Vittorio Bilò , Marios Mavronicolas , Paul G. Spirakis
{"title":"The contest game for crowdsourcing reviews","authors":"Vittorio Bilò , Marios Mavronicolas , Paul G. Spirakis","doi":"10.1016/j.tcs.2025.115516","DOIUrl":"10.1016/j.tcs.2025.115516","url":null,"abstract":"<div><div>We consider a <em>contest game</em> with discrete strategies, modelling a contest where reviews for a <em>proposal</em> are crowdsourced from <em>n players</em>. Player <em>i</em> has a <em>skill</em> <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, strategically chooses a <em>quality</em> <span><math><mi>q</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>Q</mi><mo>}</mo></math></span> for her review and pays an <em>effort</em> <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>≥</mo><mn>0</mn></math></span>, strictly increasing with <em>q</em>. Under <em>voluntary participation,</em> a player may opt to not write a review, paying zero effort; <em>mandatory participation</em> excludes this option. For her effort, she is awarded a <em>payment</em> per her <em>payment function</em>, which is either <em>player-invariant</em>, like, e.g., the popular <em>proportional allocation</em>, or <em>player-specific</em>; it is <em>oblivious</em> when it does not depend on the loads on other qualities. The <em>utility</em> to player <em>i</em> is the difference between her payment and her <em>cost,</em> calculated by a <em>skill-effort</em> function <span><math><mi>Λ</mi><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></math></span>. Skills may vary for <em>arbitrary players</em>; when players are <em>anonymous</em>, <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span> for each player <em>i</em>. In a <em>pure Nash equilibrium,</em> no player could increase her utility by unilaterally switching to another quality. We show the following results about the (in)existence and the computation of a pure Nash equilibrium:<ul><li><span>•</span><span><div>A contest game with arbitrary players and player-invariant and oblivious payments is an unweighted <em>congestion game with player-specific constants</em> on parallel links <span><span>[42]</span></span>; so it has a generalized ordinal potential, the <em>Finite Improvement Property</em> (<em>FIP</em>) and a pure Nash equilibrium, which can be computed in <span><math><mi>PLS</mi></math></span>. However, under the assumption that the payment function is monotonically nonincreasing, a pure Nash equilibrium can be computed efficiently by resorting to <span><span>[44, Theorem 2]</span></span>.</div><div>In contrast, a pure Nash equilibrium might not exist for <em>(i)</em> anonymous players and player-invariant but not oblivious payments, <em>(ii)</em> arbitrary players and proportionally allocated payments, and <em>(iii)</em> anonymous players and player-specific and oblivious payments; in the latter case, it is <span><math><mi>NP</mi></math></span>-hard to decide existence even if players are anonymous. These counterexamples prove the tightness of our existence r","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1055 ","pages":"Article 115516"},"PeriodicalIF":1.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921828","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}
{"title":"On the minimal components of substitution subshifts","authors":"Raphaël Henry","doi":"10.1016/j.tcs.2025.115517","DOIUrl":"10.1016/j.tcs.2025.115517","url":null,"abstract":"<div><div>In this paper we study substitutions on <span><math><msup><mrow><mi>A</mi></mrow><mrow><mi>Z</mi></mrow></msup></math></span> where <em>A</em> is a finite alphabet. We precisely characterize the minimal components of substitution subshifts, give an optimal bound for their number and describe their dynamics. The explicitness of these results provides a method to algorithmically compute and count the minimal components of a given substitution subshift.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115517"},"PeriodicalIF":1.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890951","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}
{"title":"All for one and one for all: An O(1)-musketeers generic transformation for rotating robots","authors":"Matthew Connor , Othon Michail , George Skretas","doi":"10.1016/j.tcs.2025.115521","DOIUrl":"10.1016/j.tcs.2025.115521","url":null,"abstract":"<div><div>In this paper, we study the main open question of [Michail, Skretas, Spirakis, ICALP'17], asking what are the families of two-dimensional geometric shapes, drawn on a square grid, that can be transformed into each other by a sequence of rotation operations, none of which disconnects the shape. The model represents programmable matter systems consisting of interconnected robotic modules that perform the minimal mechanical operation of 90° rotations around each other. The goal is to transform an initial connected shape of modules <em>A</em> into a target connected shape <em>B</em>. Under the necessary assumption that the two shapes have identical colour cardinalities on a checkered colouring of the grid, and using at most a constant number of auxiliary modules to trigger the transformation, we prove that almost any pair of such shapes can be transformed into each other within an optimal <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> rotation operations none of which disconnects the shape.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115521"},"PeriodicalIF":1.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893039","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}
