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

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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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272 views

How can I do minus on plaintexts in the Paillier cryptosystem?

We have $E(a)$, $E(b)$ encrypted under the same Paillier key. As we all know, we can get $E(a+b)$ by calculating $E(a)*E(b)$. But can we get $E(a-b)$, by calculating $E(a)/E(b)$? I tried to ...
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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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Why multiple homomorphic operations on a ciphertext leaks no information about the plaintext?

Scenario: Assume I encrypt message $m$ using Paillier encryption, so I would get $c=E(m)$. I give the identical $c$ to two different parties, parties $D$ and $E$. Party $D$ computes: $c_{D}= ...
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Alice answering Bob without knowing he question

I'm a student and I don't know how to solve the following problem : Alice is proposing a 10 questions list to Bob. Bob choose only 1 question and wants to know the answer without Alice knowing the ...
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1answer
65 views

Usefulness of Damgård–Jurik

I am trying to understand what are the benefits of using Damgård–Jurik over Paillier. I understand that expansion factor decreases as s increases. But isn't it the ...
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Are there any real-world E-voting systems in use with the Paillier cryptosystem?

There are a lot of theories of Paillier cryptosystem with references to e-voting. Are there any real-world E-voting systems in use with the Paillier cryptosystem?
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46 views

Making Pascal Paillier' output absolute

Can we make subtraction result of cipher texts encrypted by Pascal Paillier absolute. Just like we use method Math.abs() in Java ? For example, if we subtract 0 from 1: 1-0 = 1, it is positive but 0-1 ...
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1answer
35 views

How to calculate Enc(-m) from Enc(m) in Paillier cryptosystem?

The encryption in Paillier cryptosystem is like this according to Wikipedia: Let $m$ be a message to be encrypted where $m \in \mathbb{Z}_n$ Select random $r$ where $r \in \mathbb{Z}_n^*$ Compute ...
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Paillier cryptosystem, small integers and range of values

First, this a different take on my previous question: Pailler encryption of small integers to 32-bit integers I have to encode small integers (range 0-50) using the Paillier cryptosystem. Those ...
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105 views

Paillier Cryptosystem - Practical applications?

I wonder: are there any real-world practical applications using the Paillier cryptosystem , as introduced in [1], or some derivations of it? I'm aware of quite a few schemes proposed in literature ...
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What if the p and q used in keys generation of Pailler cryptosystem are composite?

I've seen a few implementations of Paillier cryptosystem that uses probable primes to choose $p$ and $q$. Assuming that a keypair is generated with $p$ and $q$ that are coprime and that $pq$ is ...
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117 views

Paillier Encryption: problems with double encryption

Given have two public keys $k1$ and $k2$, $E_{k1}(E_{k2}(m_1))$ and $m_2$. Is it possible to calculate $E_{k1}(E_{k2}(m_1 + m2))$? (or with multiplication instead of addition) At a first glance, I ...
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590 views

Paillier can add and multiply, why is it only partially homomorphic?

I've seen that it's widely accepted that before Gentry's breakthrough (which is not practical yet) in 2009 there were no known full homomorphic encryption scheme. I've read here in another answer ...
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1answer
167 views

ElGamal and Paillier key sizes for short messages

I am using ElGamal and Paillier schemes to encrypt a large number of short messages: typical 4-byte integers. I do this for the homomorphic properties of these schemes. However, the way the ...
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110 views

Pailler encryption of small integers to 32-bit integers

I want to encrypt very small integers in the range 0-44 using the Paillier cryptosystem. Is there a way to select p, ...
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Does the Paillier system remain secure if it is used to encrypt only binary values, i.e. {0, 1}?

