| Operation | Hyperproofs cost | Verkle trees cost (KZG, arity = B) | Our cost |
|---|---|---|---|
Commit | n ๐พ1 | ~ n ๐พ1 | |
Compute all proofs | n log(n) ๐พ1 | ~n lgB | |
Update digest | 1 ๐พ1 | ๐พ1 | |
Update all proofs (โstateโ) | log n ๐พ1 | ๐พ1 | |
Verify 1 proof | log n โ | โ | |
Aggregate m proofs | m log n (๐พ1+๐พ2+โ) | ||
Verify aggr. of m proofs | m log n (๐พ2+๐พT+โ) | no aggregation | |
Size of one proof | log n ๐พ1 | +1 ) ๐พ1 | |
Size of aggregated proof | log(m log n) ๐พT | no aggregation | |
Group requirements | |||
Aggregation | via IPA (costly) | no aggregation | |
Updates | Yes | No updates | |
Maintainability (update all) | Yes | Yes | |
Compute/Update a fraction โ of the tree | |||
Total # of proofs in Verkle Trees | NA | ๐พ1 | |
Notes | NA | d is depth of VT; B is branching factor. It holds that , i.e., |