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 this homomorphic encryption correct?

In LTV-FHE, section 3.3.2 Formal description, a ciphertext looks like this $c=hs+2e+b = (2g/f)s+2e+b$, where $h = 2g/f$ is the public key, $f$ is the secret key, $g, s$ and $e$ are chosen randomly, ...
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22 views

For the LTV-FHE scheme, after how many additions should modulus switching be used?

From the LTV-FHE paper I find out that after every multiplication there must be a modulus switch to mitigate the noise in the resulting ciphertext, besides relinearization. But, assuming the ...
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34 views

Partially homomorphic addition - not all parties present

I often see homomorphic encryption as a solution to a problem where a server wants to know the sum of $n$ users' numbers but can not know each individual users' number plaintexts. My question is: if ...
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45 views

How to deal with different setup in Multikey FHE?

The scenario : using a Multikey FHE scheme, let's say LTV-FHE scheme, parties delegate the computation of some function to the mighty cloud. In LTV-FHE scheme the parties generate their keys and ...
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59 views

Should we use modulus switching when dealing with ciphertexts encrypted in different rings?

Having a homomorphic encryption scheme like BGV or LTV-FHE at some point it is possible in the homomorphic evaluation to deal with ciphertexts that are encrypted with respect to different moduli. ...
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37 views

Encryption of both data and code [duplicate]

Suppose we have 3 parties: Alice possesses invaluable data $x_1, x_2, ...$; Bob can compute some extremely useful function $f$; Carol owns a world's largest data center which have enough resources to ...
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76 views

Is there an additive homomorphic encryption that supports exponentation

For example say we have two numbers a and b. Now is there any partial homomorphic encryption scheme that allows to compute (a-b)^2 over the ciphertexts of a and b without round trips.
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93 views

Convert ciphertexts of one encryption scheme to another without decryption

I want to convert ciphertexts of one encryption scheme to another without decrypting them under the first scheme and then encrypting with the second scheme. For example convert OPE encryption to ...
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130 views

How can we define division operation by using Fully homomorphic encryption

Last fews months, I'm working with homomorphic encryption. Now I am dealing with some computational problems with integers or real-numbers (like arithmetic mean, standard deviation) where division is ...
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117 views

Performing simple arithmetic operations on compressed, and both compressed and encrypted data

We all know it is possible to perform addition and multiplication operations on encrypted data by means of homomorphic encryption methods. My questions are: Is there any cryptosystem that is able to ...
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1answer
119 views

Elliptic curve ElGamal with homomorphic mapping

I am interested in ElGamal due to the fact that you can achieve some degree of homomorphic properties. I became interested in applying ElGamal to elliptic curves, and found this other question with an ...
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128 views

How can comparision like (>=,==) be done using homomorphic encryption?

Since we know that Homomorphic encryption allow computation on encrypted data. Let two n-bit integers $(x,y)$ are encrypted using some LWE public key cryptography. For example - if $x'= HEnc(x,pk)$ ...
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An MPC protocol from Elgamal is a good solution a homomorphic multiplication?

I want to compute a multiplication between many secret values and then distribute the result to everyone involved. For this, I thought about an MPC protocol built from Threshold Homomorphic Elgamal. ...
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1answer
255 views

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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88 views

How can I implement decryption for NTRU homomorphic encryption scheme?

I have come across this paper On-the-fly multiparty computation via on-the-cloud Multikey from Fully Homomorphic Encryption by Lopez-Alt et al., where authors describe a NTRU-based homomorphic ...
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1answer
110 views

Why gcd(r,(p-1)/r) needs to be 1 in benaloh cryptosystem

I recently discovered the benaloh cryptosystem. I am working with the system as it is discribed in the following link: https://en.wikipedia.org/wiki/Benaloh_cryptosystem However I need some help in ...
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113 views

Example of FHEI scheme?

I am reading this paper Toward Secure Multikeyword Top-k Retrieval over Encrypted Cloud Data. I am trying to work out an example of the FHEI (Fully homomorphic Encryption over Integers) scheme ...
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Security parameter p =O(n)

In many homomorphic encryption scheme, a security parameter is calculated as p =O(n). How to use the complexity order as values? Is there any specific method with an appropriate example?
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Homomorphic encryption diagram and trouble about a paper

I'm reading a paper based on Homomorphic Encryption: “Fully Homomorphic Encryption over the Integers: From Theory to Practice” (PDF). Now, I need a diagram of this algorithm if possible with all the ...
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56 views

Can homomorphic operations on many different ciphertexts be multiplied by a same constant?

