We introduce the notion of “non-malleable codes” which relaxes the notion of error correction and error detection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In contrast to error correction and error detection, non-malleability can be achieved for very rich classes of modifications. We construct an efficient code that is non-malleable with respect to modifications that affect each bit of the codeword arbitrarily (i.e., leave it untouched, flip it, or set it to either 0 or 1), but independently of the value of the other bits of the codeword. Using the probabilistic method, we also show a very strong and general statement: there exists a non-malleable code for every “small enough” family F of functions via which codewords can be modified. Although this probabilistic method argument does not directly yield efficient constructions, it gives us efficient non-malleable codes in the random-oracle model for very general classes of tampering functions—e.g., functions where every bit in the tampered codeword can depend arbitrarily on any 99% of the bits in the original codeword. As an application of non-malleable codes, we show that they provide an elegant algorithmic solution to the task of protecting functionalities implemented in hardware (e.g., signature cards) against “tampering attacks.” In such attacks, the secret state of a physical system is tampered, in the hopes that future interaction with the modified system will reveal some secret information. This problem was previously studied in the work of Gennaro et al. in 2004 under the name “algorithmic tamper proof security” (ATP). We show that non-malleable codes can be used to achieve important improvements over the prior work. In particular, we show that any functionality can be made secure against a large class of tampering attacks, simply by encoding the secret state with a non-malleable code while it is stored in memory.
{"title":"Non-Malleable Codes","authors":"Stefan Dziembowski, Krzysztof Pietrzak, D. Wichs","doi":"10.1145/3178432","DOIUrl":"https://doi.org/10.1145/3178432","url":null,"abstract":"We introduce the notion of “non-malleable codes” which relaxes the notion of error correction and error detection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In contrast to error correction and error detection, non-malleability can be achieved for very rich classes of modifications. We construct an efficient code that is non-malleable with respect to modifications that affect each bit of the codeword arbitrarily (i.e., leave it untouched, flip it, or set it to either 0 or 1), but independently of the value of the other bits of the codeword. Using the probabilistic method, we also show a very strong and general statement: there exists a non-malleable code for every “small enough” family F of functions via which codewords can be modified. Although this probabilistic method argument does not directly yield efficient constructions, it gives us efficient non-malleable codes in the random-oracle model for very general classes of tampering functions—e.g., functions where every bit in the tampered codeword can depend arbitrarily on any 99% of the bits in the original codeword. As an application of non-malleable codes, we show that they provide an elegant algorithmic solution to the task of protecting functionalities implemented in hardware (e.g., signature cards) against “tampering attacks.” In such attacks, the secret state of a physical system is tampered, in the hopes that future interaction with the modified system will reveal some secret information. This problem was previously studied in the work of Gennaro et al. in 2004 under the name “algorithmic tamper proof security” (ATP). We show that non-malleable codes can be used to achieve important improvements over the prior work. In particular, we show that any functionality can be made secure against a large class of tampering attacks, simply by encoding the secret state with a non-malleable code while it is stored in memory.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"67 5","pages":"1 - 32"},"PeriodicalIF":0.0,"publicationDate":"2018-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91477331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O(√ log Δ)+ 2O(√log log n) rounds in a graph of maximum degree Δ. This implies that the (Δ +1)-coloring problem is easier than the maximal independent set problem and the maximal matching problem, due to their lower bounds of Ω(min(√/log n log log n, /log Δ log log Δ)) by Kuhn, Moscibroda, and Wattenhofer [PODC’04]. Our algorithm also extends to list-coloring where the palette of each node contains Δ +1 colors. We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.
