This thesis aims to study zero-knowledge arguments, a cryptographic primitive that allows proving a statement while yielding nothing beyond its truth. Specifically, we focus on a family of arguments whose construction is based on a secure multiparty computation. It is well known that, given any functionality f, there exists a secure multiparty protocol computing it with passive security. Let us take any one-way function f, and a secure multiparty protocol computing f. It has been shown seventeen years ago that we can build a zero-knowledge argument for the NP-problem of finding a pre-image of f. This construction was considered only theoretical until a few years ago, and this thesis contributes to the emergence of new techniques as well as efficient applications.
As an appetizer, we develop simple zero-knowledge protocols that significantly improve the state-of-the-art communication complexity for some well-known problems. Our first substantial contribution, with a desire to share small elements over large fields, is the introduction of a sharing over the integers that is securely embedded in our protocols with some artificial abortion. In line with our sharing over the integers, we propose a cryptographic string commitment scheme based on subset sum problems. Then, we present a proof construction employing conversion between additive and multiplicative secret sharings, leading to efficient proofs of linear and multiplicative relations. Finally, leaving aside protocols conception, we explore cryptography foundations with multi-prover zero-knowledge proofs, a framework for distributing the prover's computation of zero-knowledge proofs.