Efficient Cryptographic Primitives for Non-Interactive Zero-Knowledge Proofs and Applications

Non-interactive zero-knowledge (NIZK) proofs have enjoyed much interest in cryptography since they were introduced more than twenty years ago by Blum et al. [BFM88]. While quite useful when designing modular cryptographic schemes, until recently NIZK could be realized efficiently only using certain heuristics. However, such heuristic schemes have been widely criticized. In this work we focus on designing schemes which avoid them. In [GS08], Groth and Sahai presented the first efficient (and currently the only) NIZK proof system in the standard model. The construction is based on bilinear maps and is limited to languages of certain satisfiable system of equations. Given this expressibility limitation of the system of equations, we are interested in cryptographic primitives that are “compatible” with it. Equipped with such primitives and the Groth-Sahai proof system, we show how to construct cryptographic schemes efficiently in a modular fashion. In this work, we describe properties required by any cryptographic scheme to mesh well with Groth-Sahai proofs. Towards this, we introduce the notion of “structurepreserving” cryptographic schemes. We present the first constant-size structurepreserving signature scheme for messages consisting of general bilinear group elements. This allows us (for the first time) to instantiate efficiently a modular construction of round-optimal blind signature based on the framework of Fischlin [Fis06]. Our structure-preserving homomorphic trapdoor commitment schemes yield the