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., |