{"title":"The traveling tournament problem: Improved algorithms based on cycle packing","authors":"Jingyang Zhao, Mingyu Xiao, Chao Xu","doi":"10.1016/j.tcs.2025.115519","DOIUrl":"10.1016/j.tcs.2025.115519","url":null,"abstract":"<div><div>The Traveling Tournament Problem (TTP) is a well-known benchmark problem in the field of tournament timetabling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, minimizing the total distance traveled by all <em>n</em> teams (<em>n</em> is even). TTP-<em>k</em> is the problem with one more constraint that each team can have at most <em>k</em>-consecutive home games or away games. In this paper, we investigate schedules for TTP-<em>k</em> and analyze the approximation ratio of the solutions. Most previous schedules were constructed based on a Hamiltonian cycle of the graph. We will propose a novel construction based on a <em>k</em>-cycle packing. Then, combining our <em>k</em>-cycle packing schedule with the Hamiltonian cycle schedule, we obtain improved approximation ratios for TTP-<em>k</em> with deep analysis. The case where <span><math><mi>k</mi><mo>=</mo><mn>3</mn></math></span>, TTP-3, is one of the most investigated cases. We improve the approximation ratio of TTP-3 from <span><math><mo>(</mo><mn>1.667</mn><mo>+</mo><mi>ε</mi><mo>)</mo></math></span> to <span><math><mo>(</mo><mn>1.598</mn><mo>+</mo><mi>ε</mi><mo>)</mo></math></span>, for any <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span>. For TTP-4, we improve the approximation ratio from <span><math><mo>(</mo><mn>1.750</mn><mo>+</mo><mi>ε</mi><mo>)</mo></math></span> to <span><math><mo>(</mo><mn>1.700</mn><mo>+</mo><mi>ε</mi><mo>)</mo></math></span>. By a refined analysis of the Hamiltonian cycle construction, we also improve the approximation ratio of TTP-<em>k</em> from <span><math><mo>(</mo><mfrac><mrow><mn>5</mn><mi>k</mi><mo>−</mo><mn>7</mn></mrow><mrow><mn>2</mn><mi>k</mi></mrow></mfrac><mo>+</mo><mi>ε</mi><mo>)</mo></math></span> to <span><math><mo>(</mo><mfrac><mrow><mn>5</mn><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mi>k</mi><mo>+</mo><mn>3</mn></mrow><mrow><mn>2</mn><mi>k</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>+</mo><mi>ε</mi><mo>)</mo></math></span> for any constant <span><math><mi>k</mi><mo>≥</mo><mn>5</mn></math></span>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115519"},"PeriodicalIF":1.0,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886693","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}
Daniel Gibney , Paul MacNichol , Sharma V. Thankachan
{"title":"Non-overlapping indexing in BWT-runs bounded space","authors":"Daniel Gibney , Paul MacNichol , Sharma V. Thankachan","doi":"10.1016/j.tcs.2025.115512","DOIUrl":"10.1016/j.tcs.2025.115512","url":null,"abstract":"<div><div>We revisit the non-overlapping indexing problem for an efficient repetition-aware solution. The problem is to index a text <span><math><mi>T</mi><mo>[</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi><mo>]</mo></math></span>, such that whenever a pattern <span><math><mi>P</mi><mo>[</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>p</mi><mo>]</mo></math></span> comes as a query, we can report the largest set of non-overlapping occurrences of <em>P</em> in <em>T</em>. A previous index by Cohen and Porat [ISAAC 2009] takes linear space and optimal <span><math><mi>O</mi><mo>(</mo><mi>p</mi><mo>+</mo><mrow><mi>oc</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>no</mi></mrow></msub></mrow><mo>)</mo></math></span> query time, where <span><math><mi>oc</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>no</mi></mrow></msub></math></span> denotes the output size. We present an index of size <span><math><mi>O</mi><mo>(</mo><mi>r</mi><mo>)</mo></math></span>, where <em>r</em> denotes the number of runs in the Burrows Wheeler Transform (BWT) of <em>T</em>. The parameter <em>r</em> is significantly smaller than <em>n</em> for highly repetitive texts. The query time of our index is <span><math><mi>O</mi><mo>(</mo><mi>p</mi><mi>log</mi><mo></mo><msub><mrow><mi>log</mi></mrow><mrow><mi>w</mi></mrow></msub><mo></mo><mi>σ</mi><mo>+</mo><mrow><mi>sort</mi></mrow><mo>(</mo><mrow><mi>oc</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>no</mi></mrow></msub></mrow><mo>)</mo><mo>)</mo></math></span>, where <em>σ</em> denotes the alphabet size, <em>w</em> denotes the machine word size in bits and <span><math><mrow><mi>sort</mi></mrow><mo>(</mo><mi>x</mi><mo>)</mo></math></span> denotes the time for sorting <em>x</em> integers within the range <span><math><mo>[</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>]</mo></math></span>. We also study the counting version of this problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115512"},"PeriodicalIF":1.0,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865698","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}
Nina Klobas , George B. Mertzios , Hendrik Molter , Paul G. Spirakis
