The following benchmarks compare three different commitment schemes: Merkle Tree with LDE, Pedersen Commitments, and Ajtai Hash-based Commitments. These benchmarks were performed on:

CPU: Intel i7-12700F (single core)

RAM: 32GB

OS: Linux(Archlinux)

Repository: https://github.com/NethermindEth/commitment-schemes-comparison

Each scheme was tested with varying configurations:

Merkle Tree + LDE: Tested with Keccak, Poseidon, and Poseidon2 hash functions, using different witness lengths (2^16 to 2^20) and blow-up factors (2, 4, 8)
Pedersen Commitments: Evaluated with three witness types (constant 1, constant (Mod -1)/2, random) and varying lengths (2^16 to 2^20)
Ajtai Hash-based Commitments: Tested with different matrix dimensions (10 to 50 rows) and witness lengths (2^16 to 2^20), including NTT/iNTT performance measurements

Merkle tree + LDE

These benchmarks were conducted using the Goldilocks field (modulus 2^64 - 2^32 + 1),

Keccak

Witness length	Blow-up factor	LDE time	Commit time
2^16	2	4.4ms	51.6ms
2^16	4	7.5ms	103.1ms
2^16	8	13.0ms	206.0ms
2^17	2	11.3ms	103.0ms
2^17	4	16.4ms	206.2ms
2^17	8	27.4ms	412.3ms
2^18	2	25.1ms	206.2ms
2^18	4	35.05ms	412.5ms
2^18	8	63.3ms	824.1ms
2^19	2	52.6ms	412.6ms
2^19	4	76.1ms	825.0ms
2^29	8	137.7ms	1653.0ms
2^20	2	109.7ms	824.5ms
2^20	4	168.7ms	1651.8ms
2^20	8	311.9ms	3.3s

Poseidon

Witness length	Blow-up factor	LDE time	Commit time
2^16	2	4.3ms	530.3ms
2^16	4	7.5ms	1060.6ms
2^16	8	13.0ms	2.1s
2^17	2	11.3ms	1063.0ms
2^17	4	16.3ms	2.1s
2^17	8	27.5ms	4.2s
2^18	2	25.0ms	2.1s
2^18	4	35.3ms	4.2s
2^18	8	60.3ms	8.5s
2^19	2	52.5ms	4.2s
2^19	4	74.1ms	8.5s
2^29	8	137.8ms	17.1s
2^20	2	107.3ms	8.5s
2^20	4	167.7ms	17.0s
2^20	8	310.5ms	33.9s

Poseidon 2

Witness length	Blow-up factor	LDE time	Commit time
2^16	2	4.3m	227.9ms
2^16	4	7.5ms	455.8ms
2^16	8	13.0ms	912.3ms
2^17	2	11.3ms	456.1ms
2^17	4	16.3ms	911.4ms
2^17	8	27.6ms	1823.2ms
2^18	2	25.1ms	912.2ms
2^18	4	35.0ms	1822.6ms
2^18	8	62.1ms	3.6s
2^19	2	52.6ms	1823.6ms
2^19	4	76.1ms	3.6s
2^29	8	137.9ms	7.3s
2^20	2	109.1ms	3.6s
2^20	4	165.7ms	7.3s
2^20	8	312.3ms	14.6s

Pedersen

Witness length	Witness type	Commit time
2^16	1 in all entries	19.3ms
2^16	(Mod -1)/2 in all entries	132.1ms
2^16	Random witness	305.3ms
2^17	1 in all entries	39.0ms
2^17	(Mod -1)/2 in all entries	256.3ms
2^17	Random witness	589.9ms
2^18	1 in all entries	89.5ms
2^18	(Mod -1)/2 in all entries	469.2ms
2^18	Random witness	1142.5ms
2^19	1 in all entries	179.6ms
2^19	(Mod -1)/2 in all entries	931.7ms
2^19	Random witness	2.1s
2^20	1 in all entries	345.8ms
2^20	(Mod -1)/2 in all entries	1846.1ms
2^20	Random witness	4.1s