2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)最新文献

{"title":"Leakage-Resilient Secret Sharing Against Colluding Parties","authors":"Ashutosh Kumar, R. Meka, A. Sahai","doi":"10.1109/FOCS.2019.00045","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00045","url":null,"abstract":"In this work, we consider the natural goal of designing secret sharing schemes that ensure security against an adversary who may learn some “leaked'' information about all the shares. We say that a secret sharing scheme is p-party leakage-resilient, if the secret remains statistically hidden even after a computationally unbounded adversary learns a bounded amount of leakage, where each bit of leakage adaptively and jointly depends on the shares of an adaptively chosen subset of p parties. Existing multi-party secret sharing schemes (Dziembowski and Pietrzak FOCS 07), (Goyal and Kumar STOC 18) and (Benhamouda, Degwekar, Ishai and Rabin CRYPTO 18) have focused on handling non-adaptive and individual leakage for (limited special cases of) threshold secret sharing schemes. • We give an unconditional compiler that transforms any secret sharing scheme on n parties into a p-party leakage-resilient one for p upto O(log n). This yields the first multi-party secret sharing schemes that are secure against adaptive or joint leakage. • As a natural extension, we initiate the study of leakage-resilient non-malleable secret sharing. We empower the adversary to adaptively leak from each of the shares and then use the leakage to tamper with all of them arbitrarily and independently. Leveraging our p-party leakage-resilient schemes, we compile any secret sharing scheme into a non-malleable one ensuring that any such tampering either preserves the secret or completely `destroys' it. This improves upon the non-malleable secret sharing scheme of (Goyal and Kumar CRYPTO 18) where no leakage was permitted. Leakage-resilient non-malleable codes can be seen as 2-out-of-2 schemes satisfying our guarantee and have already found many applications in cryptography. • Our constructions rely on a clean connection we draw to communication complexity in the well-studied number-on-forehead (NOF) model and rely on functions that have strong communication-complexity lower bounds in the NOF model (in a black-box way). We get efficient p-party leakage-resilient schemes for p upto O(log n) as our share sizes have exponential dependence on p. We observe that improving this exponential dependence, even for simultaneous, non-adaptive leakage, will lead to progress on longstanding open problems in complexity theory.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126691836","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}

{"title":"Laconic Conditional Disclosure of Secrets and Applications","authors":"Nico Döttling, Sanjam Garg, Vipul Goyal, Giulio Malavolta","doi":"10.1109/FOCS.2019.00046","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00046","url":null,"abstract":"In a Conditional Disclosure of Secrets (CDS) a verifier V wants to reveal a message m to a prover P conditioned on the fact that x is an accepting instance of some NP-language L. An honest prover (holding the corresponding witness w) always obtains the message m at the end of the interaction. On the other hand, if x ∉ L we require that no PPT P* can learn the message m. We introduce laconic CDS, a two round CDS protocol with optimal computational cost for the verifier V and optimal communication cost. More specifically, the verifier’s computation and overall communication grows with poly(|x|; λ; log(T)), where λ is the security parameter and T is the verification time for checking that x ∊ L (given w). We obtain constructions of laconic CDS under standard assumptions, such as CDH or LWE. Laconic CDS serves as a powerful tool for maliciousifying semi-honest protocols while preserving their computational and communication complexities. To substantiate this claim, we consider the setting of non-interactive secure computation: Alice wants to publish a short digest corresponding to a private large input x on her web page such that (possibly many) Bob, with a private input y, can send a short message to Alice allowing her to learn C(x; y) (where C is a public circuit). The protocol must be reusable in the sense that Bob can engage in arbitrarily many executions on the same digest. In this context we obtain the following new implications. 1) UC Secure Bob-optimized 2PC: We obtain a UC secure protocol where Bob’s computational cost and the communication cost of the protocol grows with poly(|x|; |y|; λ; d), where d is the depth of the computed circuit C. 2) Malicious Laconic Function Evaluation: Next, we move on to the setting where Alice’s input x is large. For this case, UC secure protocols must have communication cost growing with |x|. Thus, with the goal of achieving better efficiency, we consider a weaker notion of malicious security. For this setting, we obtain a protocol for which Bob’s computational cost and the communication cost of the protocol grows with poly(|y|; λ; d), where d is the depth of the computed circuit C.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"114 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114044676","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}

