<div><div>In this paper, we consider the partial gathering problem of mobile agents in synchronous dynamic bidirectional ring networks. The partial gathering problem is a generalization of the (well-investigated) total gathering problem, which requires that all <em>k</em> agents distributed in the network terminate at a non-predetermined single node. The partial gathering problem requires, for a given positive integer <em>g</em> ( < <em>k</em>), that agents terminate in a configuration such that either at least <em>g</em> agents or no agent exists at each node. When <em>k</em> ≥ 2<em>g</em>, the requirement for the partial gathering problem is strictly weaker than that for the total gathering problem, and thus it is interesting to clarify the difference in the move complexity between them. So far, the partial gathering problem has been considered in static graphs. In this paper, we start considering partial gathering in dynamic graphs. As a first step, we consider this problem in 1-interval connected rings, that is, one of the links in a ring may be missing at each time step. In such networks, focusing on the relationship between the values of <em>k</em> and <em>g</em>, we fully characterize the solvability of the partial gathering problem and analyze the move complexity of the proposed algorithms when the problem can be solved. First, we show that the <em>g</em>-partial gathering problem is unsolvable when <em>k</em> ≤ 2<em>g</em>. Second, we show that the problem can be solved with <em>O</em>(<em>n</em>log <em>g</em>) time and the total number of <em>O</em>(<em>gn</em>log <em>g</em>) moves when <span><math><mrow><mn>2</mn><mi>g</mi><mo>+</mo><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>3</mn><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math></span>. Third, we show that the problem can be solved with <em>O</em>(<em>n</em>) time and the total number of <em>O</em>(<em>kn</em>) moves when <span><math><mrow><mn>3</mn><mi>g</mi><mo>−</mo><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>8</mn><mi>g</mi><mo>−</mo><mn>4</mn></mrow></math></span>. Notice that since <span><math><mrow><mi>k</mi><mo>=</mo><mi>O</mi><mo>(</mo><mi>g</mi><mo>)</mo></mrow></math></span> holds when <span><math><mrow><mn>3</mn><mi>g</mi><mo>−</mo><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>8</mn><mi>g</mi><mo>−</mo><mn>4</mn></mrow></math></span>, the move complexity <em>O</em>(<em>kn</em>) in this case can be represented also as <em>O</em>(<em>gn</em>). Finally, we show that the problem can be solved with <em>O</em>(<em>n</em>) time and the total number of <em>O</em>(<em>gn</em>) moves when <span><math><mrow><mi>k</mi><mo>≥</mo><mn>8</mn><mi>g</mi><mo>−</mo><mn>3</mn></mrow></math></span>. These results mean that the partial gathering problem can be solved also in dynamic rings when <span><math><mrow><mi>k</mi><mo>≥</mo><mn>2</mn><mi>g</mi><mo>+</mo><mn>1</mn></mrow></math></span>. In addition, agents require a total number of Ω(<em>gn</em>) (resp., Ω(<em>kn</em>)) moves to solve the par
{"title":"Partial gathering of mobile agents in dynamic rings","authors":"Masahiro Shibata , Yuichi Sudo , Junya Nakamura , Yonghwan Kim","doi":"10.1016/j.tcs.2025.115684","DOIUrl":"10.1016/j.tcs.2025.115684","url":null,"abstract":"<div><div>In this paper, we consider the partial gathering problem of mobile agents in synchronous dynamic bidirectional ring networks. The partial gathering problem is a generalization of the (well-investigated) total gathering problem, which requires that all <em>k</em> agents distributed in the network terminate at a non-predetermined single node. The partial gathering problem requires, for a given positive integer <em>g</em> ( < <em>k</em>), that agents terminate in a configuration such that either at least <em>g</em> agents or no agent exists at each node. When <em>k</em> ≥ 2<em>g</em>, the requirement for the partial gathering problem is strictly weaker than that for the total gathering problem, and thus it is interesting to clarify the difference in the move complexity between them. So far, the partial gathering problem has been considered in static graphs. In this paper, we start considering partial gathering in dynamic graphs. As a first step, we consider this problem in 1-interval connected rings, that is, one of the links in a ring may be missing at each time step. In such networks, focusing on the relationship between the values of <em>k</em> and <em>g</em>, we fully characterize the solvability of the partial gathering problem and analyze the move complexity of the proposed algorithms when the problem can be solved. First, we show that the <em>g</em>-partial gathering problem is unsolvable when <em>k</em> ≤ 2<em>g</em>. Second, we show that the problem can be solved with <em>O</em>(<em>n</em>log <em>g</em>) time and the total number of <em>O</em>(<em>gn</em>log <em>g</em>) moves when <span><math><mrow><mn>2</mn><mi>g</mi><mo>+</mo><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>3</mn><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math></span>. Third, we show that the problem can be solved with <em>O</em>(<em>n</em>) time and the total number of <em>O</em>(<em>kn</em>) moves when <span><math><mrow><mn>3</mn><mi>g</mi><mo>−</mo><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>8</mn><mi>g</mi><mo>−</mo><mn>4</mn></mrow></math></span>. Notice that since <span><math><mrow><mi>k</mi><mo>=</mo><mi>O</mi><mo>(</mo><mi>g</mi><mo>)</mo></mrow></math></span> holds when <span><math><mrow><mn>3</mn><mi>g</mi><mo>−</mo><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>8</mn><mi>g</mi><mo>−</mo><mn>4</mn></mrow></math></span>, the move complexity <em>O</em>(<em>kn</em>) in this case can be represented also as <em>O</em>(<em>gn</em>). Finally, we show that the problem can be solved with <em>O</em>(<em>n</em>) time and the total number of <em>O</em>(<em>gn</em>) moves when <span><math><mrow><mi>k</mi><mo>≥</mo><mn>8</mn><mi>g</mi><mo>−</mo><mn>3</mn></mrow></math></span>. These results mean that the partial gathering problem can be solved also in dynamic rings when <span><math><mrow><mi>k</mi><mo>≥</mo><mn>2</mn><mi>g</mi><mo>+</mo><mn>1</mn></mrow></math></span>. In addition, agents require a total number of Ω(<em>gn</em>) (resp., Ω(<em>kn</em>)) moves to solve the par","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1063 ","pages":"Article 115684"},"PeriodicalIF":1.0,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-09DOI: 10.1016/j.tcs.2025.115677
A. Hosseinabadi, M. Haddadi
This paper investigates the support-preorder, a reflexive and transitive relation that can be defined on any finitely supported Cb-set using the notion of support. Finitely supported Cb-sets extend the concept of nominal sets. We introduce the category consisting of finitely supported Cb-sets and sp-preserving morphisms. We analyze its characteristics, including the existence of products and coproducts, and regularity, highlighting differences from the category of support-preordered nominal sets. A key distinction is the non-equivariance of the support-preorder on finitely supported Cb-sets. We also characterize strongly finitely supported Cb-sets, where the support-preorder is equivariant, and investigate the behavior of support under actions within these sets. Our research contributes to a deeper understanding of the structure and interrelations between nominal sets and finitely supported Cb-sets, with significant implications for fields such as formal systems and homotopy type theory.
{"title":"Support preorder on finitely supported Cb-Sets","authors":"A. Hosseinabadi, M. Haddadi","doi":"10.1016/j.tcs.2025.115677","DOIUrl":"10.1016/j.tcs.2025.115677","url":null,"abstract":"<div><div>This paper investigates the support-preorder, a reflexive and transitive relation that can be defined on any finitely supported <strong>Cb</strong>-set using the notion of support. Finitely supported <strong>Cb</strong>-sets extend the concept of nominal sets. We introduce the category <span><math><mrow><mtext>sp-</mtext><msub><mrow><mo>(</mo><mi>Cb</mi><mtext>-</mtext><mtext>Set</mtext><mo>)</mo></mrow><mrow><mrow><mi>f</mi></mrow><mi>s</mi></mrow></msub></mrow></math></span> consisting of finitely supported <strong>Cb</strong>-sets and sp-preserving morphisms. We analyze its characteristics, including the existence of products and coproducts, and regularity, highlighting differences from the category of support-preordered nominal sets. A key distinction is the non-equivariance of the support-preorder on finitely supported <strong>Cb</strong>-sets. We also characterize strongly finitely supported <strong>Cb</strong>-sets, where the support-preorder is equivariant, and investigate the behavior of support under actions within these sets. Our research contributes to a deeper understanding of the structure and interrelations between nominal sets and finitely supported <strong>Cb</strong>-sets, with significant implications for fields such as formal systems and homotopy type theory.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1064 ","pages":"Article 115677"},"PeriodicalIF":1.0,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.tcs.2025.115654
Shai Michael Dimant, Sven O. Krumke
