Understanding multiparty encryption

[uo257724]

I'm trying to understand how multiparty encryption works in detail, I understand that the pary encrypt with a collective public key and for decryption, anyone in the party can use his secret key for it. is this correct?
Secondly, when the decryption comes from an external party, the key used for decryption is generated by the party for this purpose. Is this also correct?
The example I've been reading is this

Thank you all in advance.

[ChristianMct]

I'm trying to understand how multiparty encryption works in detail

It is probably easier to start from theoretical material to understand how multiparty HE works. Our PETS'21 paper on the topic is a good resource for that. See also the video of its presentation for a more condensed version.

I understand that the pary encrypt with a collective public key and for decryption, anyone in the party can use his secret key for it. is this correct?
No. When encrypting with the collective encryption-key, ALL parties in the set need to collaborate in order to decrypt (when using the basic threshold setting as in the mentioned PIR example).

Secondly, when the decryption comes from an external party, the key used for decryption is generated by the party for this purpose. Is this also correct?

Assuming that you are referring to external receiver parties (as defined in the sense of the paper), yes. The receiver party generates a public-private encryption key pair and sends the public one to the parties. The parties then re-encrypt the messages from the collective key to the receiver key.

Hope this helps.