Hello, for multiparty scenario, if one private‑key share is lost or leaked, the entire key set (all shares + public key + evaluation keys) must be regenerated, right? This is just to doble check, Thank you
The short answer is yes. If a secret-key share is leaked, it is like the security threshold drops from n-1 to n-2, so in order to be under the same security conditions, new shares have to be generated. The public key and the evaluation keys depend on the secret key, so if the overall secret key changes, they should also be regenerated.
To be complete, if you tolerate the leakage of a secret-key share (all parties will know it), confidentiality is not broken and you will still be able to evaluate and decrypt. However, if that share is completely lost, then no decryption functionality is available as all n shares are required to decrypt.