Seminar

We typically have seminars on Wednesday at noon in Malone 228.  All seminar announcements will be sent to the theory mailing list.

Dec
6
Wed
[Theory] Venkata Gandikota @ Malone 228
Dec 6 @ 12:00 pm – 1:00 pm

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).

Dec
13
Wed
[Theory Seminar] Amirbehshad Shahrasbi @ Malone 228
Dec 13 @ 12:00 pm – 1:00 pm

Speaker: Amirbehshad Shahrasbi
Affiliation:Carnegie Mellon University

Title: Synchronization Strings
In this talk, I will introduce “synchronization strings”, mathematical objects which provide a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions in communication problems. Synchronization errors are strictly more general and much harder to deal with than more commonly studied symbol corruption and symbol erasure errors. For every eps > 0, synchronization strings allow to index a sequence such that one can efficiently transform k synchronization errors into (1+eps)k erasure and corruption errors. This powerful new technique has many applications.
A straight forward application of our synchronization string based indexing method gives a simple black-box construction which transforms any error correcting code (ECC) into an equally efficient insertion-deletion code with only a small increase in the alphabet size. This instantly transfers much of the highly developed understanding for regular ECCs into the realm of insertion-deletion codes. Most notably, for the complete noise spectrum, we obtain efficient near-MDS insertion-deletion codes which get arbitrarily close to the optimal rate-distance trade-off given by the Singleton bound.
Further applications of synchronization strings will be discussed including a general method of simulating symbol corruption channels over any given insertion-deletion channel, an efficient and near-optimal coding scheme for interactive communication over insertion-deletion channels, and list-decodable insertion-deletion codes.
This talk is based on joint works with Bernhard Haeupler and Ellen Vitercik from CMU.
Mar
14
Wed
[Theory Seminar] Samson Zhou
Mar 14 @ 12:00 pm – 1:00 pm

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.

Jul
2
Mon
[Theory Seminar] Sai Lakshmi Bhavana Obbattu
Jul 2 @ 12:00 pm – 1:00 pm

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.

Aug
23
Thu
[Theory Seminar] Akash Kumar @ Malone 338
Aug 23 @ 12:00 pm – 1:00 pm

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).

Sep
5
Wed
[Theory Seminar] Welcome and Introductions
Sep 5 @ 12:00 pm – 1:00 pm

Welcome and Introductions

Sep
12
Wed
[Theory Seminar] Zhengzhong Jin
Sep 12 @ 12:00 pm – 1:00 pm

Speaker: Zhengzhong Jin
Affiliation: JHU

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

Abstract: TBA

Feb
13
Wed
[Theory Seminar] Martin Farach-Colton
Feb 13 @ 12:00 pm – 1:00 pm

Speaker: Martin Farach-Colton
Affiliation: Rutgers University

Title: TBA

Abstract: TBA