Homomorphic Signatures for Digital Photographs

We describe two homomorphic signature schemes for digital photographs such that an intermediate party in possession of a signed photograph can construct a scaled, cropped, and lossily compressed version of the photograph along with a new, valid signature, without knowing the private signing key. In other words, our signature schemes are simultaneously homomorphic with respect to cropping, scaling, and JPEG-like compression. Unlike prior ad-hoc schemes for photographic signatures, our first scheme is provably secure and quite practical. For example, a scaling-homomorphic signature scheme using our techniques requires less than 100KB of signature data for typical digital photographs. Our second signature scheme has weaker security but reduces typical signature sizes to 15KB. Both schemes extend naturally to authenticate movies and other digital media and use novel, multi-dimensional variations of Merkle hashing and GGM trees related to constructions used in computational geometry that may be of independent interest.