# Questions tagged [paillier]

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

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### Possibility of computing a and b values from the ciphertext?

Using paillier encryption, $N$ is the product of two large prime numbers, $s$ is sampled randomly from $Z_{N^2}$ we get $C \leftarrow g^ms^N \bmod N^2$ where $g=1+N$, By multiplying the cipher $c$ ...
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### Elliptic curve subgroup with $p$ elements in field of characteristic $p$

Are there any elliptic curves defined over a finite field $\mathrm{GF}(p^k)$ with a subgroup of order $p$ where the discrete log (and preferably DDH) problem is hard? Elliptic curve with prime ...
0answers
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### Identify the value of the plaintext from a noised expression

Having the following instructions: Using Paillier encryption to encrypt $m$. So, we get $Enc(m)$ Multiply $Enc(m)$ and $A$ to Get $C$. So, $C = Enc(m).A$ Decrypt $C$ using Paillier Decryption ...
1answer
330 views

### 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 $(g_0, n_0)$ ...
0answers
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### Can a partially homomorphic encryption scheme be made CCA1 Secure? [duplicate]

Can a partially homomorphic encryption scheme be made CCA1 Secure? like paillier ? what is the highest security for any PHE?
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### How to store the ciphertext generated by the paillier encryption in a pixel?

Goal: I want to implement a paillier algorithm to encrypt images and hide some data reversibly. This is the paper that proposed this algorithm: https://www.sciencedirect.com/science/article/abs/pii/...
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### Paillier Decryption?

Let $c_1$ and $c_2$ two encryptions of $m_1$ and $m_2$ using the Paillier Cryptosystem. $c_1= E(m_1,r_1) = g^{m_1} r_1^n \bmod n^2$ and $c_2= E(m_2,r_2) = g^{m_2} r_2^n \bmod n^2$ Paillier ...
1answer
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### Proof of lemma 1 Paillier encryption

In the original paper of Paillier, lemma 1 shows why $n$ must divide the order of $g$. What I don't understand in the proof of this lemma is why $g^{x_2-x_1}(y_2/y_1)^n$ implies $g^{\lambda(x_2-x_1)}$....
1answer
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### Paillier scheme and noise growth

Does the problem of noise growth exist in the Paillier homomorphic scheme ?
2answers
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### Do any probabilistic hashing algorithms have additive homomorphism?

What I am looking for is a function that meets the following criteria: For each possible input (assume integers from [0, 255]), there must be trillions of possible outputs so as to prevent preimage ...
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### Homomorphic encrypted streams (Paillier)

Situation: Alice (violin) and Bob (drums) play music together and want to (real-time) stream the concert to Carol. In order for Carol to save bandwidth, the stream is sent through a server which ...
1answer
79 views

### random mask reversible after homomorphic encryption

I would like to know if this process is feasible under homomorphic encryption, ideally under paillier or any other additive scheme Apply a mask X to obfuscate a message A ie. Am = A (op) X where (op)...
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### Order of g in Paillier Scheme

I'm trying to understand the Paillier Scheme but there's something I can't understand in the keyGen algorithm: Ensure $n$ divides the order of $g$ by checking the existence of the following ...
1answer
68 views

### Is it possible to calculate the random factor $r$ from a encrypted message and the private key in a Paillier cryptosystem?

I have already done my research and found various sources that state that it is possible but there are also a lot of them that says it is not possible to recover $r$. This Q/A on this site for example ...
1answer
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### Deterministic procedure for mapping an arbitrary value into a 𝑝,𝑞 pair for public key cryptography

I want public key cryptosystem to used for re-encryption as describe in Can Paillier ,RSA or any other schemes be used for universal re-encryption like elGamal? Now i have little solution for ...
1answer
59 views

### Paillier Complex Residuosity problem?

Paillier Cryptosystem depends on both the factorization where $n = p.q$ and the complex residuosity problem which is defined in the original paper as: The problem of deciding n-th residuosity, i.e. ...
1answer
364 views

### Comparison of values in Paillier homomorphic encryption

For a project, I am using homomorphic encryption with the Paillier cryptosystem, and I have to compare two values... Can this be done using homomorphic encryption? And I know subtraction can be done ...
3answers
9k views

### What are some disadvantages of homomorphic encryption schemes?

I'm doing some self-teaching / research for my own benefit in homomorphic cryptography. I've studied both additive and multiplicative schemes (Paillier and RSA respectively), but all I can seem to ...
1answer
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### Weakening of Paillier cryptosystem due to ciphertext equivalence and order in CryptDB

The Paillier cryptosystem is probabilistic in nature and IND-CPA secure. By design given two ciphertexts one cannot distinguish whether decrypting those two ciphertexts will result in same or ...
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### Why is the Paillier cryptosystem not considered fully homomorphic encryption? [duplicate]

Paillier is an additive homomorphic encryption system that can achieve the encrypted version of its sums. However, we can calculate the encrypted version of their multiplications by raising an ...
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### Compute ln function of a Paillier encrypted value [closed]

If I have an encrypted value $Enc(x)$ with Paillier cryptosystem, is it feasible to compute an encryption form of $\ln(x)$ or its approximation using homomorphic properties? The input $x$ is always ...
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### 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 ...
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### How Paillier cryptosystem can be used practically to encrypt and decrypt big messages “m”?

I want to use the Paillier cryptosystem for encryption and decryption purposes in my research work. But i haven't found a way to encrypt big input messages; As i want to encrypt the message i,e m : <...
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### Is there any relationship between Paillier Cryptosystem's random r and other factors

I want to try run an example of Paillier cryptosystem(Algorithm), So i just started with some basic examples, but cannot obtain correct result/decryption. I just change random factor ...
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### In which public key encryption algorithms are the private and public key not reversible?

The RSA public key encryption system has the characteristic that the public key and the private key can be reversed. That is, information encrypted with the public key can be decrypted with the ...
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### Homomorphic/Paillier crypto system for use case?: overflow for multiple counter exponent possible? Different cipher factor needed all the time?

Recently I read about homomorphic cryptosystem. They might solve a problem. To do this there need to be some modifications from standard version. Using Paillier here but a solution for other also ...
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159 views

### Zero-knowledge proof for Paillier parameters

For RSA one can give a non-interactive zero-knowledge proof that RSA with parameters $(e,N)$ form a permutation and a proof of knowledge of the associated RSA secret key. For example, such a proof can ...
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### homomorphic division with scaling/Paillier

Let's say that I have to use fractions instead of integers and I am using Paillier cryptosystem. So, I use scaling to obtain integers. Assume that I have a secure division protocol. What happens if ...
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### Verification in Threshold RSA or Threshold Paillier

In the key generation of the threshold version of RSA or the threshold version of the Paillier cryptosystem (e.g. "Shoup - 2000 - Practical threshold signatures" or "Fouque et al. - 2000 - Sharing ...
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### The way to calculate $r$ from $c=r^t\mod{n}$ where $(c,t,n)$ is known

I want to know if there is a easy way to calculate $r$ from $c=r^t\mod{n}$ where $(c,t,n)$ is known and $t=pq$ is an RSA? If $n=t^2$, is it more easier?
0answers
145 views