In the Partial Scenario Set Cover problem (PSSC), given a finite ground set Q, a collection of subsets of Q with associated nonnegative costs, and a second collection of subsets of Q, the goal is to select a minimum-cost sub-collection of that covers at least l sets from . In this paper, we focus on two natural generalizations of PSSC. In the first generalization, called Partial PSSC (PPSSC), each scenario has a demand, and the task is to find a minimum-cost sub-collection of that satisfies the demand of at least l scenarios. We present a primal-dual algorithm for this problem whose approximation ratio improves over the previously best known for a special case of PPSSC. In the second generalization, given a finite set N, a non-negative cost function c over N, and integer-valued submodular non-decreasing functions over 2N together with integer demands and an additional integer l, we ask for a minimum-cost subset S⊆N such that at least l covering constraints of the form fi(S) ≥ di are satisfied. This is the partial cover version of the Multi-Submod-Cover problem studied in the literature, which we call Partial-Multi-Submod-Cover (PMSC). From the presented primal-dual algorithm we derive an algorithm for PMSC, which can be viewed as a generalization of Wolsey’s greedy algorithm for Submodular Set Cover. Finally, we highlight the broad applicability of the presented algorithms, which unlike previous algorithms for PSSC are purely combinatorial.
{"title":"On generalizations of partial scenario set cover","authors":"Shai Michael Dimant, Sven O. Krumke","doi":"10.1016/j.tcs.2025.115654","DOIUrl":"10.1016/j.tcs.2025.115654","url":null,"abstract":"<div><div>In the <em>Partial Scenario Set Cover problem</em> (PSSC), given a finite ground set <em>Q</em>, a collection <span><math><mi>S</mi></math></span> of subsets of <em>Q</em> with associated nonnegative costs, and a second collection <span><math><mi>U</mi></math></span> of subsets of <em>Q</em>, the goal is to select a minimum-cost sub-collection of <span><math><mi>S</mi></math></span> that covers at least <em>l</em> sets from <span><math><mi>U</mi></math></span>. In this paper, we focus on two natural generalizations of PSSC. In the first generalization, called <em>Partial PSSC</em> (PPSSC), each scenario has a demand, and the task is to find a minimum-cost sub-collection of <span><math><mi>S</mi></math></span> that satisfies the demand of at least <em>l</em> scenarios. We present a primal-dual algorithm for this problem whose approximation ratio improves over the previously best known for a special case of PPSSC. In the second generalization, given a finite set <em>N</em>, a non-negative cost function <em>c</em> over <em>N</em>, and integer-valued submodular non-decreasing functions <span><math><mrow><msub><mi>f</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>f</mi><mi>r</mi></msub></mrow></math></span> over 2<sup><em>N</em></sup> together with integer demands <span><math><mrow><msub><mi>d</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>d</mi><mi>r</mi></msub></mrow></math></span> and an additional integer <em>l</em>, we ask for a minimum-cost subset <em>S</em>⊆<em>N</em> such that at least <em>l</em> covering constraints of the form <em>f<sub>i</sub></em>(<em>S</em>) ≥ <em>d<sub>i</sub></em> are satisfied. This is the partial cover version of the Multi-Submod-Cover problem studied in the literature, which we call <em>Partial-Multi-Submod-Cover</em> (PMSC). From the presented primal-dual algorithm we derive an algorithm for PMSC, which can be viewed as a generalization of Wolsey’s greedy algorithm for Submodular Set Cover. Finally, we highlight the broad applicability of the presented algorithms, which unlike previous algorithms for PSSC are purely combinatorial.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1063 ","pages":"Article 115654"},"PeriodicalIF":1.0,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.tcs.2025.115679
Chunjian Liang , Jiafei Liu , Chia-Wei Lee , Jingli Wu , Gaoshi Li
Assessing the diagnosability of multiprocessor systems is vital for maintaining reliability and fault-tolerance, especially in extensive interconnection networks where precise reliability assessments are crucial for system stability and resilience against processor failures. In this paper, we introduce a novel diagnosability metric called h-extra r-component diagnosability, which extends traditional models by considering both component-level robustness and structural constraints. Specifically, for a graph G, a vertex subset F ⊂ V(G) is termed an h-extra r-component vertex-cut if is disconnected with at least r connected components, each containing at least vertices. The h-extra r-component diagnosability of G, denoted by , is defined as the maximum integer t such that G is conditionally t-diagnosable under this constraint. We establish theoretical characterization for hypercube networks Qn under the condition that there does not exist exactly one isolated node in for two distinct sets F1, F2. Specifically, we show that for n ≥ 7 and for n ≥ 13 under the MM* diagnostic model. To enhance fault identification efficiency, we propose a two-stage diagnosis algorithm (TSDA-MM*), leveraging network structural properties to improve diagnostic accuracy and efficiency. Extensive simulation experiments on hypercube networks and the data center networks Bcube(n, k) demonstrate that TSDA-MM* achieves high performance in terms of Accuracy, TrueNegativeRate, TruePositiveRate, and Precision, thereby providing a promising solution for practical fault diagnosis in large-scale systems.