{"title":"Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders","authors":"Sepehr Assadi, Sahil Singla","doi":"10.1109/FOCS.2019.00024","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00024","url":null,"abstract":"A longstanding open problem in Algorithmic Mechanism Design is to design computationally-efficient truthful mechanisms for (approximately) maximizing welfare in combinatorial auctions with submodular bidders. The first such mechanism was obtained by Dobzinski, Nisan, and Schapira [STOC'06] who gave an O(log^2m) -approximation where m is number of items. This problem has been studied extensively since, culminating in an O(√log m) -approximation mechanism by Dobzinski~[STOC'16]. We present a computationally-efficient truthful mechanism with approximation ratio that improves upon the state-of-the-art by an exponential factor. In particular, our mechanism achieves an O((log logm)^3) -approximation in expectation, uses only O(n) demand queries, and has universal truthfulness guarantee. This settles an open question of Dobzinski on whether Θ(√log m) is the best approximation ratio in this setting in negative.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114915341","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}

{"title":"FOCS 2019 Awards","authors":"","doi":"10.1109/focs.2019.00009","DOIUrl":"https://doi.org/10.1109/focs.2019.00009","url":null,"abstract":"","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125118851","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}

{"title":"Breaking of 1RSB in Random Regular MAX-NAE-SAT","authors":"Z. Bartha, Nike Sun, Yumeng Zhang","doi":"10.1109/FOCS.2019.00086","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00086","url":null,"abstract":"For several models of random constraint satisfaction problems, it was conjectured by physicists and later proved that a sharp satisfiability transition occurs. In the unsatisfiable regime, it is natural to consider the problem of max-satisfiability: violating the least number of constraints. This is a combinatorial optimization problem on the random energy landscape defined by the problem instance. In the bounded density regime, a very precise estimate of the max-sat value was obtained by Achlioptas, Naor, and Peres (2007), but it is not sharp enough to indicate the nature of the energy landscape. Later work (Sen, 2016; Panchenko, 2016) shows that for very large but bounded density, the max-sat value approaches the mean-field (complete graph) limit: this is conjectured to have an \"FRSB\" structure where near-optimal configurations form clusters within clusters, in an ultrametric hierarchy of infinite depth inside the discrete cube. A stronger form of FRSB was shown in several recent works to have algorithmic implications (again, in complete graphs). Consequently we find it of interest to understand how the model transitions from 1RSB near the satisfiability threshold, to (conjecturally) FRSB at large density. In this paper we show that in the random regular NAE-SAT model, the 1RSB description breaks down by a certain threshold density that we estimate rather precisely. This is proved by an explicit perturbation in the 2RSB parameter space. The choice of perturbation is inspired by the \"bug proliferation\" mechanism proposed by physicists (Montanari and Ricci-Tersenghi, 2003; Krzakala, Pagnani, and Weigt, 2004), corresponding roughly to a percolation-like threshold for a subgraph of dependent variables.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126261946","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}

{"title":"Faster Matroid Intersection","authors":"Deeparnab Chakrabarty, Y. Lee, Aaron Sidford, Sahil Singla, Sam Chiu-wai Wong","doi":"10.1109/FOCS.2019.00072","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00072","url":null,"abstract":"In this paper we consider the classic matroid intersection problem: given two matroids M_1=(V, I_1) and M_2=(V, I_2) defined over a common ground set V, compute a set S∊I_1 ∩ I_2 of largest possible cardinality, denoted by r. We consider this problem both in the setting where each M_i is accessed through an independence oracle, i.e. a routine which returns whether or not a set S ∊ I_i in T_ind time, and the setting where each M_i is accessed through a rank oracle, i.e. a routine which returns the size of the largest independent subset of S in M_i in T_rank time. In each setting we provide faster exact and approximate algorithms. Given an independence oracle, we provide an exact O(nr log r⋅T_ind) time algorithm. This improves upon previous best known running times of O(nr^1.5⋅T_ind) due to Cunningham in 1986 and Õ(n^2⋅T_ind+n^3) due to Lee, Sidford, and Wong in 2015. We also provide two algorithms which compute a (1-ε)-approximate solution to matroid intersection running in times Õ(n^1.5/ε^1.5⋅T_ind) and Õ((n^2r^-1ε^-2+r^1.5ε^-4.5)⋅T_ind), respectively. These results improve upon the O(nr/ε⋅T_ind) -time algorithm of Cunningham (noted recently by Chekuri and Quanrud). Given a rank oracle, we provide algorithms with even better dependence on n and r. We provide an O(n√rlog n⋅T_rank) -time exact algorithm and an O(nε^-1 log n⋅T_rank) -time algorithm which obtains a (1-ε) -approximation to the matroid intersection problem. The former result improves over the Õ(nr⋅T_rank+n^3) -time algorithm by Lee, Sidford, and Wong. The rank oracle is of particular interest as the matroid intersection problem with this oracle is a special case (via Edmond's minimax characterization of matroid intersection) of the submodular function minimization (SFM) problem with an evaluation oracle, and understanding SFM query complexity is an outstanding open question.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128235352","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}

