# Questions tagged [paillier]

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

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### Paillier VS RSA

I was wondering if there are major pros or cons of choosing the Paillier algorithm over RSA except for Pailliers being additively homomorphic and RSA multiplicative?
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### How do I choose blind sizes?

I am currently developing a service that calculates statistics (currently only sum/average) on homomorphically encrypted user data, and then gives the results to a third party. Because encryption is ...
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### How to apply two consecutive Paillier encryptions?

The plaintext space for Paillier encryption is $\mathbb{Z}_n$ and the ciphertext space is $\mathbb{Z}_{n^2}$. How can I apply two consecutive encryptions? I mean, if $c$ is the ciphertext of $m$, how ...
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### Lagrange Gauss Reduction Algorithm

Sorry if my question is trivial. My question is related to a post "Paillier Homomorphic encryption to calculate the means" where a member suggests Lagrange Gauss Reduction Algorithm for reducing a ...
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### Zero knowledge proof for Paillier addition under multiple keys

Suppose $m_0, m_1, m_2 \in \mathbb{N}$ such that $m_0 = m_1 + m_2$, $m_i > 0$ (none of them can be 0 or lower) Under a Paillier cryptosystem, set $e_0 = E(m_0, r_0)$ for a public key $(g_0, n_0)$ ...
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### Paillier Homomorphic encryption to calculate the means

Paillier Homomorphic encryption supports addition and multiplication with plaintext value. Can I use these properties to calculate the means of cipher-text values? I try to use the following steps: ...
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### In Paillier homomorphic encryption, do we need to take modulo after multiplication of 2 ciphertexts?

The multiplication of 2 ciphertexts generated using Paillier encryption will result in encryption of sum of corresponding plaintexts. I need to do a linear combination operation of N integers in ...
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### In Paillier homomorphism, how do you deal with bit length? [closed]

I'm trying to figure out homomorphic encryption and would like to multiply two paillier encrypted numbers. Like so: [a].[b]=[a+b] To try this I got this Paillier.java and tried the following: <...
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### identifying presence of encryption of zero in additive homomorphic encryption

Lets say the server has corpus of ciphertext contains $enc(a),enc(b),enc(c), \dotsc enc(x)$. The encryption function is an additive homomorphic scheme (like Paillier). The server knows only the public ...
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### Equality checking using additive homomorphic encryption

Given two ciphertexts $c_1 = enc(p_1)$ and $c_2= enc(p_2)$ using any additive homomorphic encryption scheme (or specifically Paillier). Can we find out whether the underlying plaintexts $p_1,p_2$ ...
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### Zero-knowledge proof for the product of additive Paillier ciphers

Suppose that Alice received the cipher values: $E(x_1), E(x_2), ..., E(x_n)$ that are encrypted using Paillier cryptosystem by $n$ entities with Bob's public key. Alice computes $E(\sum x_i)$ from ...
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### Additively homomorphic cryptosystem with non-interactive zero-knowledge proof of non-negativity

I need a cryptosystem that is additively homomorphic. Paillier preferably, but not neccessarily. Also, for every ciphertext the private key holder must be able to prove non-interactively that the ...
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### Why is Paillier Cryptosystem called probabilistic?

The definition of Paillier Cryptosystem says that it is a probabilistic asymmetric key algorithm for public key cryptography. Can some body explain why it is called "probabilistic"?
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### Performance bottlenecks in Paillier encryption

I'm implementing Paillier encryption and I'd like some recommendations about improving its performance. Firstly, I have to note the following: I have already set g=1+n to get rid of one ...