{"title":"An efficient two-stage diagnostic algorithm for assessing system reliability","authors":"Chunjian Liang , Jiafei Liu , Chia-Wei Lee , Jingli Wu , Gaoshi Li","doi":"10.1016/j.tcs.2025.115679","DOIUrl":"10.1016/j.tcs.2025.115679","url":null,"abstract":"<div><div>Assessing the diagnosability of multiprocessor systems is vital for maintaining reliability and fault-tolerance, especially in extensive interconnection networks where precise reliability assessments are crucial for system stability and resilience against processor failures. In this paper, we introduce a novel diagnosability metric called <em>h</em>-extra <em>r</em>-component diagnosability, which extends traditional models by considering both component-level robustness and structural constraints. Specifically, for a graph <em>G</em>, a vertex subset <em>F</em> ⊂ <em>V</em>(<em>G</em>) is termed an <em>h</em>-extra <em>r</em>-component vertex-cut if <span><math><mrow><mi>G</mi><mo>−</mo><mi>F</mi></mrow></math></span> is disconnected with at least <em>r</em> connected components, each containing at least <span><math><mrow><mi>h</mi><mo>+</mo><mn>1</mn></mrow></math></span> vertices. The <em>h</em>-extra <em>r</em>-component diagnosability of <em>G</em>, denoted by <span><math><mrow><msubsup><mi>t</mi><mrow><mi>r</mi></mrow><mi>h</mi></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, is defined as the maximum integer <em>t</em> such that <em>G</em> is conditionally <em>t</em>-diagnosable under this constraint. We establish theoretical characterization for hypercube networks <em>Q<sub>n</sub></em> under the condition that there does not exist exactly one isolated node in <span><math><mrow><msub><mi>Q</mi><mi>n</mi></msub><mo>−</mo><mrow><mo>(</mo><msub><mi>F</mi><mn>1</mn></msub><mo>∪</mo><msub><mi>F</mi><mn>2</mn></msub><mo>)</mo></mrow></mrow></math></span> for two distinct sets <em>F</em><sub>1</sub>, <em>F</em><sub>2</sub>. Specifically, we show that <span><math><mrow><mn>4</mn><mi>n</mi><mo>−</mo><mn>8</mn><mo>≤</mo><msubsup><mi>t</mi><mrow><mn>2</mn></mrow><mn>1</mn></msubsup><mrow><mo>(</mo><msub><mi>Q</mi><mi>n</mi></msub><mo>)</mo></mrow><mo>≤</mo><mn>4</mn><mi>n</mi><mo>−</mo><mn>7</mn></mrow></math></span> for <em>n</em> ≥ 7 and <span><math><mrow><msubsup><mi>t</mi><mrow><mn>3</mn></mrow><mn>1</mn></msubsup><mrow><mo>(</mo><msub><mi>Q</mi><mi>n</mi></msub><mo>)</mo></mrow><mo>=</mo><mn>6</mn><mi>n</mi><mo>−</mo><mn>15</mn></mrow></math></span> for <em>n</em> ≥ 13 under the MM* diagnostic model. To enhance fault identification efficiency, we propose a two-stage diagnosis algorithm (TSDA-MM*), leveraging network structural properties to improve diagnostic accuracy and efficiency. Extensive simulation experiments on hypercube networks and the data center networks <em>Bcube</em>(<em>n, k</em>) demonstrate that TSDA-MM* achieves high performance in terms of <em>Accuracy, True</em> <em>Negative</em> <em>Rate, True</em> <em>Positive</em> <em>Rate</em>, and <em>Precision</em>, thereby providing a promising solution for practical fault diagnosis in large-scale systems.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1063 ","pages":"Article 115679"},"PeriodicalIF":1.0,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-07DOI: 10.1016/j.tcs.2025.115685
Taekang Eom , Seungjun Lee , Hee-Kap Ahn
