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An algebraic attack on the key exchange protocol based upon a modified tropical structure
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-28 DOI: 10.1016/j.ic.2024.105259
J. Jackson, R. Perumal
{"title":"An algebraic attack on the key exchange protocol based upon a modified tropical structure","authors":"J. Jackson,&nbsp;R. Perumal","doi":"10.1016/j.ic.2024.105259","DOIUrl":"10.1016/j.ic.2024.105259","url":null,"abstract":"<div><div>In this paper, we analyze the key exchange protocol based on an algebraic structure derived from a tropical semiring. The security of this key exchange scheme depends on an attacker's inability to solve a system of non-linear equations to obtain the private parameters. However, we propose an algebraic attack on this key exchange scheme using only the public parameters. We thoroughly evaluate the protocol's security against algebraic attacks through comprehensive cryptanalysis. We study the behavior of matrix sequences produced during key exchange, looking for any almost linear periodicity property that could affect the cryptanalysis. We provide the algorithm and an example to illustrate our attack, demonstrating that this key exchange protocol is not secure. Additionally, we examine how different parameter selections and matrix sizes impact the protocol's security. Ultimately, this cryptanalysis enhances tropical cryptography by expanding our understanding of the security implications of modified tropical semiring-based key exchange protocols.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105259"},"PeriodicalIF":0.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759453","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}
引用次数: 0
Distributed fractional local ratio and independent set approximation 分布式分数局部比率和独立集近似值
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-22 DOI: 10.1016/j.ic.2024.105238
Magnús M. Halldórsson , Dror Rawitz
{"title":"Distributed fractional local ratio and independent set approximation","authors":"Magnús M. Halldórsson ,&nbsp;Dror Rawitz","doi":"10.1016/j.ic.2024.105238","DOIUrl":"10.1016/j.ic.2024.105238","url":null,"abstract":"<div><div>We consider the <span>Maximum Weight Independent Set</span> problem, with a focus on obtaining good approximations for graphs of small maximum degree Δ. We give deterministic local algorithms running in time <span><math><mi>poly</mi><mo>(</mo><mi>Δ</mi><mo>,</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> that come close to matching the best centralized results known and improve the previous distributed approximations by a factor of about 2. More precisely, we obtain approximations below <span><math><mfrac><mrow><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, and a further improvement to <span><math><mn>8</mn><mo>/</mo><mn>5</mn><mo>+</mo><mi>ε</mi></math></span> when <span><math><mi>Δ</mi><mo>=</mo><mn>3</mn></math></span>.</div><div>Technically, this is achieved by leveraging the <em>fractional local ratio</em> technique, for a first application in a distributed setting.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105238"},"PeriodicalIF":0.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723840","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}
引用次数: 0
A parallel algorithm for counting parse trees 解析树计数并行算法
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-19 DOI: 10.1016/j.ic.2024.105237
Margarita Mikhelson, Alexander Okhotin
{"title":"A parallel algorithm for counting parse trees","authors":"Margarita Mikhelson,&nbsp;Alexander Okhotin","doi":"10.1016/j.ic.2024.105237","DOIUrl":"10.1016/j.ic.2024.105237","url":null,"abstract":"<div><div>A parallel algorithm for computing the number of parse trees of a given string according to a fixed context-free grammar is defined. More generally, the algorithm applies to computing the weight of a string in a weighted grammar over any semiring. The algorithm is first implemented on an arithmetic circuit of depth at most <span><math><mn>6</mn><msup><mrow><mo>(</mo><msub><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⁡</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> and with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></math></span> elements, where the constant factors in the big-O notation depend on the grammar. Then, the circuit is improved using fast matrix multiplication to use only <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>5.38</mn></mrow></msup><mo>)</mo></math></span> elements, while preserving depth <span><math><mi>O</mi><mo>(</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105237"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723839","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}
引用次数: 0
Asymptotically optimal synthesis of reversible circuits 可逆电路的渐进优化合成
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-08 DOI: 10.1016/j.ic.2024.105235
Xian Wu, Lvzhou Li
