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Questions tagged [paillier]

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

The Paillier cryptosystem was invented in Pascal Paillier in 1999. It is a public-key cryptosystem which, due to its additive homomorphic property, is starting to be used in a number of research systems. It is semantically secure without modification unlike RSA which requires random padding to be semantically secure. It is based on the difficulty of computing n-th residue classes.

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How to prove correct decryption in Paillier cryptosystem

Bob sends a ciphertext obtained by Paillier encryption to Alice. Alice has the private key. She decrypts the ciphertext and returns the plaintext to Bob. How can Alice convince Bob that the plaintext is correct to this ciphertext? Bob only has the…
bin
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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.
Mustafa Khairallah
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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 plaintext P. Assuming I know the private key,how…
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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 to PHE apart from the traditional approach and…
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Paillier's scheme generalisation

Paillier's scheme assume has message and ciphertext space equal to $\mathbb{Z}_N$ with $N=pq$, that is $N$ is the product of two different primes. Is there a way to generalise this for $N$ that is the product of many ($>2$) different primes?
Bellali
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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 whether this restriction is to ensure the following…
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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. My question is, is it necessary for us to think…
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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 $\mathbb{Z}_{n}^{*}$. Prove…
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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 knew the randomness values in both ciphertexts,…
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algorithmic scheme to compare these two number encrypted using paillier cryptosystem

I have been going through https://eprint.iacr.org/2006/287.pdf (Conjunctive, Subset, and Range Queries on Encrypted Data by Dan boneh) I am trying to implement the paillier system to create a secure tunnel for gps related data on cloud. There is a…
Ramakrishna Mamidi
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How to apply two consecutive Paillier encryptions?

The plaintext space for Paillier encryption is $\mathbb{Z}_n$ and the ciphertext space is $\mathbb{Z}_{n^2}$. How can I apply two consecutive encryptions? I mean, if $c$ is the ciphertext of $m$, how to encrypt $c$?
user48832
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Lagrange Gauss Reduction Algorithm

Sorry if my question is trivial. My question is related to a post "Paillier Homomorphic encryption to calculate the means" where a member suggests Lagrange Gauss Reduction Algorithm for reducing a decrypted value to a rational number. How to use…
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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?
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Paillier Crypto System : Pros and Cons?

Can you please list the pros and cons of the Paillier crypto system you have encountered or found?
user8702
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