Given a convex polygon with k vertices and a polygonal domain consisting of polygonal obstacles with n vertices in total in the plane, we study the optimization problem of finding a largest similar copy of the polygon that can be placed in the polygonal domain without intersecting the obstacles. We present an upper bound O(k2n2λ4(k)) on the number of combinatorial changes occurring to the underlying structure during the rotation of the polygon, together with an O(k2n2λ4(k)log n)-time deterministic algorithm for the problem, where λs(n) is the length of the longest Davenport–Schinzel sequence of order s including n distinct symbols. This improves upon the previously best known results by Chew and Kedem [SoCG89, CGTA93] and Sharir and Toledo [SoCG91, CGTA94] on the problem in more than 27 years. Our result also improves the time complexity of the high-clearance motion planning algorithm by Chew and Kedem.
{"title":"Largest similar copies of convex polygons in polygonal domains","authors":"Taekang Eom , Seungjun Lee , Hee-Kap Ahn","doi":"10.1016/j.tcs.2025.115685","DOIUrl":"10.1016/j.tcs.2025.115685","url":null,"abstract":"<div><div>Given a convex polygon with <em>k</em> vertices and a polygonal domain consisting of polygonal obstacles with <em>n</em> vertices in total in the plane, we study the optimization problem of finding a largest similar copy of the polygon that can be placed in the polygonal domain without intersecting the obstacles. We present an upper bound <em>O</em>(<em>k</em><sup>2</sup><em>n</em><sup>2</sup><em>λ</em><sub>4</sub>(<em>k</em>)) on the number of combinatorial changes occurring to the underlying structure during the rotation of the polygon, together with an <em>O</em>(<em>k</em><sup>2</sup><em>n</em><sup>2</sup><em>λ</em><sub>4</sub>(<em>k</em>)log <em>n</em>)-time deterministic algorithm for the problem, where <em>λ<sub>s</sub></em>(<em>n</em>) is the length of the longest Davenport–Schinzel sequence of order <em>s</em> including <em>n</em> distinct symbols. This improves upon the previously best known results by Chew and Kedem [SoCG89, CGTA93] and Sharir and Toledo [SoCG91, CGTA94] on the problem in more than 27 years. Our result also improves the time complexity of the high-clearance motion planning algorithm by Chew and Kedem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1063 ","pages":"Article 115685"},"PeriodicalIF":1.0,"publicationDate":"2025-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-06DOI: 10.1016/j.tcs.2025.115680
Ke Wang , Haodong Jiang , Zhenfeng Zhang , Long Chen , Huiqin Xie
Key reuse security is an important security property considered in the NIST post-quantum cryptography algorithm standardization. At PKC’20, Zhang et al. proposed Aigis.KEM, a key encapsulation mechanism based on asymmetric MLWE. Aigis.KEM provides flexible parameter selection, has high comprehensive performance, and won the first prize of the China’s National cryptographic algorithm competition. However, its key reuse security is currently unclear. This paper studies the key reuse security of Aigis.KEM. Aigis.KEM is derived from public key encryption Aigis.PKE, so we will first assess its key reuse resilience using key recovery under plaintext-checking attack (KR-PCA). Then, we optimize the attack and proposes a two-positional KR-PCA attack to further approach the lower bound of attack complexity. We also verify these attacks through experiments, and discuss the further optimization and improvement. Finally, based on the KR-PCA attacks on Aigis.PKE, we further propose practical attacks on Aigis.KEM by utilizing side-channel attacks or fault-injection attacks. In response to these attacks, we explored possible countermeasures. The work helps to clarify the potential risks of Aigis.KEM and guide its application in practice.
