We typically have seminars on Wednesdays at noon in Malone 228. For Fall 2021, we will be having seminars virtually using Zoom in this room. All seminar announcements will be sent to the theory mailing list.

Speaker: Dana Dachman Soled, UMD

**Title: Tight Upper and Lower Bounds for Leakage-Resilient, Locally Decodable and Updatable Non-Malleable Codes**

**Abstract: **In a recent result, Dachman-Soled et al.~(TCC ’15) proposed a new notion called locally decodable and updatable non-malleable codes, which informally, provides the security guarantees of a non-malleable code while also allowing for efficient random access. They also considered locally decodable and updatable non-malleable codes that are leakage-resilient, allowing for adversaries who continually leak information in addition to tampering. Unfortunately, the locality of their construction in the continual setting was Omega(log n), meaning that if the original message size was n, then Omega(log n) positions of the codeword had to be accessed upon each decode and update instruction.

In this work, we ask whether super-constant locality is inherent in this setting. We answer the question affirmatively by showing tight upper and lower bounds. Specifically, in any threat model which allows for a rewind attack-wherein the attacker leaks a small amount of data, waits for the data to be overwritten and then writes the original data back-we show that a locally decodable and updatable non-malleable code with block size Chi in poly(lambda) number of bits requires locality delta(n) in omega(1), where n = poly(lambda) is message length and lambda is security parameter. On the other hand, we re-visit the threat model of Dachman-Soled et al.~(TCC ’15)-which indeed allows the adversary to launch a rewind attack-and present a construction of a locally decodable and updatable non-malleable code with block size Chi in Omega(lambda^{1/mu}) number of bits (for constant 0 < mu < 1) with locality delta(n), for any delta(n) in omega(1), and n = poly(lambda).

Speaker: Mohammad Hajiesmaili

Affiliation: Johns Hopkins University

Title: Online storage management in electricity market

Abstract:

With unprecedented benefits in terms of efficiency, economy, reliability, and environmental awareness, in the recent years, there has been a rapid proliferation of renewable energy sources such as solar and wind in electric power systems. Despite these benefits, the inherent uncertainty in renewables places severe challenges on the management of the entire energy systems, including electricity market. Leveraging energy storage systems is a promising approach to mitigate the uncertainty of renewables, by charging and discharging during the mismatched periods. Energy storage systems, however, offers a new design space for additional optimization. That is, a storage system can capture energy during periods when the market prices are low and surrender stored energy when energy prices are high.

In this talk, we consider different scenarios of storage management in both supply and demand sides of the electricity market. The uncertainties in both renewable output and electricity market price, emphasizes the need for online solution design. The underlying theoretical problems could be described as extensions of conversion problems in financial markets, i.e., the search for best prices to buy and/or sell assets. The difference with the conversion problems, is that in addition to the uncertainty in the price, our problems suffer from another uncertainty originated from renewable output. We follow online algorithm design and use competitive ratio as the performance measure of our algorithms. We present our recent results in designing competitive online algorithms that achieve constant competitive ratios. In addition, we briefly talk about the case of utilizing aggregate potentials distributed small-scale storage systems, such as EVs or residential storages, to participate in electricity market through an aggregator. This setting is more challenging than the previous one, since the distributed sources also arrive in online manner with heterogeneous profiles.

Overall, we believe that changing the landscape of electric power system from a centralized predictable system to a distributed uncertain system opens a new research direction for leveraging online framework designs in this relatively under-explored area.

Speaker: Kuan Cheng

Affiliation: Johns Hopkins University

Title: Near-Optimal Secret Sharing and Error Correcting Codes in $\AC^0$

Abstract:

We study the question of minimizing the computational complexity of (robust) secret sharing schemes and error correcting codes. In standard instances of these objects, both encoding and decoding involve linear algebra, and thus cannot be implemented in the class $\AC^0$. The feasibility of non-trivial secret sharing schemes in $\AC^0$ was recently shown by Bogdanov et al.\ (Crypto 2016) and that of (locally) decoding errors in $\AC^0$ by Goldwasser et al.\ (STOC 2007).

In this paper, we show that by allowing some slight relaxation such as a small error probability, we can construct much better secret sharing schemes and error correcting codes in the class $\AC^0$. In some cases, our parameters are close to optimal and would be impossible to achieve without the relaxation. Our results significantly improve previous constructions in various parameters.

