The International Research Fellowship Program enables U.S. scientists and engineers to conduct nine to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.
This award will support a thirteen month research fellowship by Dr. David Freeman to work with Dr. Ronald Cramer at the Centrum voor en Informatica in the Netherlands. Co-support for this project has been provided by the Math and Physical Science?s Office of Multidisciplinary Activities (OMA).
This project topic is how to extend the uses of curves and abelian varieties over finite fields in secure multi-party computation and pairing-based cryptography. A majority of the research at CWI and Leiden focuses on understanding and developing the relationship between arithmetic geometry and secure multi-party computation. Secure multi-party computation (MPC) is a process by which a number of parties, each holding a private value, compute a function of all the private values with no player learning anything about any other player's value. Recently, techniques of arithmetic geometry have been applied to problems in MPC, with the result being schemes that are more efficient and flexible than any previously known. For example, the MPC protocol of Chen and Cramer uses curves over finite fields to greatly increase the number of players than can participate in a computation of a given size. The PI is working to expand and generalize the Chen-Cramer scheme and related protocols, with a goal of producing new MPC protocols that are more efficient than existing schemes, as well as protocols that have new and useful functionalities.
The remainder of the research time will be spent developing curves and abelian varieties over finite fields for use in pairing-based cryptography. Pairing-based cryptography is an emerging subdiscipline that uses bilinear maps on arithmetic-geometric objects to implement cryptographic protocols. The objects used in these protocols are rare and thus require specialized constructions. Initially pairing-based protocols used elliptic curves over finite fields, but recently some researchers have proposed using abelian varieties, which is a larger category of objects that includes elliptic curves. At present very little is known about general abelian varieties in the context of pairing-based cryptography. The PI is working to understand the properties that make an abelian variety useful for pairing-based cryptography, and to use this knowledge to construct abelian varieties that are competitive with elliptic curves in terms of performance and security.
The ultimate goal is to produce algorithms that will be implemented in real-life cryptographic applications. Applications of pairing-based cryptography include encrypting medical records and authenticating ?smart cards,? while efficient multi-party computation protocols ensure that participants in a security system cannot ?cheat? by disobeying the rules of the system. Beyond its technological impact, this collaboration with CWI and Universiteit Leiden will help build connections between the international communities of mathematicians and cryptographers, benefiting both research and education in these two fields.
