# Membership Proofing on Synthetic Membership Proof Sets Source: [Membership Proofing on Synthetic Membership Proof Sets]() Collection index: [llms.txt]() Data updated: 2026-04-13T07:09:30.756Z Evaluation of Membership Proofing algorithms using the Synthetic Membership Proof Sets dataset, focusing on proof size and average path length metrics. A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. | Scope | Recorded value | | --- | --- | | Task | Membership Proofing | | Dataset (including any stated split) | Synthetic Membership Proof Sets | | Metric | Proof Size (bytes) | | Unit | SIZE | | Direction | Lower is better | | Results loaded | 32 of 32 | | Coverage | All results currently returned for this benchmark | Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol. ## Metrics - [Proof Size (bytes)](): Lower is better; unit: SIZE. - [Average Path Length](): Lower is better; unit: SCALAR. ## Recorded results | Method | Proof Size (bytes) | Result date | Report paper | | --- | --- | --- | --- | | Patricia-Merkle | 41.7 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 160 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 224 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 224 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 224 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 224 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 224 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 224 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 224 | Not recorded | 68fa753a1e209131cea66948 | | OR-Aggregation | 224 | Not recorded | 68fa753a1e209131cea66948 | | Patricia-Merkle | 489.05 | Not recorded | 68fa753a1e209131cea66948 | | Patricia-Merkle | 890.47 | Not recorded | 68fa753a1e209131cea66948 | | Patricia-Merkle | 1270.88 | Not recorded | 68fa753a1e209131cea66948 | | Patricia-Merkle | 1695.27 | Not recorded | 68fa753a1e209131cea66948 | | Patricia-Merkle | 2104.16 | Not recorded | 68fa753a1e209131cea66948 | | Patricia-Merkle | 2513.06 | Not recorded | 68fa753a1e209131cea66948 | | Patricia-Merkle | 2921.95 | Not recorded | 68fa753a1e209131cea66948 | ### Patricia-Merkle Proof Size (bytes): 41.7. Result ID: 69dc957947f34ce924c315c0. [Reporting paper]() Recorded evaluation configuration: {"Number of Elements":"100"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315c1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100","Cryptographic Primitive":"Ed25519"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315c2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100","Cryptographic Primitive":"secp256r1"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315c5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"1,000","Cryptographic Primitive":"Ed25519"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315c6. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"1,000","Cryptographic Primitive":"secp256r1"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315c9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"10,000","Cryptographic Primitive":"Ed25519"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315ca. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"10,000","Cryptographic Primitive":"secp256r1"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315cd. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100,000","Cryptographic Primitive":"Ed25519"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315ce. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100,000","Cryptographic Primitive":"secp256r1"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315d1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"1,000,000","Cryptographic Primitive":"Ed25519"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315d2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"1,000,000","Cryptographic Primitive":"secp256r1"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315d5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"10,000,000","Cryptographic Primitive":"Ed25519"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315d6. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"10,000,000","Cryptographic Primitive":"secp256r1"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315d9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100,000,000","Cryptographic Primitive":"Ed25519"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315da. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100,000,000","Cryptographic Primitive":"secp256r1"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315dd. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"300,000,000","Cryptographic Primitive":"Ed25519"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 160. Result ID: 69dc957947f34ce924c315de. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"300,000,000","Cryptographic Primitive":"secp256r1"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 224. Result ID: 69dc957947f34ce924c315c3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100","Cryptographic Primitive":"BLS12-381"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 224. Result ID: 69dc957947f34ce924c315c7. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"1,000","Cryptographic Primitive":"BLS12-381"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 224. Result ID: 69dc957947f34ce924c315cb. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"10,000","Cryptographic Primitive":"BLS12-381"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 224. Result ID: 69dc957947f34ce924c315cf. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100,000","Cryptographic Primitive":"BLS12-381"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 224. Result ID: 69dc957947f34ce924c315d3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"1,000,000","Cryptographic Primitive":"BLS12-381"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 224. Result ID: 69dc957947f34ce924c315d7. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"10,000,000","Cryptographic Primitive":"BLS12-381"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 224. Result ID: 69dc957947f34ce924c315db. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"100,000,000","Cryptographic Primitive":"BLS12-381"}. This record does not assert independent reproduction. ### OR-Aggregation Proof Size (bytes): 224. Result ID: 69dc957947f34ce924c315df. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Number of Elements":"300,000,000","Cryptographic Primitive":"BLS12-381"}. This record does not assert independent reproduction. ### Patricia-Merkle Proof Size (bytes): 489.05. Result ID: 69dc957947f34ce924c315c4. [Reporting paper]() Recorded evaluation configuration: {"Number of Elements":"1,000"}. This record does not assert independent reproduction. ### Patricia-Merkle Proof Size (bytes): 890.47. Result ID: 69dc957947f34ce924c315c8. [Reporting paper]() Recorded evaluation configuration: {"Number of Elements":"10,000"}. This record does not assert independent reproduction. ### Patricia-Merkle Proof Size (bytes): 1270.88. Result ID: 69dc957947f34ce924c315cc. [Reporting paper]() Recorded evaluation configuration: {"Number of Elements":"100,000"}. This record does not assert independent reproduction. ### Patricia-Merkle Proof Size (bytes): 1695.27. Result ID: 69dc957947f34ce924c315d0. [Reporting paper]() Recorded evaluation configuration: {"Number of Elements":"1,000,000"}. This record does not assert independent reproduction. ### Patricia-Merkle Proof Size (bytes): 2104.16. Result ID: 69dc957947f34ce924c315d4. [Reporting paper]() Recorded evaluation configuration: {"Number of Elements":"10,000,000"}. This record does not assert independent reproduction. ### Patricia-Merkle Proof Size (bytes): 2513.06. Result ID: 69dc957947f34ce924c315d8. [Reporting paper]() Recorded evaluation configuration: {"Number of Elements":"100,000,000"}. This record does not assert independent reproduction. ### Patricia-Merkle Proof Size (bytes): 2921.95. Result ID: 69dc957947f34ce924c315dc. [Reporting paper]() Recorded evaluation configuration: {"Number of Elements":"300,000,000"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.