Applications of Structure-Preserving Cryptography and Pairing-Based NIZK Proofs
Benoît Libert · HAL (Le Centre pour la Communication Scientifique Directe) · 2015
This habilitation thesis deals with cryptographic primitives that preserve the algebraic structure of underlying objects (messages, keys, etc) and their applications to the design of non-interactive zero-knowledge proofs and privacy-enhancing cryptographic primitives.In 2008, Groth and Sahai showed how to make these proof systems relatively efficient in abelian groups endowed with a bilinear map. These techniques, however, require to work with lower-level primitives where handled objects all live in a cyclic abelian group. Among other things, we need to sign messages without destroying their algebraic structure (in particular, without hashing them first) so as to be able to efficiently prove properties about hidden signed messages. The first part of this thesis describes a structure-preserving signature scheme which was the first efficient realization under previously studied algorithmic assumptions. These tools are also utilized in the design of a novel revocation mechanism for group signatures, which allow users to anonymously sign messages on behalf of a population they belong to. The second part of this thesis considers structure-preserving signatures endowed with homomorphic properties. We show how to use them in the design of non-malleable cryptographic primitives. Using linearly homomorphic structurepreserving signatures, we notably obtain non-malleable commitments to group elements and non-interactive zero-knowledge proofs, as well as public-key encryption schemes that resist chosen-ciphertext attacks.