Zero-knowledge proofs have become an important tool for addressing privacy and scalability concerns in cryptographic protocols. For zero-knowledge proofs used in blockchain applications, it is desirable to have small proof sizes and fast verification. Yet by design, existing constructions with these properties such as zk-SNARKs also have a secret trapdoor embedded in a relation dependent structured reference string (SRS). Knowledge of this trapdoor suffices to break the security of these proofs. The SRSs required by zero-knowledge proofs are usually constructed with multiparty computation protocols, but the resulting parameters are specific to each individual circuit. In this thesis, we propose a model for constructing zero-knowledge arguments (i.e. zero-knowledge proofs with computational soundness) in which the generation of the SRS is directly considered in the security analysis. In our model the same SRS can be used across multiple applications. Further, the model is updatable i.e. users can update the universal SRS and the SRS is considered secure provided at least one of these users is honest. We propose two zero-knowledge arguments with updatable and universal SRSs, as well as a third which is neither updatable nor universal, but which through similar techniques achieves simulation extractability. The proposed arguments are practical, with proof sizes never more than a constant number of group elements. Verification for two of our constructions consist of a small number of pairing operations. For our other construction, which has the desirable property of a linear sized updatable and universal SRS, we describe efficient batching techniques so that verification is fast in the amortised setting
