Pick the batching implementation from #8 to the wrapper code

[yczhangsjtu]

Pick the batching implementation from #8 to the wrapper code

[yczhangsjtu]

Benchmark results for num vars = 20:

For single polynomial:

• Commit: 118.89 ms
• Open: 237.44 ms
• Verify: 1.0043 ms

For 64 polynomials:

• Commit: 5.4084 s
• Open: 2.3355 s
• Verify: 1.3665 ms

[yczhangsjtu]

For comparison with BaseFold:

1 poly:

• Commit: 162.23 ms
• Open: 192.95 ms
• Verify: 3.6355 ms

64 polys:

• Commit: 1.5916 s
• Open: 226.44 ms
• Verify: 3.8251 ms

[yczhangsjtu]

With some fixes: make some loops parallel, remove an unnecessary clone.

For 64 polys with 20 variables:

• Commit: 3.2243 s
• Open: 252.23 ms
• Verify: 3.0184 ms

[yczhangsjtu]

• For 64 polys with 20 variables:
  • Commit: 3.0252 s (originally 5.4084 s)
  • Open: 200.19 ms (originally 2.3355 s)
  • Verify: 1.6396 ms (originally 1.3665 ms)

[yczhangsjtu]

Proof size:

WHIR for num var = 20

• Single poly: 87704 Bytes (BaseFold 1303205 Bytes)
• 64 polys: 1412408 Bytes (BaseFold 1506405 Bytes) This is problematic, shouldn't increase that much. Maybe because of unnecessary Merkle paths for the extra polynomials?