Boomy: Batch Opening Of Multivariate polYnomial commitment

We present Boomy, a multivariate polynomial commitment scheme enabling the proof of the evaluation of multiple points, i.e., batch opening. Boomy is the natural extension of two popular protocols: the univariate polynomial commitment scheme of Kate, Zaverucha and Goldberg[KZG10] and its multivariate counterpart from Papamanthou, Shi and Tamassia[PST13]. Our construction is proven secure under the selective security model. In this paper, we present Boomy's complexity and the applications on which it can have a significant impact. In fact, Boomy is perfectly suited to tackling blockchain problems by greatly improving data availability sampling and shrinking existing challenges. We also present special lower-complexity cases that occur frequently in practical situations.