What was the bug for the Bitcoin value overflow in 2010?

Question

In 2010, there was an incident of value overflow on Bitcoin.

I am not a developer, but I want to know what the bug was in more detail. #1 is the only answer I found online, and #2-3 are my attempts to alternative answers.

1. Source: https://bitfalls.com/2018/01/14/curious-case-184-billion-bitcoin/

Total outputs were greater than 184,467,440,737.09551615, the maximum number that could be stored, by 50.51. And 50.51 was equal to the input value, so the tx was processed.

This was the tx, according to the source.

• from my address which has 50.51 BTC
• send 92233720368.54277039 to address A
• send 92233720368.54277039 to address B
• send 50.51 BTC to address C

But I am not sure. Looking at the block on jgarzik's original post, it looks like 50.51 was a separate tx from the two 92233720368.54277039 txs. And the input value for those 2 large txs seems to be 0.5. It doesn't really make sense. So, here are my alternative possible answers.

2. The combined outputs of two large txs, 184,467,440,737(decimals cut off for simplicity), is subtracted from the input of 0.5, which results in -184,467,440,736.5. But because the variable was an unsigned number, it was wrapped (around the max number of 184,467,440,737.09551615) to end up as 0.5 (or smaller). This is equal to the input value, so the tx is included.

3. Similar to #1, but I saw somewhere that negative sign could erroneously be interpreted as another number digit. So (rather than wrapped around the max number) -184,467,440,736.5 is seen as a larger positive number. I don't know what number it will become. 1,000,000,000,000 + 184,467,440,736.5? Or 2 x 184,467,440,736.5?

Maybe something else? Please let me know what you think really happened. Thank you in advance.

Answer 1

Your first source is wrong.

The block in question contained three transactions: the first is a coinbase transaction, the second is the one that did the overflow. The third is unknown, and not relevant.

The overflow transaction does not spend from the first transaction, rather it spends a UTXO that was created in an earlier transaction, which is actually in the blockchain and can be looked up today. The UTXO it spends is 0.5 BTC.

The two outputs of the overflow transaction are each 92233720368.54277039 whose bytes are 7ffffffffff863af in hex. The most significant bit of this number is the sign bit - if it is 1 then the number is negative, 0 it is positive. In this case, these values are positive. This allows these values to pass the check that the output values are not negative.

The next relevant check is that the amount in the inputs can provide for the amount in the outputs. However the way this was done was not by checking the values directly, but rather the fee was calculated (input amounts - output amounts), and the fee is checked to be non-negative.

But because the output values are so large, when they are added together, they overflow the maximum signed integer and become negative. Subtracting this sum from the 0.5 BTC input becomes an addition as subtracting a negative number is addition. So the calculated fee is greater than 0 and this last check passes.

There are two inflationary effects of this bug. The first is the obvious one of the two extremely large outputs. The second is the transaction fee. The miner of that block can collect the miscalculated transaction fee of the overflow transaction, and so there is an additional 0.00997538 Bitcoin created.