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Is it possible to make a Dos-Attack on the Monero network, by creating multiple transactions with small amounts and flooding the network?

How many Moneros would be required to do so?

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Something like this had already happened, with no impact to the network performance. It was a prelude to the actual attack, the infamous block 202612 attack. Quoting fluffypony in the bitcointalk thread (emphasis mine):

The fork was the intention and the net-effect. They would have had to mine two of those blocks in parallel and dump them both on the network. It's such a bizarre, unknown, unidentified edge-case that I can't imagine someone stumbling across this AND figuring out how to exploit it (and to what end??). There's no monetary gain to the attacker, and with the hike in fees to mitigate the previous attack I can only imagine that this would've cost them a pretty penny.

The attacker had to first raise the max. block size limit to be able to carry out the attack. On the positive side, this served as a test of Monero dynamic block size which performed well. As said above, it had probably cost the attacker a significant amount in transaction fees, and it would likely cost more today.

Yes, it's possible to flood the network, but it would adapt by dynamically increasing the block size so there would be still be enough room for all the transactions.

The attack would have an insignificant and ever-increasing cost to sustain (tx-fees), making it impossible to sustain the attack.

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