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It's always been told that ECDSA is more secure "per bit of key size", such that it offers same security with a shorter key, or offers stronger security with the same key length.
However, per my understanding, if the length of the key is fixed, it means that the amount of entropy is also fixed (e.g. 160-bit ECDSA key contains no more entropy than 2^160, and a 192-bit AES key contains no more entropy than 2^192). So why is ECDSA considered "more secure" at the same level of entropy?