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Has this address shown its key?

Paste an address. The scanner reads its code, how many transactions it has sent and what it holds, and finds the transaction that revealed its public key. Everything is read from public nodes; nothing is sent.

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What exposure means

An Ethereum account signs with secp256k1. Its address is a hash of the public key, so the key stays out of sight until the account signs its first transaction: from then on anyone can recover the public key from the signature. A quantum computer able to solve the discrete logarithm on secp256k1 could turn that public key into the private key and spend from the account.

Contracts have no key to expose, but the keys that control them do. Under EIP-7702 a delegated account keeps its original key live, so it stays exposed. The remedy is to move the funds to an account whose root key is post-quantum.