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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Why is “semantically secure” important for cryptosystems?

The first question: what is the exact definition of semantically secure? Basically, a cryptosystem is semantically secure if given the public key and the ciphertext, an adversary cannot learn any ...
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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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Is there an additively homomorphic encryption scheme that supports calculating a square root on the ciphertext?

I need an additively homomorphic encryption scheme that satisfies: $D(\sqrt{E(m)}) \approx \sqrt{m}$. It seems that the lifted ElGamal satisfies this, but it is hard to do decryption if the message ...
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How can I multiply an additively homomorphic encrypted value by a float number?

As we all know, if $E()$ is an additively homomorphic encryption, we can multiply $E(a)$ by an integer $b$, then we will get $E(ab)$. But what if $a$ is a float number? Can we still get $E(ab)$? Which ...
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Designing Secure Multi-Party Computation Sub-Protocols Based on Homomorphic Encryption

When designing SMPC protocols using secret-sharing, it is a common approach to compose a protocol from several sub-protocols (each proven secure under the formal definition of security w.r.t. semi-...
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Changing encryption key without revealing the original key

Say that Alice encrypts a $\text{plaintext}$ with $\text{key}_{m}$ and gives the $\text{ciphertext}_m$ to Bob. Alice wants to send several gigabytes of $\text{plaintext}$ to Eve but she is on a mobile ...
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Scale-Invariant DGHV Scheme - Decryption

I have just started reading the Scale-Invariant Fully Homomorphic Encryption over the Integers paper and I'm a bit confused about something: When decrypting the ciphertext: $c = r + (m+2r^*) \cdot \...
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Can homomorphic decryption of DES be practical?

I was reading this paper Homomorphic evaluation of the AES Circuit by Gentry et al. when I thought if something similar can be done with DES or 3DES, e.g. it is plausible to decrypt DES ...
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How to find the value of a vector modulo a basis in lattice-based cryptography

In Gentry's paper on fully homomorphic encryption using ideal lattices, he finds the values of vectors modulo a certain basis. For instance: $\psi \leftarrow \psi' \mod B$ Taken from page 69 of ...
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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 ...