On 26 August 2020 at 2.15 p.m., in Zoom room, Behzad Abdolmaleki will defend his thesis On Succinct Non-Interactive Zero-Knowledge Protocols Under Weaker Trust Assumptions for obtaining the degree of Doctor of Philosophy (Computer Science).
Prof. Helger Lipmaa (Institute of Computer Science UT and Simula UiB Norway);
Prof. Olivier Blazy (University of Limoges, France); PhD Carla Ràfols (Universitat Pompeu Fabra, Spain).
Quite central primitives in cryptographic protocols are (Universally composable (UC)) commitment schemes and zero-knowledge proofs that getting frequently employed in real-world applications. A (UC) commitment scheme enables a committer to compute a commitment to a secret message, and later open it in a verifiable manner (UC protocols can seamlessly be combined with other UC protocols and primitives while the entire protocol remains secure). A zero-knowledge proof is a protocol usually between a prover and a verifier that allows the prover to convince the verifier of the legality of a statement without disclosing any more information. Zero-knowledge proofs and in particular Succinct non-interactive zero-knowledge proofs (SNARKs) and quasi adaptive NIZK (QA-NIZK) are of particular interest in the real-world applications, with cryptocurrencies or more generally distributed ledger technologies being the prime examples. The two serious issues and the main drawbacks of the practical usage of NIZKs are (i) the demand for a trusted setup for generating the common reference string (CRS) and (ii) providing the UC security. In this thesis, we essentially investigate the aforementioned issues and propose concrete constructions for them. We first investigate subversion SNARKs (Sub zk- SNARKs) when the CRS is subverted. In particular, we build a subversion of the most efficient SNARKs. Then we initiate the study of subversion QA-NIZK (Sub-QA-NIZK) and construct subversion of the most efficient QA-NIZKs. For the second issue, providing UC-security, we first using hash proof systems or smooth projective hash functions (SPHFs), we introduce a new cryptographic primitive called publicly computable SPHFs (PC-SPHFs) and construct the currently most efficient non-interactive UC-secure commitment. Finally, we develop a new technique for constructing UC-secure commitments schemes that enables one to generate CRS of NIZKs by using MPC in a UC-secure manner.