Key Setup and Definitions

Data Sizes: 256 KB, 512 KB, 1024 KB, and 2048 KB.

Chunk and Column:

• Each chunk is 32 bytes.
• Each row contains 2048 chunks.
• Each row is determined by dividing the total number of chunks by the fixed number of columns (2048).

Commitment and Proof Sizes:

• Each commitment is 48 bytes.
• Each proof is 48 bytes (only used for the chunk-by-chunk scenario).

Number of Rows Calculation

Steps:

1. Calculate the total number of chunks: $\text{Total Chunks} = \frac{\text{Data Size (Bytes)}}{\text{Chunk Size (Bytes)}}$
2. Calculate the number of rows: $\#\text{ofRows} = \frac{\text{Total Chunks}}{\text{Number of Columns}}$

Bandwidth Calculations

a) Whole Column Scenario

• A whole column is sent to one sampling node.
• Bandwidth for one column includes:
  • Total data in the column: $\#\text{ofRows} \times \text{Chunk Size (Bytes)}$
  • The column commitment: $\text{Commitment Size (Bytes)}$

The total bandwidth for all 2048 columns:

$\text{Whole Column Bandwidth} = \#\text{ofColumns} \times (\#\text{ofRows} \times \text{Chunk Size} + \text{Commitment Size})$

b) Chunk-by-Chunk Scenario

• A single chunk is sent to one sampling node.
• Bandwidth for each chunk includes:
  • Chunk data: $\text{Chunk Size (Bytes)}$
  • Proof for the chunk: $\text{Proof Size (Bytes)}$
• The column commitment is also sent (once per column): $\text{Commitment Size (Bytes)}$