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I'm implementing a simple door access control with smart keyfobs. At the moment I send a 32 byte message to the keyfob which it signs with ECDSA and I verify the authenticity with the public key.

There would also be the possibility to send an encrypted message to the card and let it decrypt it.

Which of the two methods is more practicable or more common? (secure?)

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In public key cryptography you perform authentication by signing a message that the other end verifies it using your public key.

Since in your case you only need to authenticate, this is exactly what you need.

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