The Quadratic Sighash Problem

Before SegWit, there was a serious scalability issue in Bitcoin called the Quadratic Sighash problem.

It made signature validation slow, especially for transactions with many inputs, and opened the door to denial-of-service attacks.

What Happened?

In 2015, F2Pool mined a block containing one huge “mega-transaction” (≈1 MB, 522 inputs).

It took about 25 seconds for a full node to validate just that transaction.

Slow validation means fewer people can run full nodes
→ which increases the risk of centralization.

Why Does It Happen?

Imagine a transaction with 2 inputs.

To verify each signature, Bitcoin must hash a modified version of the transaction.

So for 2 inputs, we hash 2 different messages:

Input #1 → message #1  
Input #2 → message #2

So far, this looks linear:
2 inputs → 2 messages

The Trick: Each Message Contains All Inputs

When signing input i:

include every input
but remove scriptSig from all other inputs
(so they can't change the message being signed)

That means each input needs its own version of the transaction to hash.

So with 2 inputs:

2 inputs × 2 messages = 4 hashing operations

Scaling Up

Now imagine 3 inputs:

Each message now contains 3 inputs:

3 inputs × 3 messages = 9 units of work

In general:

n inputs  →  n × n  =  n²  hashing work

That’s why it’s called Quadratic Sighash -> cost grows as n².

Example Table

Inputs	Messages	Total Work
1	1	1
2	2	4
3	3	9
10	10	100
100	100	10,000

Why This Was Dangerous

A miner could include a single huge multi-input tx that takes seconds/minutes to validate.

Slow full nodes can’t keep up
They fall behind the chain tip
They aren’t participating in consensus
Network centralizes to only fast validators

Why "just limit transaction size" failed

Proposed fix: cap tx size to 100 KB. Rejected because: ❌ Doesn't fix root cause ❌ Just delays the attack ❌ Breaks legitimate large-input transactions (eg batching)

SegWit Fixed This

SegWit changed how transactions are serialized and hashed. It reduced sighash cost back to O(n) (we’ll explain it in the next posts)

Follow @Bitcoin_Devs for more technical explainers.