{"title":"Distributed (Δ +1)-Coloring in Sublogarithmic Rounds","authors":"David G. Harris, Johannes Schneider, Hsin-Hao Su","doi":"10.1145/3178120","DOIUrl":"https://doi.org/10.1145/3178120","url":null,"abstract":"We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O(√ log Δ)+ 2O(√log log n) rounds in a graph of maximum degree Δ. This implies that the (Δ +1)-coloring problem is easier than the maximal independent set problem and the maximal matching problem, due to their lower bounds of Ω(min(√/log n log log n, /log Δ log log Δ)) by Kuhn, Moscibroda, and Wattenhofer [PODC’04]. Our algorithm also extends to list-coloring where the palette of each node contains Δ +1 colors. We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"17 1","pages":"1 - 21"},"PeriodicalIF":0.0,"publicationDate":"2018-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90836009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Flavio Chierichetti, George Giakkoupis, Silvio Lattanzi, A. Panconesi
In this article, we study the completion time of the PUSH-PULL variant of rumor spreading, also known as randomized broadcast. We show that if a network has n nodes and conductance φ then, with high probability, PUSH-PULL will deliver the message to all nodes in the graph within O(log n/φ) many communication rounds. This bound is best possible. We also give an alternative proof that the completion time of PUSH-PULL is bounded by a polynomial in log n/φ, based on graph sparsification. Although the resulting asymptotic bound is not optimal, this proof shows an interesting and, at the outset, unexpected connection between rumor spreading and graph sparsification. Finally, we show that if the degrees of the two endpoints of each edge in the network differ by at most a constant factor, then both PUSH and PULL alone attain the optimal completion time of O(log n/φ), with high probability.
{"title":"Rumor Spreading and Conductance","authors":"Flavio Chierichetti, George Giakkoupis, Silvio Lattanzi, A. Panconesi","doi":"10.1145/3173043","DOIUrl":"https://doi.org/10.1145/3173043","url":null,"abstract":"In this article, we study the completion time of the PUSH-PULL variant of rumor spreading, also known as randomized broadcast. We show that if a network has n nodes and conductance φ then, with high probability, PUSH-PULL will deliver the message to all nodes in the graph within O(log n/φ) many communication rounds. This bound is best possible. We also give an alternative proof that the completion time of PUSH-PULL is bounded by a polynomial in log n/φ, based on graph sparsification. Although the resulting asymptotic bound is not optimal, this proof shows an interesting and, at the outset, unexpected connection between rumor spreading and graph sparsification. Finally, we show that if the degrees of the two endpoints of each edge in the network differ by at most a constant factor, then both PUSH and PULL alone attain the optimal completion time of O(log n/φ), with high probability.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"1 1","pages":"1 - 21"},"PeriodicalIF":0.0,"publicationDate":"2018-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89805951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Invited Article section of this issue consists of the article “Worst-Case Optimal Join Algorithms” by Hung Q. Ngo, Ely Porat, Christopher Ré, and Atri Rudra, which won the best paper award at the 35th Annual ACM SIGMOD/PODS International Conference on Management of Data (PODS’12). We would like to thank the PODS’12 Program Committee for their help in selecting this invited work, and we also thank editor Phokion Kolaitis for handling the paper.
本期特邀文章部分由Hung Q. Ngo, Ely Porat, Christopher r和Atri Rudra的文章“最坏情况下最优连接算法”组成，该文章在第35届ACM SIGMOD/PODS国际数据管理会议(PODS ' 12)上获得最佳论文奖。我们要感谢PODS ' 12 Program Committee在选择这篇受邀作品时的帮助，我们也要感谢编辑Phokion Kolaitis对论文的处理。
{"title":"Invited Article Foreword","authors":"É. Tardos","doi":"10.1145/3186892","DOIUrl":"https://doi.org/10.1145/3186892","url":null,"abstract":"The Invited Article section of this issue consists of the article “Worst-Case Optimal Join Algorithms” by Hung Q. Ngo, Ely Porat, Christopher Ré, and Atri Rudra, which won the best paper award at the 35th Annual ACM SIGMOD/PODS International Conference on Management of Data (PODS’12). We would like to thank the PODS’12 Program Committee for their help in selecting this invited work, and we also thank editor Phokion Kolaitis for handling the paper.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"5 1","pages":"1 - 1"},"PeriodicalIF":0.0,"publicationDate":"2018-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78479905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that the existence of a coin-flipping protocol safe against any nontrivial constant bias (e.g., .499) implies the existence of one-way functions. This improves upon a result of Haitner and Omri (FOCS’11), who proved this implication for protocols with bias √ 2−1/2 − o(1) ≈ .207. Unlike the result of Haitner and Omri, our result also holds for weak coin-flipping protocols.
