My research is centered around using hidden structures found in mathematical hardness for building advanced cryptography with provable security. I use hardness of well-studied mathematical problems, and design systems by developing new mechanisms for embedding algebraic structures that leverage this hardness into unbreakability of the designed system. A special theme in my research has been to expand the boundaries of lattice-based cryptography, as it is the leading candidate to offer post-quantum security along with advanced cryptographic functionality.
Through my research, I have significantly progressed current cryptographic capabilities. I have constructed numerous advanced systems such as secure program obfuscation schemes for compiling computer programs into unintelligible code, traceable encryption systems for countering unauthorized access and piracy prevention, decentralized proof systems and multi-user encryption systems for protection against subversion, and more. My work has: (1) settled the 25-year-old open problem of traitor tracing, (2) provided the most powerful quantum-safe obfuscation scheme with provable security, and (3) resolved fundamental conjectures about circular security of bit encryption systems, and more.
I have also studied applications of quantum information in cryptography, built fundamental cryptographic objects with advanced features and diverse security, and proved impossibility results. Send me an email if you are interested in learning more about my research.