{"title":"FOCS 2019 Program Committee","authors":"","doi":"10.1109/focs.2019.00007","DOIUrl":"https://doi.org/10.1109/focs.2019.00007","url":null,"abstract":"","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134048734","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}

{"title":"Radio Network Coding Requires Logarithmic Overhead","authors":"K. Efremenko, Gillat Kol, Raghuvansh R. Saxena","doi":"10.1109/FOCS.2019.00030","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00030","url":null,"abstract":"We consider the celebrated radio network model for abstracting communication in wireless networks. In this model, in any round, each node in the network may broadcast a message to all its neighbors. However, a node is able to hear a message broadcast by a neighbor only if no collision occurred, meaning that it was the only neighbor broadcasting. While the (noiseless) radio network model received a lot of attention over the last few decades, the effect of noise on radio networks is still not well understood. In this paper, we take a step forward and show that making radio network protocols resilient to noise may require a substantial performance overhead. Specifically, we construct a multi-hop network and a communication protocol over this network that works in T rounds when there is no noise. We prove that any scheme that simulates our protocol and is resilient to stochastic noise, requires at least cT log(n) rounds, for some constant c. This stands in contrast to our previous result (STOC, 2018), showing that protocols over the single-hop (clique) network can be made noise resilient with only a constant overhead. Our result also settles a recent conjecture by Censor-Hillel, Haeupler, Hershkowitz, Zuzic (2018). We complement the above result by giving a scheme to simulate any protocol with a fixed order of transmissions with only an O(log (n)) overhead.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130338633","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}

{"title":"Inapproximability of Clustering in Lp Metrics","authors":"Vincent Cohen-Addad, K. C. S.","doi":"10.1109/FOCS.2019.00040","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00040","url":null,"abstract":"Proving hardness of approximation for min-sum objectives is an infamous challenge. For classic problems such as the Traveling Salesman problem, the Steiner tree problem, or the k-means and k-median problems, the best known inapproximability bounds for L-p metrics of dimension O(log n) remain well below 1.01. In this paper, we take a significant step to improve the hardness of approximation of the k-means problem in various L-p metrics, and more particularly on Manhattan (L-1), Euclidean (L-2), Hamming (L-0) and Chebyshev (L-infinity) metrics of dimension log n and above. We show that it is hard to approximate the k-means objective in O(log n) dimensional space: (1) To a factor of 3.94 in the L-infinity metric when centers have to be chosen from a discrete set of locations (i.e., the discrete case). This improves upon the result of Guruswami and Indyk (SODA'03) who proved hardness of approximation for a factor less than 1.01. (2) To a factor of 1.56 in the L-1 metric and to a factor of 1.17 in the L-2 metric, both in the discrete case. This improves upon the result of Trevisan (SICOMP'00) who proved hardness of approximation for a factor less than 1.01 in both the metrics. (3) To a factor of 1.07 in the L-2 metric, when centers can be placed at arbitrary locations, (i.e., the continuous case). This improves on a result of Lee-Schmidt-Wright (IPL'17) who proved hardness of approximation for a factor of 1.0013. We also obtain similar improvements over the state of the art hardness of approximation results for the k-median objective in various L-p metrics. Our hardness result given in (1) above, is under the standard NP is not equal to P assumption, whereas all the remaining results given above are under the Unique Games Conjecture (UGC). We can remove our reliance on UGC and prove standard NP-hardness for the above problems but for smaller approximation factors. Finally, we note that in order to obtain our result for the L-1 and L-infinity metrics in O(log n) dimensional space we introduce an embedding technique which combines the transcripts of certain communication protocols with the geometric realization of certain graphs.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125272116","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}

{"title":"Conditional Hardness Results for Massively Parallel Computation from Distributed Lower Bounds","authors":"M. Ghaffari, F. Kuhn, Jara Uitto","doi":"10.1109/FOCS.2019.00097","DOIUrl":"https://doi.org/10.1109/FOCS.2019.00097","url":null,"abstract":"We present the first conditional hardness results for massively parallel algorithms for some central graph problems including (approximating) maximum matching, vertex cover, maximal independent set, and coloring. In some cases, these hardness results match or get close to the state of the art algorithms. Our hardness results are conditioned on a widely believed conjecture in massively parallel computation about the complexity of the connectivity problem. We also note that it is known that an unconditional variant of such hardness results might be somewhat out of reach for now, as it would lead to considerably improved circuit complexity lower bounds and would concretely imply that NC_1 is a proper subset of P. We obtain our conditional hardness result via a general method that lifts unconditional lower bounds from the well-studied LOCAL model of distributed computing to the massively parallel computation setting.","PeriodicalId":407139,"journal":{"name":"2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128719622","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}