Questions tagged [paillier]

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

Filter by
Sorted by
Tagged with
1 vote
0 answers
18 views

Paillier cryptosystem for verifiable shuffles

I am looking for some algorithm or implementation on Pailler cryptosystem-based verifiable shuffles for mixNet. So far, all the verifiable shuffles and mixNet are available for ElGamal cryptosystems ...
  • 31
2 votes
0 answers
33 views

How to prove an RSA ciphertext matches a Paillier ciphertext?

Suppose I know an RSA public key $(n,e)$ and I create two ciphertexts: An RSA ciphertext $C_1 = m^e \mod n$ and a Paillier ciphertext $C_2 = g^m \cdot r^n \mod n^2$. Is there a known efficient method ...
  • 166
1 vote
1 answer
33 views

Is it possible to use Batching with any of the Partial Homomorphic Cryptosystems?

I'm familiar with the concept of batching in the context of (Fully) Homomorphic Encryption - whereby many values can be encrypted as a single ciphertext and operated on simultaneously in an SIMD/...
  • 177
1 vote
0 answers
56 views

Additive Homomorphic Encryption scheme with very small ciphertext size

I'm looking for a Additive Homomorphic Encryption scheme which can allow a ciphertext of size smaller than 128 bit. I started studying this topic very recently so I don't have much knowledge, but I ...
0 votes
1 answer
27 views

can I get individual data by paillier decryption if we send aggregated encrypted data?

suppose there are different user data for n Smart meters. we encrypt all the individual data and then add them together. After decrypting the summation, how can we retrieve the original data? We are ...
1 vote
1 answer
57 views

Working with Paillier and ECDSA - Order issue

I'm trying to implement two party computation for ECDSA signing using Paillier cryptosystem. But my problem is that the order of Paillier is different from the order of the curve (secp256k1 in my case)...
  • 113
3 votes
1 answer
92 views

Is the discrete log in general hard in Paillier groups?

https://en.wikipedia.org/wiki/Paillier_cryptosystem Paillier cryptosystem exploits the fact that certain discrete logarithms can be computed easily. If I were to select $g \in \mathbb{Z}_{n^2}^*$ ...
1 vote
1 answer
29 views

Internal direct product of group of invertible elements in a Paillier modulus

Let $p$ and $q$ are Sophie-Germain primes such that $p=2p'+1$ and $q=2q'+1$. Also let $n=pq$ and $n'=p'q'$. In Section 8.2.1 of this paper, the internal direct product of $\mathbb{Z}_{n^2}^*$ is shown ...
0 votes
1 answer
108 views

How to prove that paillier encryption is positive (zero-knowledge)?

Is it possible that the plaintext encrypted in a ciphertext using paillier encryption is positive without using a zero knowledge range proof?
2 votes
1 answer
63 views

Is this a safe zero knowledge proof that two paillier encryptions are equal?

We have encryptions $c_1$ and $c_2$, the person who knows the plaintext and randomness in both wants to prove that they know it. Let $r_1$ and $r_2$ be the randomness values in $c_1$ and $c_2$ ...
0 votes
0 answers
38 views

In paillier homomorphism, how is the randomness r changed during addition?

Two add the plaintexts encrypted in a ciphertext, you would just multiply the ciphertext and modulo it. However, how does the randomness value of the new ciphertext change? Assuming you the encryptor ...
2 votes
0 answers
56 views

Why is asked that gcd(pq,(p-1)(q-1))=1 in the Paillier encryption scheme?

I don't see this property $\gcd(p\,q,(p-1)(q-1))=1$ used in the scheme. And in Paillier's original paper, I don't find this requirement. Is it required just for the difficulty of factoring $n$? Or is ...
0 votes
1 answer
39 views

Searching in Paillier Cryptosystem

I have implemented Paillier Cryptosystem. Lets say, I have an encrypted array E(x) = [2,4,5,10,0,20] and I want to find that if 0 exist in that array. Due to the limitations of Paillier cryptosystem I ...
1 vote
1 answer
52 views

Short randomness in ElGamal and Paillier

In the Paillier cryptosystem the encryption of $m \in \mathbb{Z}_N$ with randomness $r \in \mathbb{Z}_n^*$ is $c = g^m r^n \bmod{n^2}$. My question is, what if short (E.g. 512bits) $r$ is used? ...
  • 77
1 vote
1 answer
38 views

Generation of the order $\lambda$ (which is lcm((p-1),(q-1))) element g in modified paillier, why $-a^{2n}$?

As the question states, in variants of paillier cryptosystem, such as CS01 and DT-PKC, when they want an element $g$ of order $\lambda$, they choose a random number $a$ from group $Z^*_{n^2}$ and ...
  • 73
1 vote
1 answer
110 views

Do we need to consider overflow in paillier encryption?

Homomorphic multiplication of plaintexts in Paillier cryptosystem can be constructed as follow: Dsk(E(x1)^x2 mod N^2) = x1x2 mod N. So after the decryption, we get the result of multiplication x1x2. ...
  • 73
3 votes
1 answer
112 views

$n=pq$ and $n=p^2q$. How to take the value of two $n$ is the same in security

For example, Paillier's RSA modulus is $n=pq$, but OU's RSA modulus is $p^2q$. I think when two $n$ are the same, the security of the two cryptographic schemes must be different. So for example, if I ...
3 votes
3 answers
285 views

How to calculate the n in n-bit security of a crypto algorithm?

I think I'm likely missing the term because searching for this is coming up with not so precise results. I'm looking to calculate the n-bit security of say Paillier vs ElGamal vs EC ElGamal, when I ...
  • 155
2 votes
1 answer
195 views

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 ...
  • 155
1 vote
1 answer
60 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 ...
0 votes
1 answer
51 views

How to know the exact result in Paillier cheaper-constant 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:...
1 vote
1 answer
138 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 ...
  • 31
1 vote
1 answer
88 views

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 ...
  • 11
3 votes
0 answers
66 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 ...
  • 126k
0 votes
0 answers
97 views

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 ...
  • 65
1 vote
1 answer
102 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.
  • 31
2 votes
0 answers
153 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 $c$ ...
  • 21
0 votes
1 answer
82 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?
  • 31
1 vote
1 answer
280 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.
  • 31
1 vote
1 answer
168 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 $\...
  • 21
1 vote
2 answers
140 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 ?
  • 65
2 votes
0 answers
44 views

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 $c$ ...
  • 61
1 vote
0 answers
89 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 ...
  • 243
0 votes
0 answers
24 views

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 ...
  • 61
1 vote
0 answers
71 views

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/...
  • 11
3 votes
1 answer
154 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 $g^{\lambda(x_2-x_1)}$....
  • 317
1 vote
1 answer
84 views

Paillier scheme and noise growth

Does the problem of noise growth exist in the Paillier homomorphic scheme ?
  • 65
4 votes
2 answers
203 views

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 ...
1 vote
0 answers
79 views

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 ...
1 vote
1 answer
159 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)...
  • 65
5 votes
1 answer
270 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?
  • 189
0 votes
1 answer
49 views

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 ($...
1 vote
1 answer
148 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 ...
  • 11
2 votes
1 answer
152 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) \...
1 vote
1 answer
103 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. ...
1 vote
1 answer
105 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 ...
  • 11
2 votes
0 answers
84 views

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 ...
  • 41
-1 votes
1 answer
54 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 ...
2 votes
1 answer
224 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 ...
0 votes
0 answers
34 views

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 ...