A public-key cryptosystem invented by Pascal Paillier in 1999.

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Homomorphic (encrypted) comparison to an integer

When working with an additive homomorphic encryption scheme (say Pallier's), is there an efficient way to get the encrypted value of a comparison test to an integer value (I realise that an ...
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How hard are discrete logarithms problems in $\mathbb Z^{*}_{n}$ and $\mathbb Z^{*}_{n^2}$, where $n$ is the RSA $n=pq$

Use the notations form the Wikipedia article Paillier Cryptosystem , assume that the chipertext $c$ and $c^{\lambda} \mod n^2$ are both given, is it possible to compute $\lambda$ easily?
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How to verify a number encrypted with an unknown key

Alice and Bob are going to follow the protocol below. Are there any crypto-constructions to help Bob verify the correctness of the answer he gets?: Alice encrypts a set of numbers using some ...
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Is equal length of primes in Paillier cryptosystem is mandate for security reasons?

In continuation to this question about length of primes , I am in doubt about the restriction on length of primes itself . In Paillier cryptosystem , equal length of primes are used . My doubt is ...
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Choosing primes in the Paillier cryptosystem

In the first step of key generation phase in Paillier cryptosystem given here. It's given that ( length($p$) == length($q$) )$\implies$ gcd$(pq,(p-1(q-1)))$=1 where length($k$) = # bits in ...
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Security relevance of random factor in Paillier

In the Paillier cryptosystem [1] the encryption of $m \in \mathbb{Z}_N$ with randomness $r \in \mathbb{Z}_n^*$ is $c = g^m r^n \bmod{n^2}$. The additive-homomorphic property of the system shows that ...