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OperationHyperproofs costVerkle trees cost (KZG, arity = B)Our cost
Commit
n ๐”พ1
~ n ๐”พ1
Compute all proofs
n log(n) ๐”พ1
~n lgB
Update digest
1 ๐”พ1
๐”พ1
Update all proofs (โ€stateโ€)
log n ๐”พ1
๐”พ1
Verify 1 proof
log n โ„™
โ„™
Aggregate m proofs
m log n (๐”พ1+๐”พ2+โ„™)
Verify aggr. of m proofs
m log n (๐”พ2+๐”พT+โ„™)
no aggregation
Size of one proof
log n ๐”พ1
+1 ) ๐”พ1
Size of aggregated proof
log(m log n) ๐”พT
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
๐”พ1
Notes
NA
d is depth of VT; B is branching factor. It holds that , i.e.,