Operation | Hyperproofs cost | Verkle trees cost (KZG, arity = B) | Our cost |
---|---|---|---|

n πΎ1 | ~ n πΎ1 | ||

n log(n) πΎ1 | ~n lgB | ||

1 πΎ1 | $\log_B(n)$ πΎ1 | ||

log n πΎ1 | $\log_B(n)$ πΎ1 | ||

log n β | $\log_B(n)$β | ||

m log n (πΎ1+πΎ2+β) | |||

m log n (πΎ2+πΎT+β) | no aggregation | ||

log n πΎ1 | $(\log_B(n)$+1 ) πΎ1 | ||

log( m log n) πΎT | no aggregation | ||

via IPA (costly) | no aggregation | ||

Yes | No updates | ||

Yes | Yes | ||

$O(\alpha)$ | $O(n \log B)$ | ||

NA | $B^d + B^{d-1} + ... + B$ πΎ1 | ||

NA | d is depth of VT; B is branching factor. It holds that $n = B^d$, i.e., $d = \log_B(n)$ |