
Covert twoparty computation is a stronger notion of security than standard secure twoparty computation. Like standard secure twoparty computation, covert twoparty computation allows Alice and Bob, with secret inputs x_A and x_B respectively, to compute a function f(x_A,x_B) without leaking any additional information about their inputs. In addition, covert twoparty computation guarantees that even the existence of a computation is hidden from all protocol participants unless the value of the function mandates otherwise. This allows the construction of protocols that return f(x_A,x_B) only when it equals a certain value of interest (such as "Yes, we are romantically interested in each other") but for which neither party can determine whether the other even ran the protocol whenever f(x_A,x_B) is not a value of interest.
This project will explore extending covert twoparty computation to more than two parties. The REU student will investigate covert twoparty computation and learn the necessary cryptographic tools. The undergraduate will learn the techniques of modern theoretical cryptography: proofs by simulation, definitions of semantic security, et cetera. The student will also learn about the cutting edge research in multiple areas of theoretical cryptography, such as multiparty computation and theoretical foundations of steganography. As a prerequisite, the undergraduate must have knowledge of computer science theory, especially complexity theory or cryptography. 
