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<h1 align="center">leanVM-b</h1>

Warning: highly experimental.

# Benchmarks

Machine: Mac M4 Max

### XMSS aggregation

Our XMSS is specified in [XMSS.pdf](https://github.com/leanEthereum/leanVM-b/releases/download/doc-latest/XMSS.pdf).

```bash
cargo run --release -- xmss --n-signatures 900 --log-inv-rate 1 --repeat 3
```

```
XMSS aggregation, 900 signatures
  cycles (VM steps)           : 1,542,704 = 2^20.557
    proven rows               : 1,967,104 = 2^20.908  (filled to powers of two)
    details                   : DEREF 2^18.988 (33.7%)  SET 2^18.402 (22.4%)  MUL 2^18.198 (19.5%)  BLAKE2S 2^16.996 (8.5%)  XOR 2^16.96 (8.3%)  JUMP 2^16.831 (7.6%)  PACK64X2 2^9.938 (0.1%)  MEMORY 2^21.725  TOTAL_COMMITTED 2^26.195
  signers                     : 900
  proof size                  : 356.5 KiB
  aggregating                 : 1.155 s ± 3.3%      peak memory 20.705 GiB
  per signature               : 779.378 XMSS/s
  verifying                   : 0.0128 s
```

### Recursion

```bash
cargo run --release -- recursion --n 2 --log-inv-rate 2 --repeat 3
```

```
recursion 2→1, over leaves of 900 signatures
  cycles (VM steps)           : 830,516 = 2^19.664
    proven rows               : 1,196,032 = 2^20.19  (filled to powers of two)
    details                   : DEREF 2^18.21 (36.5%)  MUL 2^17.928 (30.0%)  XOR 2^17.424 (21.2%)  SET 2^15.553 (5.8%)  BLAKE2S 2^14.462 (2.7%)  PACK64X2 2^14.384 (2.6%)  JUMP 2^13.279 (1.2%)  MEMORY 2^19.989  TOTAL_COMMITTED 2^24.863
  signers                     : 1,800
  proof size                  : 220.9 KiB
  aggregating                 : 0.604 s ± 4.3%      peak memory 26.097 GiB
  verifying                   : 0.0148 s
```

### Fibonacci

```bash
cargo run --release -- fibonacci --n 2000000 --log-inv-rate 1 --repeat 3
```

```
Fibonacci (in the exponent, i.e. modulo 2^64 - 1), N = 2,000,000
  cycles (VM steps)           : 2,127,881
    details                   : MUL 2^20.937 (98.7%)  DEREF 2^13.967 (0.8%)  SET 2^12.552 (0.3%)  JUMP 2^10.968 (0.1%)  XOR 2^10.966 (0.1%)  MEMORY 2^20.964  TOTAL_COMMITTED 2^25.263
  proof size                  : 332.5 KiB
  proving                     : 0.608 s ± 6.6%   3,499,102 cycles/s      peak memory 12.112 GiB
  verifying                   : 0.00372 s
```

## Security

- 128-bit (LDR Johnson, no proximity gaps conjecture)

## Snark machinery

- Binary field of 192 bits
- PCS: [WHIR](https://eprint.iacr.org/2024/1586) (aka [Ligerito](https://eprint.iacr.org/2025/1187))

## Credits

- [flock](https://github.com/succinctlabs/flock/tree/main)
- [binius](https://github.com/IrreducibleOSS/binius)
- [binius64](https://github.com/binius-zk/binius64)

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