# Can Paillier Encryption has independent decryption key?

As Pailliear cryptosystem secret key $$\lambda$$, depends on primes $$p$$ and $$q$$. As $$\lambda = \operatorname{lcm}(p-1,q-1)$$.

I want decryption key to independent from $$p$$ and $$q$$.

• It can be possible to generate decryption key independently?
• Could you tell the reason? Maybe you are asking x but want y. – kelalaka Sep 3 '19 at 14:05
• Can it be possible to generate a decryption key without knowledge of $p, q$ (e.g. with only knowledge of $n = pq$) - we most certainly hope not, as that would imply that Paillier is insecure. – poncho Sep 3 '19 at 14:32
• @kelalaka My requirement is crypto.stackexchange.com/questions/73023/… – abbasi_ahsan Sep 3 '19 at 19:45