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I was reading this section from Mastering Ethereum. This specific part caught my attention:

However, not all Ethereum addresses represent public–private key pairs; they can also represent contracts, which, as we will see in [smart_contracts_chapter], are not backed by private keys.

Does that mean that mathematically speaking, no private key exists in the entire set of all private keys that maps to a given smart contract's address?

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There is two address type in Ethereum.

Address owned by a private key (a random number basically) that can be use by a user.

Address that are run by a smart contract, and there is no private key for it.

It's mathematically possible to have a private key that give you an address already used by a contract. But I don't know if there is a security in EVM where you can't use this address because it only obey to code, note to a private key. Chance are so rare it will be the same thing to "steal" an address with 1 billions dollars to brute force private keys.

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