{"title":"Analysis of key reuse security for Aigis.KEM","authors":"Ke Wang , Haodong Jiang , Zhenfeng Zhang , Long Chen , Huiqin Xie","doi":"10.1016/j.tcs.2025.115680","DOIUrl":"10.1016/j.tcs.2025.115680","url":null,"abstract":"<div><div>Key reuse security is an important security property considered in the NIST post-quantum cryptography algorithm standardization. At PKC’20, Zhang et al. proposed Aigis.KEM, a key encapsulation mechanism based on asymmetric MLWE. Aigis.KEM provides flexible parameter selection, has high comprehensive performance, and won the first prize of the China’s National cryptographic algorithm competition. However, its key reuse security is currently unclear. This paper studies the key reuse security of Aigis.KEM. Aigis.KEM is derived from public key encryption Aigis.PKE, so we will first assess its key reuse resilience using key recovery under plaintext-checking attack (KR-PCA). Then, we optimize the attack and proposes a two-positional KR-PCA attack to further approach the lower bound of attack complexity. We also verify these attacks through experiments, and discuss the further optimization and improvement. Finally, based on the KR-PCA attacks on Aigis.PKE, we further propose practical attacks on Aigis.KEM by utilizing side-channel attacks or fault-injection attacks. In response to these attacks, we explored possible countermeasures. The work helps to clarify the potential risks of Aigis.KEM and guide its application in practice.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1063 ","pages":"Article 115680"},"PeriodicalIF":1.0,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-04DOI: 10.1016/j.tcs.2025.115681
Liuyu Yang , Xinxuan Zhang , Yi Deng , Zhuo Wu , Xudong Zhu
Registered attribute-based signature (registered ABS), introduced by Zhang et al. (PKC’24), eliminates the key escrow problem associated with classical attribute-based signature (ABS). It allows users to generate public/sectret key pairs themselves and register the related public key and attribute with a key curator. Different from a trusted attribute authority, the key curator is fully transparent and retains no secrets. In this paper, we propose the first generic framework for anonymous registered ABS that supports circuits as policies. We achieve this goal through an approach we call “accumulate-then-sign-then-prove”, which leverages commonly used cryptographic primitives including digital signature, accumulator, and non-interactive zero-knowledge schemes (NIZKs). We further enrich the functionality by adding user removal, making our scheme dynamic. Our generic framework can be instantiated from various combinations of inner and outer layer protocols based on different assumptions. We provide recommendations from three different perspectives for the choice of concrete cryptographic schemes. Compared with current work on registered ABS, our framework: i) provides diversity regarding the assumptions to instantiate cryptographic primitives; ii) has advantages in proof size and verification time.
{"title":"Anonymous registered attribute-based signature for circuits","authors":"Liuyu Yang , Xinxuan Zhang , Yi Deng , Zhuo Wu , Xudong Zhu","doi":"10.1016/j.tcs.2025.115681","DOIUrl":"10.1016/j.tcs.2025.115681","url":null,"abstract":"<div><div>Registered attribute-based signature (registered ABS), introduced by Zhang et al. (PKC’24), eliminates the key escrow problem associated with classical attribute-based signature (ABS). It allows users to generate public/sectret key pairs themselves and register the related public key and attribute with a key curator. Different from a trusted attribute authority, the key curator is fully transparent and retains no secrets. In this paper, we propose the first generic framework for anonymous registered ABS that supports circuits as policies. We achieve this goal through an approach we call “accumulate-then-sign-then-prove”, which leverages commonly used cryptographic primitives including digital signature, accumulator, and non-interactive zero-knowledge schemes (NIZKs). We further enrich the functionality by adding user removal, making our scheme dynamic. Our generic framework can be instantiated from various combinations of inner and outer layer protocols based on different assumptions. We provide recommendations from three different perspectives for the choice of concrete cryptographic schemes. Compared with current work on registered ABS, our framework: i) provides diversity regarding the assumptions to instantiate cryptographic primitives; ii) has advantages in proof size and verification time.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1063 ","pages":"Article 115681"},"PeriodicalIF":1.0,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-03DOI: 10.1016/j.tcs.2025.115678
Yuanrui Zhang , Xinxin Liu
We study a phenomenon called “image reflection” on a type of characterization graphs — LLEE charts — for 1-free regular expressions modulo bisimularity. This property, stating that the images of a bisimulation function from an LLEE chart actually impose a special LEE structure corresponding to the LLEE chart, is recognized by our proposed “well-structured looping-back charts” as a sub-LLEE-structure of LLEE charts. As an application, our study naturally leads to a novel proof for the completeness of the inference system for 1-free regular expressions, due to the correspondence between 1-free regular expressions and the provable solutions of LEE/LLEE charts. Compared to the previous approach, our proof is more direct in the sense that it does not rely on a graph transformation procedure on LLEE charts in which at each step two bisimilar nodes have to be carefully selected and merged together according to selection rules. Our observation on LLEE charts is useful to understand the completeness problems of regular expressions modulo bisimilarity from a new angle, and can be also helpful for solving the completeness problems of other expressions that share similar graph structures.
