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Decryption of an El Gamal re encryption mixnet

cn flag

I have interest in e-voting and am currently trying to understand El Gamal re-encryption mixnet.

I understand how El Gamal encryption works and how mixnet works but what's not cristal clear for me is how the decryption is done after the re-encryption.

As I understand it, I just need the secret key to decrypt the encrypted vote that went through the mixnet but I can't find any sources that gives me a detailled way of how the decryption of the output of the mixnet is done.

Am I right?

Can someone provide me a source or the calculation needed to decrypt the output of the re-encryption mixnet ?

Thank you

kelalaka avatar
in flag
Are you asking for this? [How is a re-encryption done with elGamal?](https://crypto.stackexchange.com/q/43425/18298). Note that there are many [mixnet](https://crypto.stackexchange.com/search?q=mixnet) questions here, too.
knaccc avatar
es flag
The re-encryption process has the property that decryption can be done using the same private key that would be used if it were not re-encrypted. So you just use the decryption key that the original votes were designed to be decrypted by.
Xavier avatar
cn flag
@knacc So I can use the same private key but what's still not clear is do I have to do only one decryption or do I need to do as many decryption as the mixnet the original ciphertet goes through ? If it's only one decryption can you provide my a link or an explanation on how it works
Xavier avatar
cn flag
@kelalaka was not really asking for this but it defenitly helps me in my understanding process.
kelalaka avatar
in flag
Well, to be honest, I consider that we have dupe other than that but couldn't find it. It is a just modifications of the linked one, if you like you can answer your question.
knaccc avatar
es flag
No matter how many times something is re-encrypted, the original decryption key works as if it had only been encrypted once.
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