| Operation | Hyperproofs cost | Verkle trees cost (KZG, arity = B) | Our cost |
|---|---|---|---|
n πΎ1 | ~ n πΎ1 | ||
n log(n) πΎ1 | ~n lgB | ||
1 πΎ1 | logBβ(n) πΎ1 | ||
log n πΎ1 | logBβ(n) πΎ1 | ||
log n β | logBβ(n)β | ||
m log n (πΎ1+πΎ2+β) | |||
m log n (πΎ2+πΎT+β) | no aggregation | ||
log n πΎ1 | (logBβ(n)+1 ) πΎ1 | ||
log(m log n) πΎT | no aggregation | ||
via IPA (costly) | no aggregation | ||
Yes | No updates | ||
Yes | Yes | ||
O(Ξ±) | O(nlogB) | ||
NA | Bd+Bdβ1+...+B πΎ1 | ||
NA | d is depth of VT; B is branching factor. It holds that n=Bd, i.e., d=logBβ(n) |