybrid sequences and residual leakage functionals. Computational instantiations include timing-leakage IND-CPA, deterministic encryption leakage bounds, and nonce-refreshing authenticated-encryption state machines, with an optimization-control interpretation for sensor design.","arXiv :2607 .036 10v 1 [ cs .CR] 3 Jul 2026  \nObserver-Quotient Security: Composable Leakage Bounds for  \nHidden State Continuations  \nFaruk Alpay∗ Levent Sarıoğlu  \nDepartment of Computer Engineering, Bahçeşehir University, Istanbul, Türkiye {faruk. alpay, [levent. sarioglu}@bahcesehir. edu. tr](levent. sarioglu}@bahcesehir. edu. tr)  \nJuly 2026  \nAbstract  \nObserver-quotient security studies cryptographic executions through the distributions visible to an explicit observer class. The internal state of a protocol, implementation, or controlled plant may evolve inside an observer quotient while the public transcript remains unchanged; security then depends on whether later continuations, richer side channels, repeated sessions, or post-processing can turn that hidden evolution into distinguishing advantage. This paper formalizes interactive observer-quotient security games with session identifiers, oracle forwarding, adaptive observer schedulers, nonuniform environments, simulator/adaptors, ideal quotient functionalities, and scalar boundary functionals that upper-bound leakage under time evolution. The main real/ideal theorem is proved through named interface lemmas, an explicit wrapper construction, and a fully indexed hybrid sequence whose defects are observer, kernel, post-processing, simulator, statistical, and residual terms. The computational instantiations include IND-CPA encryption with timing leakage, deterministic encryption under alphabet-size and smooth max-information leakage, and nonce-refreshing authenticated-encryption state machines. The same quotient geometry yields the optimization-control layer: hidden continuations are observability kernels, observer refinement is sensor redesign, stochastic dissipativity gives residual leakage floors, and costconstrained observer synthesis converts sensor choices into concrete reductions in bounded distinguishing advantage.  \n1 Introduction  \nSecurity assertions are statements about observations. Two executions may differ internally while remaining indistinguishable to a transcript observer, and that indistinguishability may fail after the observer class is refined by timing, cache, power, electromagnetic, or profiled leakage. The relevant state space is therefore not only the implementation state space X, but the quotient of X induced by the observer family used in the security game.  \nLet Π be a family of observers. States x, x′ ∈ X are equivalent when every observer in Π gives the same distribution. A transition from x to x′ inside one equivalence class is a hidden continuation: the computation has changed, while the admitted view has not. Nonces may refresh, counters may advance, randomness may be consumed, masked shares may rotate, and microarchitectural state may move without altering the public transcript. The security question is whether an adaptive environment can later expose that continuation through a scheduled observer, a side channel, a further session, or an efficient post-processing of the transcript.  \nThis paper develops a security-game calculus for that question. The primitive object isan interactive experiment with sessions, oracle calls, observer choices, continuation commands, leakage labels, and an ideal quotient functionality. The real/ideal theorem treats hidden  \n∗ Correspondence: [alpay@lightcap.ai](alpay@lightcap.ai).  \ncontinuations as substitutable resources precisely when they remain compatible with the quotient interface and when the residual leakage functional stays below the corresponding advantage bound. The proof is organized by named interfaces and named hybrids rather than by an implicit appeal to observational equivalence.  \nThe resulting framework also has a control interpretation. An observer is a sensor, an observer quotient is an output-equivalence partition, and a hidden continuation is an element of an observability kernel. Sensor redesign refines the quotient; persistent noise or implementation drift appears as an input-to-st","cbCailUjWJbcgj2h","https://ap.wps.com/l/cbCailUjWJbcgj2h","pdf",775155,2,1,37,"English","en",105,"# Abstract\n# Introduction\n## Security assertions as observations\n## Hidden continuations and quotient dynamics\n# Related Work","[{\"question\":\"What does observer-quotient security focus on in cryptographic executions?\",\"answer\":\"It studies how executions are characterized by the distributions visible to a chosen observer class, even when internal states change while the public transcript remains the same.\"},{\"question\":\"What are “hidden continuations” in this framework?\",\"answer\":\"They are transitions within an observer equivalence class where the computation changes but the admitted view does not, meaning later distinguishability can only arise if an adaptive environment exposes the hidden evolution.\"},{\"question\":\"How does the paper obtain leakage bounds over time evolution?\",\"answer\":\"It formalizes interactive observer-quotient security games and proves a compositional real/ideal theorem using named interface lemmas, a wrapper construction, and indexed hybrid sequences with residual leakage functionals that upper-bound distinguishing 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does observer-quotient security focus on in cryptographic executions?","Question",{"text":75,"@type":76},"It studies how executions are characterized by the distributions visible to a chosen observer class, even when internal states change while the public transcript remains the same.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What are “hidden continuations” in this framework?",{"text":80,"@type":76},"They are transitions within an observer equivalence class where the computation changes but the admitted view does not, meaning later distinguishability can only arise if an adaptive environment exposes the hidden evolution.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the paper obtain leakage bounds over time evolution?",{"text":84,"@type":76},"It formalizes interactive observer-quotient security games and proves a compositional real/ideal theorem using named interface lemmas, a wrapper construction, and indexed hybrid sequences with residual leakage functionals that 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