Ligero: https://github.com/arkworks-rs/poly-commit/tree/master/poly-commit/src/linear_codes

Ligero is built around the following key components:

• Prime field arithmetic (operations are performed over a prime field $\mathbb{F}_p$)
• One-sided RS encoding
• Merkle tree commitments over encoded rows
• Randomized checking through proximity and consistency tests

Required Changes for ZODA

Field Change

• Current: Ligero operates over a prime field $\mathbb{F}_p$.
• ZODA requirement: Operations should be over a binary field $\mathbb{F}_{2^k}$.

Two-Sided RS Encoding

• Current: Ligero uses one-sided RS encoding (applied across rows).
• ZODA requirement: Two-sided RS encoding (both across rows and columns) is needed.

Randomization Step (Diagonal Scaling)

• Current: Ligero does not randomize data between RS encodings.
• ZODA requirement:
  • After row encoding to obtain $X$, we must randomly scale each column by a random field element.
  • Construct a diagonal matrix $D_r$ where $D_r[i][i] = r_i$ is random (derived via Fiat–Shamir).
  • Perform matrix multiplication $X \cdot D_r$ before column encoding.

Multiple Merkle Trees

• Current: Ligero commits to a single Merkle tree (over rows).
• ZODA requirement:
  • Construct three separate Merkle trees:
    1. root_X: Commitment to the rows of $X.$
    2. root_Y: Commitment to the columns of $Y$ (after random scaling and RS encoding).
    3. root_Z: Commitment to the final matrix $Z$.
• Verifiers will sample and check consistency across all three trees.