{"title":"Asymptotically optimal synthesis of reversible circuits","authors":"Xian Wu,&nbsp;Lvzhou Li","doi":"10.1016/j.ic.2024.105235","DOIUrl":"10.1016/j.ic.2024.105235","url":null,"abstract":"<div><div>Reversible circuits have been studied extensively and intensively, and have plenty of applications in various areas, such as digital signal processing, cryptography, and especially quantum computing. In 2003, the lower bound <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> for the synthesis of <em>n</em>-wire reversible circuits was proved. Whether this lower bound has a matching upper bound was listed as one of the future challenging open problems in the survey (Saeedi and Markov (2013) <span><span>[1]</span></span>). In this paper we propose an algorithm to implement an arbitrary <em>n</em>-wire reversible circuit with no more than <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> elementary gates, and thus close the open problem.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105235"},"PeriodicalIF":0.8,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655748","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}
引用次数: 0
Non-linear communication via graded modal session types 通过分级模式会话类型进行非线性交流
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-04 DOI: 10.1016/j.ic.2024.105234
Danielle Marshall , Dominic Orchard
{"title":"Non-linear communication via graded modal session types","authors":"Danielle Marshall ,&nbsp;Dominic Orchard","doi":"10.1016/j.ic.2024.105234","DOIUrl":"10.1016/j.ic.2024.105234","url":null,"abstract":"<div><div>Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, strict linearity is limiting since there exist useful communication patterns that rely on non-linear behaviours. For example, shared channels can repeatedly spawn a process with binary communication along a fresh linear channel. Non-linearity can be introduced in a controlled way through the concept of <em>graded modal types</em>, which are a framework encompassing various kinds of <em>coeffect</em> (describing how computations make demands on their context). This paper shows how graded modalities can work alongside session types, enabling various non-linear concurrency behaviours to be re-introduced precisely. The ideas are demonstrated using Granule, a functional language with linear, indexed, and graded modal types. We define a core calculus capturing the requisite features and our new graded primitives, then present an operational model and establish various key properties.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105234"},"PeriodicalIF":0.8,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Systems of fixpoint equations: Abstraction, games, up-to techniques and local algorithms 定点方程系统：抽象、博弈、向上技术和局部算法
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-10-24 DOI: 10.1016/j.ic.2024.105233
Paolo Baldan , Barbara König , Tommaso Padoan
{"title":"Systems of fixpoint equations: Abstraction, games, up-to techniques and local algorithms","authors":"Paolo Baldan ,&nbsp;Barbara König ,&nbsp;Tommaso Padoan","doi":"10.1016/j.ic.2024.105233","DOIUrl":"10.1016/j.ic.2024.105233","url":null,"abstract":"<div><div>Systems of fixpoint equations over complete lattices, which combine least and greatest fixpoints, often arise from verification tasks such as model checking and behavioural equivalence checking. In this paper we develop a theory of approximation in the style of abstract interpretation, where a system over some concrete domain is abstracted into a system on a suitable abstract domain, ensuring sound and possibly complete over-approximations of the solutions. We also show how up-to techniques, commonly used to simplify coinductive proofs, fit into this framework, interpreted as abstractions. Additionally, we characterise the solution of fixpoint equation systems through parity games, extending prior work limited to continuous lattices. This game-based approach allows for local algorithms that verify system properties, such as determining whether a state satisfies a formula or two states are behaviourally equivalent. We describe a local algorithm, that can be combined with abstraction and up-to techniques to speed up the computation.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105233"},"PeriodicalIF":0.8,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unifying lower bounds for algebraic machines, semantically 代数机器的统一下界，语义上
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-10-21 DOI: 10.1016/j.ic.2024.105232
Thomas Seiller , Luc Pellissier , Ulysse Léchine
{"title":"Unifying lower bounds for algebraic machines, semantically","authors":"Thomas Seiller ,&nbsp;Luc Pellissier ,&nbsp;Ulysse Léchine","doi":"10.1016/j.ic.2024.105232","DOIUrl":"10.1016/j.ic.2024.105232","url":null,"abstract":"<div><div>We present a new abstract method for proving lower bounds in computational complexity based on the notion of topological and measurable entropy for dynamical systems. It is shown to generalise several previous lower bounds results from the literature in algebraic complexity, thus providing a unifying framework for “topological” proofs of lower bounds. We further use this method to prove that <span>maxflow</span>, a <figure><img></figure> complete problem, is not computable in polylogarithmic time on parallel random access machines (<span>pram</span>s) working with real numbers. This improves on a result of Mulmuley since the class of machines considered extends the class “<span>pram</span>s without bit operations”, making more precise the relationship between Mulmuley's result and similar lower bounds on real <span>pram</span>s.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105232"},"PeriodicalIF":0.8,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Introducing variables in the evolution rules of P systems 在 P 系统的进化规则中引入变量
