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| Operation | Hyperproofs cost | Verkle trees cost (KZG, arity = B) | Our cost |
|---|---|---|---|
Commit | n πΎ1 | ~ n πΎ1 | |
Compute all proofs | n log(n) πΎ1 | ~n lgB | |
Update digest | 1 πΎ1 | πΎ1 | |
Update all proofs (βstateβ) | log n πΎ1 | πΎ1 | |
Verify 1 proof | log n β | β | |
Aggregate m proofs | m log n (πΎ1+πΎ2+β) | ||
Verify aggr. of m proofs | m log n (πΎ2+πΎT+β) | no aggregation | |
Size of one proof | log n πΎ1 | +1 ) πΎ1 | |
Size of aggregated proof | log(m log n) πΎT | no aggregation | |
Group requirements | |||
Aggregation | via IPA (costly) | no aggregation | |
Updates | Yes | No updates | |
Maintainability (update all) | Yes | Yes | |
Compute/Update a fraction β of the tree | |||
Total # of proofs in Verkle Trees | NA | πΎ1 | |
Notes | NA | d is depth of VT; B is branching factor. It holds that , i.e., |