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nashqueue committed Nov 22, 2022
1 parent 250ef36 commit 2b38fa1
Showing 1 changed file with 6 additions and 6 deletions.
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Expand Up @@ -119,11 +119,11 @@ Each row consists of one subtree root, which means if you have log(n) rows you w

![Current ni rules proof size](./assets/current-ni-rules-proof-size.png)

NMT-Node size := 32 bytes + 2\*8 bytes = 48 bytes
NMT-Node size := 32 bytes + 2\*8 bytes = 48 bytes
MT-Node size := 32 bytes

Proof size = subtree roots (rows) + subtree roots (last row) + blue nodes (parity shares) + 2 \* blue nodes (`DataRoot`)
Proof size = (log(n) + log(k) + log(n)) \* NMT-Node size + 2\*log(k) \* MT-Node size
Proof size = subtree roots (rows) + subtree roots (last row) + blue nodes (parity shares) + 2 \* blue nodes (`DataRoot`)
Proof size = (log(n) + log(k) + log(n)) \* NMT-Node size + 2\*log(k) \* MT-Node size
Proof size = 48 \* (2\*log(n) + log(k)) + 64 \*log(k)

### Proposed Non-Interactive Default Rules
Expand All @@ -132,8 +132,8 @@ Each row consists of sqrt(n)/log(n) subtree roots. Which makes in total sqrt(n)

![Proposed ni rules proof size](./assets/proposed-ni-rules-proof-size.png)

Proof size = subtree roots (all rows) + subtree roots (last row) + blue nodes (parity shares) + 2 \* blue nodes (`DataRoot`)
Proof size = (sqrt(n) + log(k) + log(n)) \* NMT-Node size + 2\*log(k) \* MT-Node size
Proof size = subtree roots (all rows) + subtree roots (last row) + blue nodes (parity shares) + 2 \* blue nodes (`DataRoot`)
Proof size = (sqrt(n) + log(k) + log(n)) \* NMT-Node size + 2\*log(k) \* MT-Node size
Proof size = 48 \* (sqrt(n) + log(k) + log(n)) + 64 \*log(k)

## 5. What is the worst constructible block with the most amount of padding with old and new non-interactive default rules?
Expand All @@ -150,7 +150,7 @@ Padding = 3 \* (k-1) \* k/8

## What is the quantified padding and proof size cost?

Proof size increases from 3024 bytes to 10704 bytes in 2 GB blocks. In the current `MaxSquareSize` it's from 2064 to 3312 bytes. For bigger messages, the number of row roots will approach sqrt(n). Before that, we will get to k/4 roots which will make the message act the same before and after the proposed non-interactive default rules.
Proof size increases from 2928 bytes to 10352 bytes in 2 GB blocks. In the current `MaxSquareSize` it's from 2096 to 3088 bytes. For bigger messages, the number of row roots will approach sqrt(n). Before that, we will get to k/4 roots which will make the message act the same before and after the proposed non-interactive default rules.

![Proof Size Result](./assets/proof-size-result.png)

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