CAREER

This project advances the understanding of number theory, geometry, and cryptography. Number theory and geometry are among the oldest and most central topics in mathematics, while their application to cryptography underlies modern cybersecurity. The project focuses on the relationships between number-theoretic information and geometric structures such as elliptic curves, circle packings, and lattices.

In an ideal world, secure software would be built as a set of mutually distrusting components that work together to accomplish goals. However, modern software is not built this way; rather, it heavily trusts a component called the operating system kernel. Fortunately, there are new methods of isolating programs from each other and from the OS kernel to minimize the damage caused if an attacker compromises a critical component. However, such solutions are too slow and are vulnerable to sophisticated implicit information flow attacks.

Obfuscation schemes are highly desirable tools for transforming programs into unintelligible ones while preserving functionality. However, so far, there lack obfuscation schemes with well-founded security guarantees. The main objective of this project is addressing this gap, by developing new approaches for designing obfuscation schemes based on standard, well-studied, assumptions. Another objective is using obfuscation as a versatile tool to enable a wide range of cryptographic and security applications.

Malicious software (malware) has become a major threat to computer security and will continue to be a central theme for computer security research for decades. This project takes a binary and virtualization centric approach to effectively and efficiently defeat malware using both online and offline analysis. Offline malware analysis aims to extract knowledge about the inner-workings for a newly discovered malware instance or software exploit, for the purpose of building up proper defense against similar attacks.

The explosion of digital data carries a wealth of opportunities. The ability to collect and mine data at scale continues to enable new applications and transform our lives. However, privacy concerns are seen as a major hurdle towards data sharing and analytics. This project develops a practical framework for "oblivious computation", which allows general computation over sensitive data, but without disclosing the data.