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decode a message with a public key (pk), you would typically need the corresponding private key (sk) that matches the public key. Without the private key, it may not be possible to decode the message encrypted with the public key.

Public key cryptography relies on encryption and decryption keys that are mathematically related. The public key is used for encryption, while the private key is used for decryption. Only the owner of the private key should have access to it, ensuring secure communication.

If you have the private key corresponding to the given public key, you can use it to decrypt the encoded message. The decryption process typically involves using the private key and the corresponding algorithm (such as RSA or ECC) to decipher the encrypted text and recover the original message.