{"title":"Temporal graph realization from fastest paths","authors":"Nina Klobas , George B. Mertzios , Hendrik Molter , Paul G. Spirakis","doi":"10.1016/j.tcs.2025.115508","DOIUrl":"10.1016/j.tcs.2025.115508","url":null,"abstract":"<div><div>In this paper, we initiate the study of the <em>temporal graph realization</em> problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrix <em>D</em> and a <span><math><mi>Δ</mi><mo>∈</mo><mi>N</mi></math></span>, the goal is to construct a Δ-periodic temporal graph with <em>n</em> vertices such that the duration of a <em>fastest path</em> from <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> to <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> is equal to <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span>, or to decide that such a temporal graph does not exist. The variations of the problem on static graphs have been well studied and understood since the 1960s (e.g. [Erdős and Gallai, 1960], [Hakimi and Yau, 1965]). As it turns out, the periodic temporal graph realization problem has a very different computational complexity behavior than its static (i.e., non-temporal) counterpart.</div><div>First, we show that the problem is NP-hard in general, but polynomial-time solvable if the so-called underlying graph is a tree. Building upon those results, we investigate its parameterized computational complexity with respect to structural parameters of the underlying static graph which measure the “tree-likeness”. We prove a tight classification between such parameters that allow fixed-parameter tractability (FPT) and those which imply W[1]-hardness. We show that our problem is W[1]-hard when parameterized by the <em>feedback vertex number</em> (and therefore also any smaller parameter such as <em>treewidth</em>, <em>degeneracy</em>, and <em>cliquewidth</em>) of the underlying graph, while we show that it is in FPT when parameterized by the <em>feedback edge number</em> (and therefore also any larger parameter such as <em>maximum leaf number</em>) of the underlying graph.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115508"},"PeriodicalIF":1.0,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860208","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}
Robert M. Alaniz , Bin Fu , Timothy Gomez , Elise Grizzell , Andrew Rodriguez , Marco Rodriguez , Robert Schweller , Tim Wylie
{"title":"Reachability in restricted chemical reaction networks","authors":"Robert M. Alaniz , Bin Fu , Timothy Gomez , Elise Grizzell , Andrew Rodriguez , Marco Rodriguez , Robert Schweller , Tim Wylie","doi":"10.1016/j.tcs.2025.115514","DOIUrl":"10.1016/j.tcs.2025.115514","url":null,"abstract":"<div><div>The popularity of molecular computation has given rise to several models of abstraction, one of the more recent ones being Chemical Reaction Networks (CRNs). These are equivalent to other popular computational models, such as Vector Addition Systems and Petri-Nets, and restricted versions are equivalent to Population Protocols. This paper continues the work on core <em>reachability</em> questions related to Chemical Reaction Networks; given two configurations, can one reach the other according to the system's rules? With no restrictions, reachability was recently shown to be Ackermann-complete, which resolved a decades-old problem.</div><div>In this work, we fully characterize monotone reachability problems based on various restrictions such as the allowed rule size, the number of rules that may create a species (<em>k</em>-source), the number of rules that may consume a species (<em>k</em>-consuming), the volume, and whether the rules have an acyclic production order (<em>feed-forward</em>). We show PSPACE-completeness of reachability with only bimolecular reactions in two-source and two-consuming rules. This proves hardness of reachability in a restricted form of Population Protocols. This is accomplished using new techniques within the motion planning framework.</div><div>We give several important results for feed-forward CRNs, where rules are single-source or single-consuming. We show that reachability is solvable in polynomial time as long as the system does not contain special <em>void</em> or <em>autogenesis</em> rules. We then fully characterize all systems of this type and show that with void/autogenesis rules, or more than one source and one consuming, the problems become NP-complete. Finally, we show several interesting special cases of CRNs based on these restrictions or slight relaxations and note future significant open questions related to this taxonomy.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115514"},"PeriodicalIF":1.0,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829614","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}
{"title":"Approximate Cartesian tree pattern matching","authors":"Sungmin Kim, Yo-Sub Han","doi":"10.1016/j.tcs.2025.115506","DOIUrl":"10.1016/j.tcs.2025.115506","url":null,"abstract":"<div><div>The Cartesian tree of a string is a binary tree, which is useful in capturing minimalities within strings. We study the approximate pattern matching problem for two Cartesian trees of two strings. We design a polynomial-time algorithm that computes the minimum edit cost when a given string is edited to match the Cartesian tree of the other string. We also design a linear-time algorithm that computes the (max,min)-convolution between two sorted arrays, which we use to speed up the algorithm computing the edit cost. Then, we adapt the algorithm that computes the edit cost to the approximate pattern matching problem, where we find all substrings of a given text that match a given Cartesian tree pattern within a given number of edit operations. We also consider variant problems such as the approximate Cartesian matching under Hamming distance, and present polynomial-time algorithms for the considered problems.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115506"},"PeriodicalIF":1.0,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860207","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}
