1. A method for determining mathematical pairings for use in cryptography, comprising: aggregating a plurality of inversions associated with a first set of elements to obtain an aggregated plurality of inversions, the first set of elements comprising a first curve point; determining mathematical pairings associated with the first set of elements using the aggregated plurality of inversions; receiving a second set of elements; determining that a second curve point comprised in the second set of elements is a same element as the first curve point; and reusing at least some of the aggregated plurality of inversions in determining mathematical pairings associated with the second set of elements, at least one of the determining mathematical pairings associated with the first set of elements or the determining mathematical pairings associated with the second set of elements comprising determining mathematical pairings in affine coordinates along a binary representation of a scalar readable from right to left, at least some of the method implemented in hardware.