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

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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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695 views

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 $M/D$ ?
3
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98 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 ...
3
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99 views

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?
3
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2answers
159 views

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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215 views

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 ...
2
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1answer
170 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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232 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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345 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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0answers
84 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
204 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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1answer
53 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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1answer
111 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 ...
1
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1answer
133 views

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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1answer
230 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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1answer
255 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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1answer
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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?