Pairings, particularly in the context of elliptic curves, have become an important cryptographic building block. In particular, pairings are used in popular zero-knowledge–proof protocols, enabling a wide variety of applications. They are also the crucial ingredient allowing fast aggregation of BLS signatures. These signatures are used by Ethereum, with efficient aggregation being essential for scaling to a high number of validators. But what are pairings? This article is the first of a two-part...