Questions tagged [paillier]
A public-key cryptosystem invented by Pascal Paillier in 1999.
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Paillier versus Lifted ElGamal for homomorphic addition for e-voting
I'm looking to create an anonymous e-Voting system which will assign a certain number of bits to each candidate during a vote, e.g. 010000 for Alice, 000100 for Bob, and 000001 for Charlie. It works ...
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41 views
Encrypting full word using Paillier Scheme
I am using Paillier scheme to encrypt a message however, I have divided the words into alphabets and then convert each alphabet to ASCII code encrypting the final result. It works fine, but I want to ...
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1answer
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How to know the exact result in Paillier chiper-costant multiplication
The encryption function $E_{k^+}: Z_n \rightarrow Z_{n^2}$.
The decryption function $D_{k^-}: Z_{n^2} \rightarrow Z_n$.
$m_1 = 42, k = 15, n=77$.
After encryption, exponentiation and decryption, I get:...
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1answer
48 views
What is the difference between Paillier additive homomorphic property and addition of two paillier ciphers
Paillier has additive homomorphic property that states:
if two ciphers c1 and c2, are multiplied, and the result is decrypted, it is equal to addition of the two plaintexts.
D(c1*c2)= m1+m2
...
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How to prove correct decryption in Goldwasser-Micali cryptosystem
In How to prove correct decryption in Paillier cryptosystem, it was asked whether Alice (in sole possession of the secret key) can convince Bob that a given plaintext is the decryption of a ciphertext ...
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55 views
Optimisation of Pailler decryption
In this article applying Pailler encryption and decryption to image bitmaps, Table II is reported to give
Execution Time (sec) of the Paillier encryption/decryption of image using different key sizes ...
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Paillier scheme : Encoding floats into integers impact on computations
In Privacy Preserving Processing Over Encrypted Images, I could understand that appropriate encoding of floats into integers (required in Paillier) only incur negligible error in computations.
Any ...
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1answer
84 views
Is Paillier a stream or block encryption
Does Paillier follow a stream encryption or block encryption technique.
If it’s a block encryption then what is the size of the block in bits or bytes.
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87 views
Efficiently prove the correctness of Paillier encryption in or “outside” a zk-SNARK
I'm working with a zk-SNARK library [1] that allows me to prove the correctness of arbitrary arithmetic circuits, and I now want to use these zk-SNARKs to prove that some Paillier [2] ciphertext $c$ ...
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1answer
64 views
Evaluate the time of Paillier decryption
If I have 4 kilobytes of Paillier encrypted data, how can I know the time needed to decrypt it?
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105 views
Security of Paillier against chosen ciphertext attack
Is there a proof by now that Paillier is secure against chosen-ciphertext attack? The original Paillier paper mentions that it is not.
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63 views
Prove the correctness of decryption process of Paillier cipher
The definition of Paillier cryptosystem is the same as the one on wikipedia.
Now the random integer $g$ is chosen of the form $$g=(1+n)^{\alpha}\beta^{n}\bmod n$$, where $\alpha$ and $\beta$ are in $\...
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1answer
57 views
can we know the sign of a ciphertext (homomorphic)
Is it possible to know the sign (positive or negative) of an homomorphic ciphertext particularly under paillier scheme ?
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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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72 views
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 ...
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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 ...
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35 views
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/...
3
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1answer
137 views
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 $g^{\lambda(x_2-x_1)}$....
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1answer
67 views
Paillier scheme and noise growth
Does the problem of noise growth exist in the Paillier homomorphic scheme ?
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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 ...
0
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1answer
113 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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1answer
213 views
Advantages of Paillier vs Goldwasser-Micali
It is easy to see that both Paillier and Goldwasser-Micali are homomorphic addition schemes and are secure, but what would be the advantages of choosing one over the other?
