How to Build Succinct Arguments From Succinct Commitments

One of the celebrated achievements of modern cryptography is formulating and constructing a multitude of proof systems that, thanks to their surprising properties, act as invaluable tools in theoretical computer science and even beyond that. This article focuses on succinct arguments, a class of proof systems that has received much attention due to their notable efficiency properties, which have made them indispensable tools in secure distributed systems. Informally, in a succinct argument for an NP language, the communication complexity is much smaller than the number of bits in the witness. In this article, we provide an introduction to succinct arguments constructed from succinct commitments. This notable class includes elegant constructions that capture numerous concrete examples of succinct arguments that have both theoretical and practical applications. In particular, this class includes the most performant succinct arguments known, including ones proved to be postquantum secure. We structure ideas in progressive generality, starting from the well-known Kilian protocol, and also touch on other topics such as the Fiat–Shamir transformation.