Our constructions combine several ingredients in pseudorandomness and combinatorics in an innovative way. Specifically, we develop a general technique to simultaneously amplify security threshold and reduce alphabet size, using a two-level concatenation of protocols together with a random permutation. We demonstrate the broader usefulness of this technique by applying it in the context of a variant of secure broadcast.

Based on a joint work with Yuval Ishai and Xin Li.

Speaker: Ilan Komargodski

Affiliation: Cornell Tech

Title: White-Box vs. Black-Box Complexity of Search Problems: Ramsey and Graph Property Testing

Abstract: Ramsey theory assures us that in any graph there is a clique or independent set of a certain size, roughly logarithmic in the graph size. But how difficult is it to find the clique or independent set? This problem is in TFNP, the class of search problems with guaranteed solutions. If the graph is given explicitly, then it is possible to do so while examining a linear number of edges. If the graph is given by a black-box, where to figure out whether a certain edge exists the box should be queried, then a large number of queries must be issued.

1) What if one is given a program or circuit (“white-box”) for computing the existence of an edge. Does the search problem remain hard?

2) Can we generically translate all TFNP black-box hardness into white-box hardness?

3) Does the problem remain hard if the black-box instance is small?

We will answer all of these questions and discuss related questions in the setting of property testing.

Joint work with Moni Naor and Eylon Yogev.

Speaker: Ran Ben Basat

Affiliation: Technion

Title: Classic Network Measurement meets Virtual Switching

Abstract: In modern cloud infrastructures, each physical server often runs multiple virtual machines and employs a software Virtual Switch (VS) to handle their traffic. In addition to switching, the VS performs network measurements, such as identifying the most frequent flows, which are essential for networking applications such as load balancing and intrusion detection.

Unlike traditional streaming algorithms, which minimize the space requirements, the bottleneck in virtual switching measurement is the CPU utilization. In this talk, I will present new hardware-oriented algorithms and acceleration methods that optimize the update time for software, at the cost of a slight memory overhead.

Bio: Ran is a Ph.D. candidate at the Technion, Israel. He does research in streaming algorithms for networking applications, focusing on efficient processing and query speeds.

Speaker: Samson Zhou

Affiliation: Purdue University

Title: Pattern Matching over Noisy Data Streams

Abstract: The identification of low-complexity structure in strings is a fundamental building block for many algorithms in computational biology or natural language processing. The general paradigm in these algorithms is to find either highly repetitive structure, in the form of periodicity or palindromes in a pre-processing stage, to filter out locations where a certain pattern cannot occur, thus improving efficiency.

Unfortunately, we must expect massive data to contain a number of small imperfections, such as through human error or mutations. This motivates the need to study structure in models of sublinear space, resilient to sources of noise. In this talk, we introduce several types of structure and noise, and discuss efficient algorithms to identify these structures over data streams.

As a warm-up, we provide an algorithm for identifying a longest common aligned substring of two inputs, resilient up to d errors of insertions, substitutions, or deletions. We then present a streaming algorithm for identifying the longest palindrome, resilient up to a threshold of d substitution errors. Finally, we discuss the problem of finding all periods of a string including up to d persistent changes or erasures. For each of these scenarios, we also provide complementary lower bounds.

Joint work with Funda Ergun, Elena Grigorescu, and Erfan Sadeqi Azer.

BIO:

Samson is a PhD candidate in the Department of Computer Science at Purdue University, under the supervision of Greg Frederickson and Elena Grigorescu. He received his undergraduate education at MIT, where he obtained a Bachelor’s in math and computer science, as well as a Master’s in computer science. He is a member of the Theory Group at Purdue, and his current research interests are sublinear and approximation algorithms, with an emphasis on streaming algorithms.

Speaker: Venkata Gandikota

Affiliation: Johns Hopkins University

Title: NP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

Abstract: Establishing the complexity of Bounded Distance Decoding for Reed-Solomon codes is a fundamental open problem in coding theory, explicitly asked by Guruswami and Vardy (IEEE Trans. Inf. Theory, 2005). The problem is motivated by the large current gap between the regime when it is NP-hard, and the regime when it is efficiently solvable (i.e., the Johnson radius).

We show the first NP-hardness results for asymptotically smaller decoding radii than the maximum likelihood decoding radius of Guruswami and Vardy. Specifically, for Reed-Solomon codes of length N and dimension K = O(N), we show that it is NP-hard to decode more than N-K-O(log N / log log N) errors.

These results follow from the NP-hardness of a generalization of the classical Subset Sum problem to higher moments, called Moments Subset Sum, which has been a known open problem, and which may be of independent interest. We further reveal a strong connection with the well-studied Prouhet-Tarry-Escott problem in Number Theory, which turns out to capture a main barrier in extending our techniques. We believe the Prouhet-Tarry-Escott problem deserves further study in the theoretical computer science community.

