«Image Authenticity: Slightly Homomorphic Digital Signatures and Privacy Preserving Folding Schemes» by Simon Erfuth

In an era where misinformation proliferates rapidly, ensuring the authenticity of digital content can be paramount. We explore two constructions, which find applications in authenticating images shared on social media. First, we construct a slightly homomorphic signature scheme for images, which allows (some) JPEG compression. A more general approach, supporting more transformations, can be obtained using SNARKs, but known constructions using this approach are still too inefficient to be used in practice. Towards making this approach usable in practice, we define and construct privacy preserving folding schemes, a natural extension of folding schemes with selective verification.

Folding schemes transform the task of creating multiple zero-knowledge proofs that statements are in a language into creating one zero-knowledge proof for a (new) statement from the same language, at the cost of verification also requiring one to check a (cheap) inclusion proof. With known constructions of folding schemes, the inclusion proofs for a statement leak other statements. Privacy preserving folding schemes ensures that verification of one statement does not leak information about other statements, at a minimal increase in inclusion proof size. This is achieved through the introduction of NP-statement hiders, which allow an instance of a relation to be hidden as a new instance in the same relation, in a verifiable way.