{"title":"Coin Flipping of Any Constant Bias Implies One-Way Functions","authors":"Itay Berman, Iftach Haitner, Aris Tentes","doi":"10.1145/2979676","DOIUrl":"https://doi.org/10.1145/2979676","url":null,"abstract":"We show that the existence of a coin-flipping protocol safe against any nontrivial constant bias (e.g., .499) implies the existence of one-way functions. This improves upon a result of Haitner and Omri (FOCS’11), who proved this implication for protocols with bias √ 2−1/2 − o(1) ≈ .207. Unlike the result of Haitner and Omri, our result also holds for weak coin-flipping protocols.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"46 1","pages":"1 - 95"},"PeriodicalIF":0.0,"publicationDate":"2018-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84108569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The theory admits deterministic and nondeterministic polynomial time recognizable problems. We prove that P is not NP in this theory if and only if P is not NP in the BSS theory over the reals. Then we develop a theory with weak and strong approximate computations. This theory is intended to model actual numerical computations that are usually performed in floating point arithmetic. It admits classes P and NP and also an NP-complete problem. We relate the P vs. NP question in this new theory to the classical P vs. NP problem.
{"title":"A Theory of NP-completeness and Ill-conditioning for Approximate Real Computations","authors":"G. Malajovich, M. Shub","doi":"10.1145/3321479","DOIUrl":"https://doi.org/10.1145/3321479","url":null,"abstract":"We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The theory admits deterministic and nondeterministic polynomial time recognizable problems. We prove that P is not NP in this theory if and only if P is not NP in the BSS theory over the reals. Then we develop a theory with weak and strong approximate computations. This theory is intended to model actual numerical computations that are usually performed in floating point arithmetic. It admits classes P and NP and also an NP-complete problem. We relate the P vs. NP question in this new theory to the classical P vs. NP problem.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"19 1","pages":"1 - 38"},"PeriodicalIF":0.0,"publicationDate":"2018-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77975052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Invited Article section of this issue consists of the article “Analysing Snapshot Isolation” by Andrea Cerone and Alexey Gotsman, which won the best paper award at the 35th Annual ACM Symposium on Principles of Distributed Computing (PODC’16). We would like to thank the PODC’16 Program Committee for their help in selecting this invited work, and we also thank editor Rachid Guerraoui for handling the paper.
{"title":"Invited Article Foreword","authors":"É. Tardos","doi":"10.1145/3186890","DOIUrl":"https://doi.org/10.1145/3186890","url":null,"abstract":"The Invited Article section of this issue consists of the article “Analysing Snapshot Isolation” by Andrea Cerone and Alexey Gotsman, which won the best paper award at the 35th Annual ACM Symposium on Principles of Distributed Computing (PODC’16). We would like to thank the PODC’16 Program Committee for their help in selecting this invited work, and we also thank editor Rachid Guerraoui for handling the paper.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"71 1","pages":"1 - 1"},"PeriodicalIF":0.0,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79364151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We determine the exact value of the freezing threshold, rfk, for k-colourings of a random graph when k≥ 14. We prove that for random graphs with density above rfk, almost every colouring is such that a linear number of vertices are frozen, meaning that their colour cannot be changed by a sequence of alterations whereby we change the colours of o(n) vertices at a time, always obtaining another proper colouring. When the density is below rfk, then almost every colouring is such that every vertex can be changed by a sequence of alterations where we change O(log n) vertices at a time. Frozen vertices are a key part of the clustering phenomena discovered using methods from statistical physics. The value of the freezing threshold was previously determined by the nonrigorous cavity method.