Is there any security compromises if the Paillier system was used to encrypt only binary message in {0, 1}? i.e., plaintexts are either 0 or 1.
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103 views

Paillier cryptosystem preserve ordering of sums for two integer sequences

According to Paillier cryptosystem the product of two ciphertexts will decrypt to the sum of their corresponding plaintexts. I have two separate integer sequences X and Y that have same number of ...
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Proving that a plaintext is the Paillier decryption of a certain ciphertext [duplicate]

Assume that Alice received 100 ciphertexts encrypted with additive homomorphic encryption, say Paillier, using the same public key that belongs to Bob. Alice added all of them, and wants to know the ...
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101 views

Formal security of recycled random blinding in a Paillier scheme

This question is a follow-up/variant on a previous question. Supposing that we are trying to generate a large number of (indistinguishable) ciphertexts of a given plaintext and want to avoid the ...
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How bad would it be to reuse the random blinding factor in a scheme like Paillier?

A secure and somewhat fast way to "re-encrypt" (refresh? anonymise?) a Paillier ciphertext, $c$, is to multiply it by an exponentiated random value: $c \gets c \cdot r^n \mod n^2$ (with $r \in ...
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263 views

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 ...
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299 views

can anyone give the java code to encrypt files using paillier [closed]

I want to implement encryption on personal files using paillier encryption. Is it possible to encrypt files using this encryption..
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RSA or Paillier is good? [closed]

I want to implement file storage in cloud using homomorphic encryption. I want to use paillier encryption. Can you suggest the drawback of RSA to store and retrieving the files. Then only i can use ...
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73 views

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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196 views

Equal length of primes in paillier cryptosystem

In the key generation step of paillier cryptosystem , In order to satisfy $\gcd(pq,(p-1)(q-1))=1$ , we can take equal length primes. Instead of taking(length as parameter to generate $p,q$) equal ...
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156 views

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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643 views

How to select $g$ in Paillier Cryptosystem

For my cryptography class project in university I have selected Paillier Cryptosystem as a course project ...
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191 views

Logical OR operation in a homomorphic additive cryptosystem

Suppose we have a cryptosystem homomorphic for addition (say Paillier's). Is there a way to perform a logical OR operation between two binary values (with a binary result). We can, of course, obtain ...
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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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Calculating ciphersize of Paillier, SSE and OPE

If I have to encrypt a 32 bit plaintext in each of Paillier, SSE and OPE, how can I make an estimate of the ciphertext sizes respectively in order to reserve the amount of space in a database?
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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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115 views

Paillier Crypto System : Pros and Cons? [closed]

Can you please list the pros and cons of the Paillier crypto system you have encountered or found?
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327 views

Bandwidth and block size for Paillier cryptosystem

Can someone clarify what is meant by the terms cryptosystem bandwidth and block size for public key cryptosystems; The context is the Paillier cryptosystem and its Damgard-Jurik generalisation. My ...
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140 views

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 ...
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348 views

Questions about proof of correct encryption in the Paillier cryptosystem

In the Paillier cryptosystem [1] the encryption of $m \in \mathbb{Z}_N$ with randomness $r \in \mathbb{Z}_n^*$ is $c = g^m r^n \bmod{n^2}$. A proof of correct encryption could look like presented in ...
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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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inverse element in Paillier cryptosystem

As I know, in Paillier cryptosystem, the encryption $c$ of a message $m$ is calculated as $c=g^m r^n \bmod n^2$. Now, I am wondering if I can derive $g^m \bmod n^2$ given that I know $c$, $r$, and ...
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516 views

Several questions about Paillier cryptosystem

I have several questions concerning the original Paillier cryptosystem as described in Paillier, Pascal (1999). "Public-Key Cryptosystems Based on Composite Degree Residuosity Classes". EUROCRYPT. ...
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334 views

Implementing Paillier Signature Scheme in Delphi

I've been trying to implement the Paillier Signature Scheme in Delphi, but I can't get it to work and I don't know where the problem is. First of all, I got my info about the scheme from this paper. ...
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329 views

ZKIP for Paillier public key correctness

I'm using the Paillier cryptosystem in a protocol similar to mental poker. In the beginning of the protocol, each player generates a Paillier public key $(n,g)$. Later in the protocol, a player may ...
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Division in paillier cryptosystem

Is division possible in the Paillier Cryptosystem? i.e. given a the cipher-text $C$ of an integer $M$ the plain-text divisor $D$, and only the public key, can one compute the cipher-text of $M/D$ ?