Cryptosystems which support computation on encrypted data. They might be partially homomorphic (support for one operation such as + or *) or they might be fully homomorphic (any sequence of + and *).

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Performance of Fully homomorphic encryption VS Paillier encryption in Practice

Consider two schemes both have computation complexity linear to the input size (i.e. number of inputs). One scheme is based on Paillier encryption and the other one is based on fully homomorphic ...
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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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How does the Efficient Fully Homomorphic Encryption from (Standard) LWE work?

I am interesting to learn the low level implementation of Efficient Fully Homomorphic Encryption from (Standard) LWE and I am wondering if anyone can answer the following questions: Does the BV ...
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research on Encryption for master [closed]

I'm tring to choose an way for an Encryption mothod for my research? So,I want to choose one-layer encryption or multilayer encryption,and I want it to be easy to applicable. when I search about it, ...
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Homomorphic Encryption vs. Garbled circuits

I'm currently trying to understand all the differences between homomorphic encryption and garbeled circuits. As I understood the use of homomorphic encryption hides either the data or the computation ...
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In bilinear pairings, is it possible to let someone be only able to decrypt ciphertexts in $G_1$ but not able to decrypt the ciphertexts in $G$?

For example, in Don Boneh et al.'s paper "Evaluating 2-DNF Formulas on Ciphertexts", they gave an encryption system that the cihpertext can be in either $G$ (when only additional homomorphic ...
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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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Is it possible to encrypt data points but still be able to select the ones “near” a given value?

We have an application where we would like to store "encrypted" data points (as in, not being able to know the original - plaintext - data just by looking at the stored - encrypted - version of it) ...
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Key Size for Symmetric Homomorphic Encryption Over the Integers

In the paper Fully Homomorphic Encryption over the Integers, it mentions a symmetric key scheme on page 1 and 2. Key Generation: Pick a random odd number $p \epsilon [2^{N-1},2^N)$ Encrypt A Bit m: $...
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In DGHV FHE, why noise $r$ can be in $(-2^{\rho'}, 0)$?

"Fully Homomorphic Encryption over the Integer" described a simple FHE scheme based on the GACD assumption. Its encryption function (on page 6) has the form $c \leftarrow (m + 2r + 2*\sum_{i \in S} ...
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Hitting a counter example in homomorphic encryption over the integers

The paper Fully Homomorphic Encryption over the Integers talks about a super simple symmetric key implementation on page 1 and 2. It says that to generate a key, you pick a random odd number between $...
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Symmetric key in homomorphic encryption over the integers

Much like this question: Public key in fully homomorphic encryption over the integers I am also reading I'm reading Fully Homomorphic Encryption over the Integers, but I'm working on implementing the ...
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Additive homomorphic encryption scheme without change in operator

I'm looking for an additive homomorphic encryption that the addition operator (+) in its plaintext space be the same as addition operator in its ciphertext space. (Schemes like Paillier do addition in ...
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Why an upside down path on the evaluation of branching program on encrypted data?

Suggested by Ricky Demer in this post, I am reading the paper "Evaluating Branching Programs on Encrypted Data"(TCC 2007), which uses one-round strong OT protocol to implement homomorphic evaluation ...
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Are there any encryption schemes that enable to permute homomorphically?

According to the Barrington's theorem, any circuit in NC1 can be converted to a branching program, whose main operation is the composition of permutations (along with the choosing of permutations ...
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Is there a partially homomorphic quantum secure public key cryptosystem with IND-CCA1 security?

I recentely asked "IND-CCA1 RSA padding?" about whether there is a IND-CCA1 secure variant of RSA. The original version of the question also allowed usage of ECC which would allow usage of ElGamal, ...
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Question about OR operation in fully homomorphic encryption

This page (which won't let me post a comment, sadly!) describes how the original FHE paper by Craig Gentry describes FHE. (Other references to this stuff can be found on this question.) It mentions ...
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Is full Homomorphic encryption quantum resistant?

Since most of our asymmetric encryption algorithms are going to be out-of-date in a couple of year due to Shor's algorithm, I was wondering about the future of FHE schemes. I have found this paper, ...
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Are there simpler FHE methods than Craig Gentry's original paper?

Craig Gentry's 2010 paper on FHE is very cool, and I'm planning on implementing a basic proof of concept FHE. I was wondering though, are there any simpler methods that have been discovered since ...
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Generating random vector for Full Homomorphic Cryptography

The site below explains that part of doing homomorphic encryption, you need to generate a vector of random numbers that have the property that its dot product against a randomly generated bit vector ...
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What consequences do the plaintext space size has on the performances in the BGV scheme?

In the BGV paper [1], the authors say in ยง5.4 that you can have $\mathbb{Z}_p$ as plaintext size with a large $p$. What is the impact of the size of $p$ on the ciphertext size and computational work ...
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Is the ring of octonions “commonly” used in Cryptography?

I've recently read "Fully Homomorphic Encryption on Octonion Ring" by Yagisawa, which is based on octonion rings over finite fields. Personally I've never encountered octonion rings in cryptography ...
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Fast attack on approximate GCD problem?

This question is about the approximate GCD problem which is defined as follows: Given any number of the approximate multiples $a_i = p \cdot q_i + r_i$ of $p$, where $p$, $q_i$ and $r_i$ are integers, ...
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AES-Paillier Homomorphic encryption [closed]

How can I implement following problem in java code for addition? (here I use Paillier homomrphic encryption): Input would be to generate a new AES key, encrypt the private data with that key, encrypt ...
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Are all homomorphic encryption schemes not CCA secure? [duplicate]

Homomorphic encryption is hyped by computer sciences because it offers great potentials. For example you can perform cloud based calculation while nobody gets to know you data. I am wondering if ...
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Inner product with homomorphic encryption

I want to do a very simple thing: Given two vectors, I want to encrypt them and do some calculation, then decrypt the result and get the inner product between both vectors. I want to do this as fast ...