{"title":"The Freezing Threshold for k-Colourings of a Random Graph","authors":"Michael Molloy","doi":"10.1145/3034781","DOIUrl":"https://doi.org/10.1145/3034781","url":null,"abstract":"We determine the exact value of the freezing threshold, rfk, for k-colourings of a random graph when k≥ 14. We prove that for random graphs with density above rfk, almost every colouring is such that a linear number of vertices are frozen, meaning that their colour cannot be changed by a sequence of alterations whereby we change the colours of o(n) vertices at a time, always obtaining another proper colouring. When the density is below rfk, then almost every colouring is such that every vertex can be changed by a sequence of alterations where we change O(log n) vertices at a time. Frozen vertices are a key part of the clustering phenomena discovered using methods from statistical physics. The value of the freezing threshold was previously determined by the nonrigorous cavity method.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"34 1","pages":"1 - 62"},"PeriodicalIF":0.0,"publicationDate":"2018-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80773200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the problem of fairly allocating indivisible goods, focusing on a recently introduced notion of fairness called maximin share guarantee: each player’s value for his allocation should be at least as high as what he can guarantee by dividing the items into as many bundles as there are players and receiving his least desirable bundle. Assuming additive valuation functions, we show that such allocations may not exist, but allocations guaranteeing each player 2/3 of the above value always exist. These theoretical results have direct practical implications.
{"title":"Fair Enough","authors":"David Kurokawa, A. Procaccia, Junxing Wang","doi":"10.1145/3140756","DOIUrl":"https://doi.org/10.1145/3140756","url":null,"abstract":"We consider the problem of fairly allocating indivisible goods, focusing on a recently introduced notion of fairness called maximin share guarantee: each player’s value for his allocation should be at least as high as what he can guarantee by dividing the items into as many bundles as there are players and receiving his least desirable bundle. Assuming additive valuation functions, we show that such allocations may not exist, but allocations guaranteeing each player 2/3 of the above value always exist. These theoretical results have direct practical implications.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"19 1","pages":"1 - 27"},"PeriodicalIF":0.0,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90879583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Snapshot isolation (SI) is a widely used consistency model for transaction processing, implemented by most major databases and some of transactional memory systems. Unfortunately, its classical definition is given in a low-level operational way, by an idealised concurrency-control algorithm, and this complicates reasoning about the behaviour of applications running under SI. We give an alternative specification to SI that characterises it in terms of transactional dependency graphs of Adya et al., generalising serialisation graphs. Unlike previous work, our characterisation does not require adding additional information to dependency graphs about start and commit points of transactions. We then exploit our specification to obtain two kinds of static analyses. The first one checks when a set of transactions running under SI can be chopped into smaller pieces without introducing new behaviours, to improve performance. The other analysis checks whether a set of transactions running under a weakening of SI behaves the same as when running under SI.
{"title":"Analysing Snapshot Isolation","authors":"A. Cerone, Alexey Gotsman","doi":"10.1145/3152396","DOIUrl":"https://doi.org/10.1145/3152396","url":null,"abstract":"Snapshot isolation (SI) is a widely used consistency model for transaction processing, implemented by most major databases and some of transactional memory systems. Unfortunately, its classical definition is given in a low-level operational way, by an idealised concurrency-control algorithm, and this complicates reasoning about the behaviour of applications running under SI. We give an alternative specification to SI that characterises it in terms of transactional dependency graphs of Adya et al., generalising serialisation graphs. Unlike previous work, our characterisation does not require adding additional information to dependency graphs about start and commit points of transactions. We then exploit our specification to obtain two kinds of static analyses. The first one checks when a set of transactions running under SI can be chopped into smaller pieces without introducing new behaviours, to improve performance. The other analysis checks whether a set of transactions running under a weakening of SI behaves the same as when running under SI.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"10 1","pages":"1 - 41"},"PeriodicalIF":0.0,"publicationDate":"2018-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72778914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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