Signing using ElGamal or Encrypting using private key

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I'm using SJCL js library: How do I use the elGamal algorithm to prove that a user posses the private key based on the public key? I also utilize the ECCDH part so I can't just use ECDSA.

I want everybody to be able to verify that the user, who posses that private key actually wrote the message, actually made the request, by using his/her public key to decrypt the message.

request message -> encrypt with private key -> send it -> everybody can decrypt the message by using his public key, proving he actually made the request

I am very new to cryptography, I have learned that in asymmetric you can use the private key to encrypt the file but I can't seem to find this tool on SJCL.

I have attached a screenshot of my attempt below please let me know where I am doing it wrong. Thank you![enter image description here]1

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