New Techniques for Public-Key Cryptography

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The aim of this proposal is to strengthen the foundations of public-key cryptography (PKC), by investigating the fundamental goals of minimizing assumption complexity and improving the efficiency of cryptographic constructions, and to develop techniques and tools that will enable the design of more efficient and robust secure-computation protocols. In recent years advances in basic problems in PKC (some of which were made in my work) have led to breakthrough results, such as new constructions of public-key encryption (PKE) schemes resisting active attacks (CCA), and new techniques for multi-party computation (MPC) problems such as private-information retrieval (PIR), private-set intersection, and non-interactive zero knowledge (NIZK). For example, my work on the first construction of trapdoor functions (TDFs) from the Computational Diffie-Hellman (CDH) Assumption led to subsequent advancements, such as the first construction of CCA-secure PKE from TDFs, the first construction of PIR from the Diffie-Hellman assumption, and the introduction of a new notion called trapdoor hash, which in turn led to new feasibility results on non-interactive zero knowledge. My proposed research will formalize this relationship further and will tackle associated problems in public-key cryptography. The investigation will put public-key cryptography on a firmer foundation, will introduce techniques that will lead to various MPC protocols with enhanced security/functionality, and will improve out understanding of capabilities and limits of cryptographic techniques. The project will focus on three main thrusts to address the above problems. First, I will realize core PKC primitives, and their families, from minimal assumptions and with improved efficiency. Examples of such primitives include trapdoor functions/permutations, trapdoor hash schemes and oblivious transfer protocols with minimal communication. Second, I will apply these techniques to design MPC problems with improved efficiency and enhanced functionality. Finally, I will identify and formalize barriers that may exist against the above goals. This will be carried out by proving lower bounds on the assumption complexity and efficiency of constructions for the above goals. Public-key cryptography plays an integral role in the design of secure protocols for the internet. In addition to advancing scientific knowledge, my proposed research will develop tools that have the potential of being deployed in various privacy-enhancing technologies. Such tools have societal benefits, enabling computation on sensitive data while keeping the data private. For example, my proposed goals for MPC problems (such as private-set intersection and private-information retrieval) will lead to efficient protocols for many important real-world applications such as privacy-preserving data analytics, secure contact tracing, etc.