Aixia Liu, Shuchang Chai, Lina Li, Chenhui Liang, Jun Yuan
{"title":"The local diagnosability of directed interconnection networks","authors":"Aixia Liu, Shuchang Chai, Lina Li, Chenhui Liang, Jun Yuan","doi":"10.1016/j.tcs.2025.115504","DOIUrl":"10.1016/j.tcs.2025.115504","url":null,"abstract":"<div><div>The diagnosability is a vital parameter to measure the self-fault diagnosis ability of interconnection networks of computer systems. The local diagnosability is a generalization of diagnosability, which focuses on the fault diagnosability at a given processor. In this paper, we discuss the local diagnosability and the good in-neighbor conditional local diagnosability of directed networks, and present some necessary and sufficient conditions for a directed network to be locally <em>ζ</em>-diagnosable or good in-neighbor conditional locally <em>ζ</em>-diagnosable at a processor. We also present an algorithm under the PMC model to determine the fault or fault-free state of a given processor in a directed network. As an empirical testing, we demonstrate that our algorithm can ascertain the state of each vertex of unidirectional hypercube <span><math><mi>U</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> if the number of faulty vertices is not more than <span><math><mi>n</mi><mo>−</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115504"},"PeriodicalIF":1.0,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144813849","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}
{"title":"Full-grained proxy re-encryption for all circuits","authors":"Yuxin Zhang , Shengli Liu , Yunxiao Zhou , Haibin Zhang","doi":"10.1016/j.tcs.2025.115507","DOIUrl":"10.1016/j.tcs.2025.115507","url":null,"abstract":"<div><div>In this paper, we proposed a new concept called <em>Full-Grained PRE</em> (FG-PRE) to which a function set <span><math><mi>F</mi></math></span> is attached. With FG-PRE, a delegator authorizes the proxy a full-grained re-encryption capability for <span><math><mi>F</mi></math></span> with a <em>single</em> re-encryption key <span><math><mi>r</mi><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi><mo>→</mo><mi>j</mi></mrow></msub></math></span>. Then, the proxy can use this <em>single</em> re-encryption key to transform <span><math><mi>c</mi><msup><mrow><mi>t</mi></mrow><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msup></math></span> encrypting message <em>m</em> for delegator <em>i</em> into an re-encrypted ciphertext <span><math><mi>c</mi><msup><mrow><mi>t</mi></mrow><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow></msup></math></span> encrypting <span><math><mi>f</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></span> with <em>arbitrary</em> <span><math><mi>f</mi><mo>∈</mo><mi>F</mi></math></span> for delegatee <em>j</em>. Thus, the proxy has a full-grained (w.r.t. <span><math><mi>F</mi></math></span>) control of the information that can be transmitted to the delegatee <em>j</em>. This is in sharp contrast to fine-grained PRE (Zhou et al. ASIACRYPT 2023), which has to generate <em>different</em> re-encryption keys to support different functions. In their fine-grained PRE, the number of re-encryption keys generated by delegator and stored by the proxy for <span><math><mi>F</mi></math></span> is linear to the size <span><math><mo>|</mo><mi>F</mi><mo>|</mo></math></span>. With our full-grained PRE, a single re-encryption key suffices.</div><div>We formalize the syntax of FG-PRE and define <span><math><mi>HRA</mi></math></span> security (security under honest re-encryption attack) and function private <span><math><mi>HRA</mi></math></span> security (<span><math><mi>FP</mi><mtext>-</mtext><mi>HRA</mi></math></span>) for FG-PRE. Compared to the <span><math><mi>CPA</mi></math></span> security (Zhou et al. ASIACRYPT 2023) and the <span><math><mi>HRA</mi></math></span> security (Zhou et al. PKC 2024) defined for the fine-grained PRE, our <span><math><mi>HRA</mi></math></span> security not only allows adversary to obtain re-encryption keys from honest users to corrupted users, but also has an enhancement: we even allow the adversary to query full-grained re-encryptions with <em>f</em> for the challenge ciphertext under the condition <span><math><mi>f</mi><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span>. We construct a FG-PRE scheme <span><math><msup><mrow><mtext>FG-PRE</mtext></mrow><mrow><mtext>lin</mtext></mrow></msup></math></span> for bounded linear function <span><math><msub><mrow><mi>F</mi></mrow><mrow><mtext>lin</mtext></mrow></msub></math></span>, enjoying single-hop, unidirectional and non-interactive properties.","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115507"},"PeriodicalIF":1.0,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829613","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}
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