This is a joint work with Badih Ghazi (MIT) and Elena Grigorescu (Purdue).

Speaker: Amirbehshad Shahrasbi

Affiliation:Carnegie Mellon University

Speaker: Samson Zhou

Affiliation: Purdue University

Title: Password Hashing and Graph Pebbling

Abstract: Although the passwords of users are no longer being stored, we show an offline attacker is compelled to crack all stolen passwords under current security recommendations. Memory hard functions have been proposed as moderately expensive cryptographic tools for password hashing. The cryptanalysis of these functions has focused on the cumulative memory complexity and the energy complexity of the function. The first metric measures how much memory users must commit to evaluating a function, while the second metric measures how much energy users must commit. We prove these evaluations reduce to pebbling games on graphs but show that a tool for exact cryptanalysis of functions is unlikely to exist. Nevertheless, we provide asymptotic upper and lower bounds on several families of functions, including Argon2i, the winner of the password hashing competition that is currently being considered for standardization by the Cryptography Form Research Group of the Internet Research Task Force.

Joint work with Jeremiah Blocki, Ben Harsha, Ling Ren

BIO:

Samson is a PhD candidate in the Department of Computer Science at Purdue University, under the supervision of Greg Frederickson and Elena Grigorescu. He received his undergraduate education at MIT, where he obtained a Bachelor’s in math and computer science, as well as a Master’s in computer science. He is a member of the Theory Group at Purdue and a winner of the Sigma Xi Research Awards Competition for graduate students in engineering. His current research interests are sublinear and approximation algorithms, with an emphasis on streaming algorithms.

Speaker: Sai Lakshmi Bhavana Obbattu

Affiliation: IISC Bangalore, India

Title: Privacy Amplification from Non-malleable Codes

The goal of a Privacy Amplification (PA) protocol is to allow two parties, who start out sharing a non-uniform secret ‘w’, to agree on a uniform secret ‘k’, in the presence of a computationally unbounded man-in-the-middle adversary. An interactive PA protocol is rated based on three parameters: 1) Number of rounds, 2) Entropy loss (entropy of w – |k|), and 3) Min-entropy requirement for w, while the asymptotically optimal parameters are 2, O(s) and O(s+log n) respectively (where s is the security parameter and n =|w|). There have been two popular approaches to solve this problem: one using use bit authentication protocols and the other using non-malleable extractors, but none of the prior protocols using these approaches had all asymptotically optimal parameters.

We give an alternate approach to solve the problem using Non-malleable Codes (NMCs). This approach results in a 8-round protocol with min-entropy requirement O(s+log n) and an entropy loss of O(s log s). Augmented NMCs with better parameters would result in optimal entropy loss of O(s). Our result is one of the first information theoretic applications of NMCs. In this talk, I will introduce NMCs and show connection of NMCs to PA.

In a concurrent and independent work, Xin Li gives a protocol with asymptotically optimal parameters based on non-malleable extractors. Because all known approaches have large hidden constants, exploring alternatives is necessary if we hope to get practical concrete parameters

The talk is based on:

Eshan Chattopadhyay, Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu and Sruthi Sekar. Privacy Amplification from Non-malleable Codes. (eprint.iacr.org/2018/293)

Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu and Sruthi Sekar. Non-malleable Randomness Encoders and their Applications (Eurocrypt 2018)

Bio: Sai Lakshmi Bhavana Obbattu is a doctoral student at Indian Institute of Science(IISc), Bangalore, advised by Dr. Bhavana Kanukurthi. Her publication venues include the Theory of Cryptography Conference (TCC) and Eurocrypt. Her TCC publication on Four-state Non-malleable Codes was invited to the Journal of Cryptology. She received her Integrated Dual Degree (B.Tech and M.Tech) from IIT(BHU), Varanasi. Her research interests include Non-malleable codes, Privacy Amplification and Applied Multi-party computation.

Speaker: Akash Kumar

Affiliation: Purdue University

Location: Malone 338 (note change of location)

Title:

Finding Minors in Sublinear time in Bounded degree graphs with (almost) optimal one-sided query complexity.