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-10-16 DOI: 10.1016/j.ic.2024.105231
Bogdan Aman
{"title":"Introducing variables in the evolution rules of P systems","authors":"Bogdan Aman","doi":"10.1016/j.ic.2024.105231","DOIUrl":"10.1016/j.ic.2024.105231","url":null,"abstract":"<div><div>In membrane systems evolution rules are constructed using only objects from a finite alphabet. In this paper we investigate rules in which variables are used. Namely, we define Variable P systems in which the rules containing variables need to be instantiated at the start of each computational step with values from some predefined sets of sets of objects.</div><div>The modelling power of variable P systems is described by simulating some basic arithmetic operations over a (multi)set of positive numbers (addition, multiplication, or a combination of them). The main advantage of using variable P systems consists in the small number of used rules regardless how many numbers are involved in the operation: e.g., the addition requires only 3 rules, while the multiplication only 27 rules.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105231"},"PeriodicalIF":0.8,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530570","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}
引用次数: 0
Perspective on complexity measures targeting read-once branching programs 以只读分支程序为目标的复杂性测量透视
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-10-15 DOI: 10.1016/j.ic.2024.105230
Yaqiao Li , Pierre McKenzie
{"title":"Perspective on complexity measures targeting read-once branching programs","authors":"Yaqiao Li ,&nbsp;Pierre McKenzie","doi":"10.1016/j.ic.2024.105230","DOIUrl":"10.1016/j.ic.2024.105230","url":null,"abstract":"<div><div>A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and studied. Some new or simpler proofs of known bounds are uncovered. Branching program resources and the new measures are compared extensively. The new variants are developed in part in the hope of tackling read-<em>k</em> branching programs for the tree evaluation problem. Other computation problems are studied as well. In particular, a common view of a function studied by Gál and a function studied by Bollig and Wegener leads to the general combinatorics of blocking sets. Technical combinatorial results of independent interest are obtained. New leads towards further progress are discussed. An exponential lower bound for non-deterministic read-<em>k</em> branching programs for the GEN function is also derived, independently from the new measures.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105230"},"PeriodicalIF":0.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530571","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}
引用次数: 0
Different strokes in randomised strategies: Revisiting Kuhn's theorem under finite-memory assumptions 随机策略中的不同招数：在有限记忆假设下重温库恩定理
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-10-10 DOI: 10.1016/j.ic.2024.105229
James C.A. Main , Mickael Randour
{"title":"Different strokes in randomised strategies: Revisiting Kuhn's theorem under finite-memory assumptions","authors":"James C.A. Main ,&nbsp;Mickael Randour","doi":"10.1016/j.ic.2024.105229","DOIUrl":"10.1016/j.ic.2024.105229","url":null,"abstract":"<div><div>Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis.</div><div>Optimal strategies may require randomisation when dealing with inherently probabilistic goals, balancing multiple objectives, or in contexts of partial information. There is no unique way to define randomised strategies. For instance, one can use so-called <em>mixed</em> strategies or <em>behavioural</em> ones. In the most general setting, these two classes do not share the same expressiveness. A seminal result in game theory — <em>Kuhn's theorem</em> — asserts their equivalence in games of perfect recall.</div><div>This result crucially relies on the possibility for strategies to use <em>infinite memory</em>, i.e., unlimited knowledge of all past observations. However, computer systems are finite in practice. Hence it is pertinent to restrict our attention to <em>finite-memory</em> strategies, defined as automata with outputs. Randomisation can be implemented in these in different ways: the <em>initialisation</em>, <em>outputs</em> or <em>transitions</em> can be randomised or deterministic respectively. Depending on which aspects are randomised, the expressiveness of the corresponding class of finite-memory strategies differs.</div><div>In this work, we study two-player concurrent stochastic games and provide a complete taxonomy of the classes of finite-memory strategies obtained by varying which of the three aforementioned components are randomised. Our taxonomy holds in games of perfect and imperfect information with perfect recall, and in games with more than two players. We also provide an adapted taxonomy for games with imperfect recall.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105229"},"PeriodicalIF":0.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441057","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}
引用次数: 0
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