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How does CryptoNote prevent a 51% attack and double-spending? I’m interested to know what is the mechanism that protects CryptoNote coins from 51% and double-spending attacks.

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The debates still remain whether 51% should be cause for concern. CryptoNote is protected against it in the same way Bitcoin deals with the issue. One difference is in that CryptoNote-based coins, especially the first ones such as Bytecoin (BCN), use egalitarian PoW (CryptoNight) which makes the coin CPU-minable and ASIC resistant. CryptoNight allows for fairer hashrate distribution among individual miners and ensures smooth currency emission. When it comes to mining pools, in theory, having comprised more than 50% of the coin’s network one might be able to affect the next few blocks, launching a double-spending attack by holding on to enough power to confirm the majority of transactions. However, this would take a huge amount of expense and the data about the double-spending taking place would likely appear on the block chain for all to see. Moreover, such an attack could possibly destroy the integrity of the system as a whole, causing the price to crash. This is not something anyone with a vested interest in the affected coin would want.

As for the double-spending problem, CryptoNote deals with it by employing ring signatures and key images. If a rogue user creates more than one ring signature using the same private key, these signatures will be linked together which indicates a double-spending attempt.

In order to provide linkability, CryptoNote introduced a special key image which is created by a user while signing a transaction. It is the value of a cryptographic one-way function of the secret key, or in other words it is actually an image of this key. It is computationally infeasible to find a collision (two different private keys, which have the same image). In case of double-spending attempt the system immediately reject any new ring signature with a duplicate key image. It won’t be able to pinpoint a misbehaving user, but it does prevent any double-spending attempts.

There was never a documented occasion of a double-spending attack in the history of Bytecoin (BCN) or any other CryptoNote -based coin.

Read this for more details https://cryptonote.org/inside/

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