Projects

• Analysis of Cryptographic Primitives: The security of most cryptographic schemes relies implicitly on the security of the cryptographic primitives used. However, most primitives used in practice are not provably secure. We are analysing such primitives, using various techniques, in order to understand their behavior better. The goal of this project is to subject such primitives to close scrutiny and find vulnerabilities in them. We hope that the understanding gained in this process shall help us build more efficient and provably secure primitives. The primitives we are currently interested include hash functions, block ciphers and message authentication codes.
• AV Codes: AV codes are a class of error correcting codes developed that have fractional minimum distance close to half and very efficient decoding algorithm. The design of the code makes it “resemble” a random code and thus inherits many properties proved by Shannon for random codes. The main advantage of the AV codes are that their asymptotic properties becomes practically true at much smaller block lengths as compared, say LDPC codes. This makes them very attractive for use in low power devices.
• Graph-matching approach to virus detection: The goal of this project is to develop an algorithm which can do robust matching and diffing at the level of binaries without access to source code. The idea is to view the binaries as their control flow graphs and trying to solve the Minimum Graph Transformation problem on the graphs. Potential applications include virus checking, efficient patching, code plagiarism detection and code duplication detection.
• Protocols for Electronic Commerce and Privacy: We have several ongoing projects in the area of cryptographic protocols, including traitor tracing protocols, group key agreement protocols, identity and privacy management protocols. We are also interested in studying their applications to electronic commerce.
• Learning in an adversarial context: Machine learning algorithms are nowadays popular in many applications like anti-spam, intrusion detection, search, etc., where security-concerns can become a serious issue. What happens when these applications themselves are subject to malicious attacks? In particular, we consider the problem of learning support vector machines from data that has been maliciously manipulated by an adversary.
• Learning-based prioritization of access control vulnerabilities: We investigate the problem of learning probability models for data constituted by structural patterns like Directed Acyclic Graphs.
• Matrix Rigidity: A matrix is rigid if many of its entries must be altered to reduce its rank, say, to a constant fraction of its original rank. Finding explicit rigid matrices is a long-standing open question in combinatorial-algebraic complexity. Recently, we proved optimal lower bounds on the rigidity of certain specific complex matrices. Proving similar lower bounds for matrices over low-dimensional number fields and finite fields is still a major challenge. In a different direction, it is conjectured that distinguishing between random matrices and matrices of low rigidity is computationally hard. Such a conjecture can be a basis for building crypto-systems.
• Coding Theory in Cryptography and Complexity: There exists an exciting synergy between error correcting codes, cryptography, and complexity. We are particularly interested in the design and analysis of various cryptographic schemes based on (conjectured) hard problems about error correcting codes. We are also interested in constructions and limitations of new classes of locally decodable and list decodable codes and their connections to cryptography and complexity theory.
• Splitting of Abelian Varieties: We are investigating some new local-global problems in the context of Abelian varieties. We are studying the splitting behaviour of the reduction of a given absolutely simple Abelian variety modulo various primes. We are pursuing a conjecture that relates this splitting behaviour with the endomorphism algebra of the given Abelian variety.
• Pairings in Cryptography: There are certain cryptographic protocols that are based on bilinear pairings defined using Elliptic curves and their torsion points. We will study such pairing based cryptographic systems and related algorithms.

Careers

We are looking for people who are trained in mathematics, computer science, and related areas of electrical engineering, programming and security. We invite applicants from India or abroad with bachelors, masters or doctoral degrees. We have exciting opportunities at various levels for researchers, interns, visitors, and research software development engineers.