Abstract:

Let G be an undirected, bounded degree graph with n vertices. Fix a finite graph H, and suppose one must remove \varepsilon n edges from G to make it H-minor free (for some small constant \varepsilon > 0). We give an n^{1/2+o(1)}-time randomized procedure that, with high probability, finds an H-minor in such a graph. For an example application, suppose one must remove \varepsilon n edges from a bounded degree graph G to make it planar. This result implies an algorithm, with the same running time, that produces a K_{3,3} or K_5 minor in G. No sublinear time bound was known for this problem, prior to this result.

By the graph minor theorem, we get an analogous result for any minor-closed property. Up to n^{o(1)} factors, this resolves a conjecture of Benjamini-Schramm-Shapira (STOC 2008) on the existence of one-sided property testers for minor-closed properties. Furthermore, our algorithm is nearly optimal, by an \Omega(\sqrt{n}) lower bound of Czumaj et al (RSA 2014).

Prior to this work, the only graphs H for which non-trivial property testers were known for H-minor freeness are the following: H being a forest or a cycle (Czumaj et al, RSA 2014), K_{2,k}, (k\times 2)-grid, and the k-circus (Fichtenberger et al, Arxiv 2017).

(Joint work with C. Seshadhri and Andrew Stolman).

Welcome and Introductions

Speaker: Zhengzhong Jin

Affiliation: JHU

Title: Deterministic Document Exchange Protocols, and Almost Optimal Binary Codes for Edit Errors

Abstract:

We study two basic problems regarding edit error, i.e. document exchange and error correcting codes for edit errors (insdel codes). For message length n and edit error upper bound k, it is known that in both problems the optimal sketch size or the optimal number of redundant bits is Θ(k log n/k). However, known constructions are far from achieving these bounds.

We significantly improve previous results on both problems. For document exchange, we give an efficient deterministic protocol with sketch size O(k log^2 n/k). This significantly improves the previous best known deterministic protocol, which has sketch size O(k^2+k log^2 n). For binary insdel codes, we obtain the following results:

1. An explicit binary insdel code which encodes an n-bit message x against k errors with redundancy O(k log^2 n/k). In particular this implies an explicit family of binary insdel codes that can correct ε fraction of insertions and deletions with rate 1−O(ε log^2(1/ε))=1−\tilde {O}(ε).

2. An explicit binary insdel code which encodes an n-bit message x against k errors with redundancy O(k log n). This is the first explicit construction of binary insdel codes that has optimal redundancy for a wide range of error parameters k, and this brings our understanding of binary insdel codes much closer to that of standard binary error correcting codes.

In obtaining our results we introduce the notion of ε-self matching hash functions and ε-synchronization hash functions. We believe our techniques can have further applications in the literature.

Speaker: Marius Zimand

Affiliation: Towson University

Title: An operational characterization of mutual information in algorithmic information theory

Abstract: An operational interpretation of the concept of mutual information in the framework of Kolmogorov complexity has been elusive till now. We show that the mutual information of any pair of strings x and y is equal, up to logarithmic precision, to the length of the longest shared secret key that two parties, one having x and the complexity profile of the pair and the other one having y and the complexity profile of the pair, can establish via a probabilistic protocol with interaction on a public channel. We establish the communication complexity of secret key agreement protocols that produce a secret key of maximal length, for protocols with public randomness. We show that if the communication complexity drops below the established threshold then only very short secret keys can be obtained.

This is joint work with Andrei Romashchenko.

Speaker: Yasamin Nazari

Affiliation: JHU

Title: Distributed Distance-Bounded Network Design Through Distributed Convex Programming

Abstract:

Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner, this is essentially the only class of linear programs for which such an algorithm is known. In this work we provide a distributed algorithm for solving a different class of convex programs which we call “distance-bounded network design convex programs”. These can be thought of as relaxations of network design problems in which the connectivity requirement includes a distance constraint (most notably, graph spanners). Our algorithm runs in O((D/ϵ)logn) rounds in the LOCAL model and finds a (1+ϵ)-approximation to the optimal LP solution for any 0<ϵ≤1, where D is the largest distance constraint. While solving linear programs in a distributed setting is interesting in its own right, this class of convex programs is particularly important because solving them is often a crucial step when designing approximation algorithms. Hence we almost immediately obtain new and improved distributed approximation algorithms for a variety of network design problems, including Basic 3- and 4-Spanner, Directed k-Spanner, Lowest Degree k-Spanner, and Shallow-Light Steiner Network Design with a spanning demand graph. Our algorithms do not require any "heavy" computation and essentially match the best-known centralized approximation algorithms, while previous approaches which do not use heavy computation give approximations which are worse than the best-known centralized bounds.

