Abstract

One of the major advances in modern cryptography has been the advent of fully homomorphic encryption. Homomorphic encryption allows data to be processed in an encrypted form without access to the key, and as such has a myriad of applications in secure computing. All known schemes which allow for universal computation on encrypted data, termed fully-homomorphic encryption, derive their security from assumptions concerning the intractability of certain computational problems. In this talk, I will address the question of whether quantum mechanics allows for unconditionally secure fully-homomorphic encryption schemes. I will begin by presenting a negative result: no scheme which is both compact and fully-homomorphic can have accessible information exactly equal to zero. Surprisingly, however, this statement is not known to hold if the constraint on accessible information is relaxed to allow for non-zero leakage of information. I will discuss the construction of encryption schemes which allow non-classical processing of the encrypted data in which the accessible information is bounded.