Benchmarks

We report benchmark results below in the following form:

• aws_instance (e.g. C7i.16xlarge, C8g.16xlarge, G6.2xlarge)
• arch (e.g. GPU/x86/aarch64)
  • Note: For x86/aarch64 we report st/mt to indicate single- vs multi-threaded operation
• Witness generation time [ms]
• Proof generation time [ms]
• Proof verification time [ms]
• Proof size [KiB]

In order to reproduce our benchmarks in AWS, you can check out our user guide.

Ethereum ECDSA Signature Aggregation

We report our ethsign (ECDSA signature over a 67-byte message) performance.

Reproduce Binius64 benchmarks using:

ETHSIGN_SIGNATURES=1 ETHSIGN_MSG_BYTES=67 cargo bench --no-default-features --bench ethsign # single threaded
ETHSIGN_SIGNATURES=1 ETHSIGN_MSG_BYTES=67 cargo bench --bench ethsign # multi threaded

Hash-based Signature Aggregation

We benchmarks a post-quantum hash-based signature aggregation scheme that combines XMSS (eXtended Merkle Signature Scheme) with Winternitz one-time signatures (WOTS), using Keccak-256 for all cryptographic operations (i.e., so suitable for Ethereum).

Configuration parameters:

• Validators: 16 concurrent signers
• XMSS tree height: 13 (8,192 signature capacity)
• WOTS paramters: 4-bit digit resolution and target sum 297

Reproduce Binius64 benchmarks using:

HASHSIGN_VALIDATORS=16 HASHSIGN_TREE_HEIGHT=13 HASHSIGN_SPEC=2 cargo bench --no-default-features -p binius-examples --bench hashsign # single threaded
HASHSIGN_VALIDATORS=16 HASHSIGN_TREE_HEIGHT=13 HASHSIGN_SPEC=2 cargo bench -p binius-examples --bench hashsign # multi threaded

Hashing

We compare our Keccak-256 and Blake2s performance against Polygon Zero's Plonky3 and StarkWare's Stwo provers, respectively.

Keccak-256

In each benchmark, we prove 1,365 keccak-f permutations (matching the benchmark Plonky3 runs):

Reproduce Binius64 benchmarks using:

KECCAK_PERMUTATIONS=1365 cargo bench --no-default-features --bench keccak # single threaded
KECCAK_PERMUTATIONS=1365 cargo bench --bench keccak # multi threaded

• Repository: https://github.com/Plonky3/Plonky3.git
• Branch: main
• Commit: 80803612ff4b6634519e12fa4bf075f679afcc1c

Blake2s

Here, we test 2,048 Blake2s compressions (matching what Stwo's benchmark does):

Reproduce Binius64 benchmarks using:

BLAKE2S_MAX_BYTES=131072 cargo bench --no-default-features -p binius-examples --bench blake2s # single threaded
BLAKE2S_MAX_BYTES=131072 cargo bench -p binius-examples --bench blake2s # multi threaded

• Repository: https://github.com/starkware-libs/stwo.git
• Branch: dev
• Commit: d9176e6e22319370a8501f799829b920c0db2eac

Hashing Throughput Comparison

We believe that a fair metric by which to compare provers is hashing throughput, i.e. the amount of input data that these provers can generate a proof-of-hash about, per unit of time. The following charts compare the hashing throughputs of Binius64, Plonky3 and Stwo provers, each generating proofs about Keccak-256 and Blake2s hashes. In each benchmark, we generate a proof about exactly 1 MiB of total input data.

Reproduce Binius64 benchmarks using:

KECCAK_PERMUTATIONS=8192 cargo bench --no-default-features --bench keccak # single threaded
KECCAK_PERMUTATIONS=8192 cargo bench --bench keccak # multi threaded
 
BLAKE2S_MAX_BYTES=1048576 cargo bench --no-default-features -p binius-examples --bench blake2s # single threaded
BLAKE2S_MAX_BYTES=1048576 cargo bench -p binius-examples --bench blake2s # multi threaded
 
BLAKE2B_MAX_BYTES=1048576 cargo bench --no-default-features -p binius-examples --bench blake2b # single threaded
BLAKE2B_MAX_BYTES=1048576 cargo bench -p binius-examples --bench blake2b # multi threaded