Speaker: Karthik Abinav Sankararaman

Affiliation: University of Maryland

Title: Adversarial Bandits with Knapsacks

Abstract: In this talk we will discuss the multi-armed bandits problem with resource constraints under the adversarial setting. In this problem, we have an interactive and repeated game between the algorithm and an adversary. Given T time-steps, d resources, m actions and budgets B1, B2, .. Bd, the algorithm chooses one of the m actions at each time-step. An adversary then reveals a reward and consumption for each of the d resources corresponding to this action. The time-step at which the algorithm runs out of the d resources (i.e., the total consumption for resource j > Bj), the game stops and the total reward is the sum of rewards obtained until the stopping time. The goal is to maximize the competitive ratio; the ratio of the total reward of the algorithm to the expected reward of a fixed distribution that knows all the rewards and consumption ahead of time. We give an algorithm for this problem whose competitive ratio is tight (matches the lower-bound). Moreover the algorithmic tools extends in an (almost) black-box fashion to also give an algorithm for the stochastic setting thus giving a “best-of-both-worlds” algorithm where the algorithm need not know a-priori if the input is adversarial or i.i.d. Finally we conclude with applications and special cases including the Dynamic Pricing problem.

This talk is based on a recent working paper with Nicole Immorlica, Rob Schapire and Alex Slivkins.

Speaker: Nithin Varma

Affiliation: Boston University

Title: Separating erasures and errors in property testing using local list decoding

Abstract:

Corruption in data can be in the form of erasures (missing data) or errors (wrong data). Erasure-resilient property testing (Dixit, Raskhodnikova, Thakurta, Varma ’16) and tolerant property testing (Parnas, Ron, Rubinfeld ’06) are two formal models of sublinear algorithms that account for the presence of erasures and errors in input data, respectively.

We first show that there exists a property P that has an erasure-resilient tester whose query complexity is independent of the input size n, whereas every tolerant tester for P has query complexity that depends on n. We obtain this result by designing a local list decoder for the Hadamard code that works in the presence of erasures, thereby proving an analog of the famous Goldreich-Levin Theorem. We also show a strengthened separation by proving that there exists another property R such that R has a constant-query erasure-resilient tester, whereas every tolerant tester for R requires n^{Omega(1)} queries. The main tool used in proving the strengthened separation is an approximate variant of a locally list decodable code that works against erasures.

Joint work with Sofya Raskhodnikova and Noga Ron-Zewi.

Speaker: Jalaj Upadhyay

Affiliation: JHU

Title: Differentially Private Spectral Sparsification of Graphs

Abstract:

In this talk, we will discuss differentially private spectral sparsification of graphs. We argue that traditional spectral sparsification where the output graph is a subgraph of the input graph is not possible with differential privacy. This motivates us to define a relaxed version of spectral sparsification of graphs.

We consider edge-level privacy, i.e., neighboring graphs differs in one edge with weight one. We give efficient $(\alpha,\beta)$-differentially private algorithms that, on input a dense graph G, construct a spectral sparsification of G. Our output graphs has $ O(n/\eps^2)$ weighted edges, which matches the best known non-private algorithms.

We can use our private sparse graph to solve various combinatorial and learning problems on graphs efficiently while preserving differential privacy. Some examples include all possible cut queries, Max-Cut, Sparse-Cut, Edge-Expansion, Laplacian eigenmaps, etc.

This talk is based on a joint work with Raman Arora and Vladimir Braverman.

Speaker: Ke Wu

Affiliation: Johns Hopkins University

Title: Synchronization Strings: Efficient and Fast Deterministic Constructions over Small Alphabets

Abstract:

Synchronization strings are recently introduced by Haeupler and Shahrasbi (STOC 2017) in the study of codes for correcting insertion and deletion errors (insdel codes). They showed that for any parameter ε>0, synchronization strings of arbitrary length exist over an alphabet whose size depends only on ε. Specifically, they obtained an alphabet size of O(ε^{−4}), which left an open question on where the minimal size of such alphabets lies between Ω(ε^{1}) and O(ε^{−4}). In this work, we partially bridge this gap by providing an improved lower bound of Ω(ε^{−3/2}), and an improved upper bound of O(ε^{−2}). We also provide fast explicit constructions of synchronization strings over small alphabets.

Further, along the lines of previous work on similar combinatorial objects, we study the extremal question of the smallest possible alphabet size over which synchronization strings can exist for some constant ε<1. We show that one can construct ε-synchronization strings over alphabets of size four while no such string exists over binary alphabets. This reduces the extremal question to whether synchronization strings exist over ternary alphabets.