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A modified question of Hazay & Lindell's Efficient Secure Two-Party protocols Book
Based on the question proposed on page 27, we propose a modified question as follows:
Suppose the protocol is based on Paillier cryptosystem and $P_2$ has generated related public and private keys ($...
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1answer
106 views
Paillier's Cryptosystem - Homomorphism
I'm lacking quite some mathematical knowledge here, but could anyone please explain to me why the Paillier cryptosystem is still (additive/multiplicative) homomorphic despite introducing a random ...
2
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1answer
131 views
Paillier Private $\mu$ and $\lambda$
The Paillier CryptoSystem has a public key that $(g,n)$ and the private key which can be exclusive to $\lambda$, where the decryption scheme is:
$m = L(c^\lambda \bmod n^2)/L(g^\lambda \bmod n^2) \...
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1answer
80 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. ...
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1answer
83 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 ...
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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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1answer
52 views
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 ...
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1answer
174 views
Can Paillier ,RSA or any other schemes be used for universal re-encryption like elGamal?
ElGamal, RSA, and Paillier cryptosystem have homomorphic property, and can be used fro re-encryption purposes. I want to use the encryption to re-encrypt ciphertext(as in proxy re-encryption but ...
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0answers
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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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1answer
176 views
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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1answer
74 views
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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1answer
1k 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 ...
3
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1answer
2k views
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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1answer
146 views
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 ...
5
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1answer
203 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 ...
3
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1answer
136 views
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 ...
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0answers
160 views
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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Pseudorandomness based on homomorphic multiplication property of Paillier cryptosystem
Given the instance $(n, g, \lambda)$ of Paillier cryptosystem with $\text{ord}(g) = n \lambda$ (symbols have their usual meaning), and $c = g^{na}$, is it possible to distinguish (computationally) $c' ...
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1answer
379 views
How to calculate random factor in Paillier cryptosystem?
I am currently learning paillier cryptosystem,and have two questions about random r.I use the characteristics of homomorphic addition to obtain the product of two ciphertexts C and the corresponding ...
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2answers
223 views
Homomorphic properties of Paillier
I'm curious about the homomorphic properties of Paillier. So, basically if I have $\textsf{Dec}(\textsf{sk}, \textsf{Enc}(\textsf{pk}, \alpha) \cdot \textsf{Enc}(\textsf{pk}, \alpha^{-1}))$, I will ...
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1answer
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Prove that some Cyphertext C encrypts some plaintext D
I have a Paillier Cyphertext C and a counterparty that controls the keypair that was used to encrypt the data D to arrive at C.
How can they prove to me that the Cyphertext C is actually the ...
4
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1answer
221 views
Can the CRT speed-up Paillier decryption by more than a factor of two?
In the Pailler cryptosystem, decryption goes $m\gets\displaystyle\left\lfloor\frac {\left(c^\lambda\bmod n^2\right)-1}n\right\rfloor\mu\bmod n$ with $\mu<n$ being a part of the private key just ...
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1answer
86 views
Combining share decryption on Paillier threshold scheme
I am trying to implement the Paillier threshold scheme described by Fouque, et al, but I am having an issue when combining share decryptions.
The scheme calculates the plaintext $M$ with the formula:
...
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1answer
288 views
Applying Chinese RemainderTheorem and Paillier Homomorphic encryption
I'm trying to optimize the decryption process for Paillier Homomorphic Encryption (PHE) using the Chinese Remainder Theorem (CRT). However, I want to check if there's a different way of applying CRT ...
3
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1answer
273 views
Paillier encryption problem when q or p divides r
I am having a problem with Paillier encryption as described on Wikipedia. It says to pick $0 < r < n$, where $n=pq$ for large, equally sized primes $p$ and $q$. However, I've been testing ...
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2answers
111 views
Bijective encryption function in Paillier cryptoststem
In Paillier cryptoststem many ciphertexts can correspond to the same plaintext. How can I modify the scheme so to make the correspondence between ciphertexts and plaintexts a one to one correspondece? ...