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Pub Date : 2025-11-29DOI: 10.1016/j.tcs.2025.115659
Chuanye Zheng, Liqiong Xu
The probability of vertex failure in interconnection networks will enhance with the increase of the system scale, so the fault diagnosis of interconnection networks deserves our attention and study. The diagnosability is a significant indicator to evaluate network reliability. For measuring the diagnosability of a given system more accurately, Ding et al. [1] came up with the non-inclusive diagnosability of a graph. Our work is to determine the lower bounds of non-inclusive diagnosability of a kind of networks under the PMC model and the MM* model, which can be applied to non-regular graphs and some graphs containing triangles. Finally, we propose the non-inclusive diagnosability of some famous networks under the two diagnostic models as applications.
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Pub Date : 2025-11-28DOI: 10.1016/j.tcs.2025.115645
Lyes Attouche , Mohamed-Amine Baazizi , Dario Colazzo , Giorgio Ghelli , Stefan Klessinger , Carlo Sartiani , Stefanie Scherzinger
<div><div>JSON Schema is a declarative language that allows one to specify the structure of JSON instances using hierarchical schema objects that combine logical and structural operators.2.2 Early versions of JSON Schema, known collectively as Classical JSON Schema, operated with a straightforward semantics where a schema’s meaning was completely determined by which JSON values it could successfully validate. This simple foundation enabled researchers to develop robust theoretical frameworks and practical tools for instance validation and also to determine whether schemas are satisfiable or equivalent to one another. However, Classical JSON Schema had a significant weakness in its inability to effectively express certain kinds of extensions of object schemas.</div><div>This limitation prompted a major overhaul in Draft 2019-09, introducing two new features that fundamentally alter how JSON Schema works. The first is <em>annotation dependency</em>, where validation now produces more than just a yes/no result. When a schema validates a JSON instance, it also generates an “annotation” that records which fields and items were “evaluated”. This annotation then influences the behavior of the new operators "<span><math><mi>unevaluatedProperties</mi></math></span>" and "<span><math><mi>unevaluatedItems</mi></math></span>", creating a dependency that did not exist before. The second feature is dynamic references, a separate mechanism that allows for the target of a reference operator to depend on the validation context. These changes were so substantial that all JSON Schema versions from Draft 2019-09 onward are called <em>Modern JSON Schema</em>.</div><div>This semantic shift invalidated much of the existing theoretical work, and the algorithms that researchers had developed for Classical JSON Schema — particularly those for determining satisfiability and schema inclusion — do not easily adapt to Modern JSON Schema’s new behavior. One approach to bridge this gap is “elimination” — converting Modern JSON Schema constructs back into equivalent Classical JSON Schema forms. Previous research successfully developed algorithms for eliminating dynamic references, but annotation dependency remained unsolved.</div><div>In this paper we solve this problem, providing three contributions: an <em>expressibility</em> result, proving that eliminating annotation-dependent operators is possible; a <em>succinctness</em> result, proving that eliminating annotation-dependent operators can generally cause schemas to grow exponentially in size, and finally a <em>practical algorithm</em> to perform annotation elimination.</div><div>Our “practical algorithm” not only matches the asymptotic lower-bound that is provided by the succinctness theorem, but it also presents some specific optimizations that we designed to exploit typical features or real-world schemas. A comprehensive experimental testing, executed on a representative set of 305 schemas retrieved from GitHub, shows tha
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