Nomos DA v1

• Total Data Size ($D$): This is given (128 KB, 256 KB, ..., 32 MB).
• Original Matrix Size:
  • Columns (𝑐) = 1024 (fixed)
  • Rows (𝑟) = $D / (c \times 32)$, since each chunk is 32 bytes.
• Extended Matrix:
  • Columns double → 2048
  • Rows remain same → r

Original Data Matrix: r × 1024

Extended Data Matrix: r × 2048

• Data Sent to Each Subnetwork (One Column of Extended Matrix):
  • Column Data = r × 32 bytes
  • Column Commitment = 48 bytes
  • Aggregate Commitment: 48 bytes
  • Aggregate Commitment Proof = 48 bytes
  • Row Commitments: r × 48 bytes
  • Row Proofs (One per Chunk) = r × 48 bytes

Formula for Data Sent Per Subnetwork

Each subnetwork is responsible for storing one column of the extended data matrix, meaning the data sent per subnetwork is:

$\text{Total Data per Subnetwork} = \text{column data} +(\text{column comm.s + proofs} )+(\text{row comm.s +proofs})$

$\text{Total Data per Subnetwork} = (r \times 32) + (48 + 48 + 48) + 2\times(r \times 48)$ byte

Nomos DA v2

Data Representation & Encoding

• The original data is structured as an $n×n$ matrix.
• Each row and column is Reed-Solomon encoded with a rate of 1/2.
• This means the extended matrix has size $2n×2n$.

Chunk Size Calculation