Towards a Theory of Homomorphic Compression

Abstract. In this talk we survey recent progress on designing homomorphic fingerprints. Fingerprinting is a classic randomized technique for efficiently verifying whether two files are equal. We will discuss two extensions of this basic functionality: a) verifying whether two text files are cyclic shifts of one another and b) when the files correspond to “address books”, verifying whether the resulting social network is connected. Underlying both results is the idea of homomorphic lossy compression, i.e., lossy data compression that supports a range of operations on the compressed data that correspond directly to operations on the original data.