Alin Tomescu

Curve trees

 
  • Dec 02, 2025

tl;dr: A few notes on the beautiful curve tree work by Campanelli, Hall-Andersen and Kamp.

$ $

$\mathbb{V}$cash anonymous payments experiments

Ran a subset of the (modified) benchmarks, in a single thread, on my Apple Macbook Pro M1 Max. The benchmared scheme does not implement a proper PRF-based nullifier scheme, AFAICT. It does prove values are in-range using Bulletproofs. (I think it combines the range proof statement with the curve tree statement over the curve used in the leaves, and proves it all in one.)

See diff here.

Results over Pasta and Vellas curves:

Single_threadedPour_Curves:pasta_L:1024_D:4_ProofSize: 3970 bytes

Single_threadedPour_Curves:pasta_L:1024_D:4/prove
                        time:   [7.1789 s 7.2110 s 7.2427 s]

Single_threadedPour_Curves:pasta_L:1024_D:4_batch_verification/1
                        time:   [298.39 ms 299.27 ms 300.13 ms]

Single_threadedPour_Curves:pasta_L:1024_D:4_batch_verification/100
                        time:   [2.1153 s 2.1255 s 2.1355 s]

Results over secp256k1 and secp256r1 curves:

Single_threadedPour_Curves:secp&q_L:1024_D:4_ProofSize: 3970 bytes

Single_threadedPour_Curves:secp&q_L:1024_D:4/prove
                        time:   [8.4621 s 8.4874 s 8.5097 s]

Single_threadedPour_Curves:secp&q_L:1024_D:4_batch_verification/1
                        time:   [347.31 ms 348.01 ms 348.73 ms]

Single_threadedPour_Curves:secp&q_L:1024_D:4_batch_verification/100
                        time:   [2.4206 s 2.4312 s 2.4428 s]

The range proofs can probably be sped up using DeKART.

References

For cited works, see below 👇👇

Search