You can use a standard asymmetric encryption like RSA. Certificates merely serve the purpose of linking things to other things, approved by some (hopefully trusted and trustworthy) entity.
What you're probably thinking about is an ID certificate which links an identity to a public key. This key is in no way encrypted. It simply occurs in a field of the certificate. Signing the certificate does not change its fields. It just adds a signature of everything else.
This means that anyone with access to the certificate has access to the public key, be the certificate signed or not. Signing the certificate mere means: "I approve of this."
Regarding your edit: When you want to decrypt something, you have that something and it's not enough to attain the plain text, given the encryption is secure. You need some other information. Note that I don't say what that other information is but we know for certain that additional information is needed because if it wasn't anyone who obtained the ciphertext could compute the plain text which would mean that the encryption is not secure.
We now need to determine a possible piece of additional information α. That information has to come from somewhere. It doesn't just emerge for no reason because some outside event happened.
You dictated in your edit that that α has to be found on the death certificate. To have any chance of encrypting something using any such information, we need to require at least that these conditions are met:
- As the encrypter, need to know some mathematical property of α. Note that we don't necessarily need to know α itself.
- α needs to be of a nature such that there are plenty of possible variations for different α with the same structure. Otherwise an attacker could brute-force α.
- The attacker must not know α or be able to reduce the solution space to a small number of known elements.
If it's not possible for the encrypter to collaborate with the authority issuing the death certificate, there is no α we can find because we can only use the information found on any normal death certificate: Name of the issuer, name of the person who died and other personal information like date of birth or address, date of death, location of death, file number, and signature of the issuer.
The name of the person and their other personal information is not a secret. As the encrypter, we don't have control over the signature of the issuer nor ever the file number as we cannot collaborate with the authority. The attacker will already know what authority issues the death certificate, so the issuer is known. So we're left with date and location.
As the date is only stated with the precision of days and we can be sure to know the date of death as an attacker, except for an uncertainty of approximately 100 years which is 36524 days and therefore 36524 possibilities (if we're generous). As the location of death is only stated to the precision of the municipality where the person died, there aren't many options for this either. Even for large countries like the US, there only are 19492 options. So we have a total solution space of 36524*19492 = 711925808 < 10^9 elements.
This is far too small to exclude brute-force attacks and this assumes we have total control over where in the country the person dies and how old they become which is both impractical.
So there are no possible α we can choose one from and therefore there cannot be any such encryption.