Assume Alice encrypts messages $m_1$,...,$m_n$ using secret keys $k_1$,...,$k_n$ on a homomorphic encryption scheme (BHHO), so she would get $c_1=Enc_{k_1}(m_1)$,...,$c_n=Enc_{k_n}(m_n)$. Then Alice ...
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1answer
67 views

How to test an implementation of a homomorphic scheme?

I want to implement the following homomorphic encryption scheme from On-the-Fly Multiparty Computation on the Cloud via Multikey Fully Homomorphic Encryption by Lopez-Alt et al. I use C++ and I want ...
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327 views

Proof that a hash matches an encrypted file

Assume that Alice has a file $F$ which she is going to send, in encrypted form to Bob. Alice possesses $F$ and an encryption key $K$. She sends to Bob the encryption of $F$ using $K$, $E(F,K)$ as ...
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232 views

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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143 views

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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Is that simple additive homomorphic scheme secure?

I am doing a little cryptography research and stuck with question. Suppose $\bar m$ is a vector of 64-bit numbers. And i want to have an additive homomorphic encryption over them. I choose large (...
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Homomorphic OR operations

Is there an encryption scheme that provides efficient homomorphic OR operations at the ciphertext space? Of course any fully homomorphic encryption can be used but I do not require or want additional ...
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193 views

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}= E(m)^{...
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243 views

Sorting over encrypted data with different symmetric keys

I'm working on a security project. I need to perform a sorting on the lists of encrypted integers and strings. The encryption used is symmetric. The clients send the encrypted data in a list to the ...
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3answers
217 views

paradox on fully homomorphic equality checking

Imagine, a client encrypts a corpus of data (say documents of text) with the public key of a Fully Homomorphic Encryption scheme (FHE) and outsources the data to an untrusted server.Now the client ...
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73 views

Fully homomorphic encryption arbitrary functions formulation

I am currently studying the interesting field of homomorphic encryption. I read that from a fully homomorphic encryption function that supports both addition and multiplication you can perform any ...
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63 views

How about a homomorphic integer sorting in a MPC context?

I want to implement the ATV-FHE scheme as described by Adriana López-Alt, Eran Tromer, Vinod Vaikuntanathan: On-the-Fly Multiparty Computation on the Cloud via Multikey Fully Homomorphic Encryption (...
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Truncating ciphertexts on ring-LWE schemes

On the section 5.4 of the paper Improved Security for a Ring-Based Fully Homomorphic Encryption Scheme, the authors explain how to discard some bits of the ciphertexts to get smaller ciphertexts and ...
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Upper bound on r* on page 7 in the Scale Invariant Fully Homomorphic Encryption over the Integers paper

I was hoping to get some clarification on how the bound on r* was calculated (bottom of page #7). I'm trying to reproduce the results that have been shown, however I keep getting a slightly smaller ...
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Are there any FHE-MPC schemes implemented?

I want to know if there are any publicly available multiparty computation schemes derived from fully homomorphic encryption schemes. An example would be the implementation of this scheme https://...
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Can the Smart-Vercauteren Homomorphic Encryption be implemented as a practical fully homomorphic encryption scheme?

Smart and Vercauteren proposed a homomorphic encryption scheme (PKC 2010) following Gentry's principles. ​ Though their scheme can achieve fully homomorphism theoretically, they admitted that "for ...
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Grouping in BGN

The below equation is mentioned in Homomorphic Encryption and the BGN Cryptosystem (pdf, page 4): Mult(pk, $C_1$, $C_2$): Choose $u \xleftarrow{R} [1, n]$ and output $D = \hat{e}(C_1, C_2) \cdot e(...
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How do I check if the secret key polynomial of the ATV-FHE (NTRU based) scheme is invertible?

I want to implement the ATV-FHE scheme as described here https://eprint.iacr.org/2014/039.pdf. To generate the secret key polynomial I compute f = 2*u + 1 , with scheme parameters chosen such that ...
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Which parameters of the ATV-FHE scheme should be kept private?

I try to implement the ATV-FHE scheme as it is described in section 2 of this paper. I also read this paper that says how parameters should be chosen. Are there some parameters that must be kept ...
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In FHE over integers is each bit of the cyphertext encrypted under the new key?

In the paper Fully Homomorphic Encryption over the Integers, a method is shown for doing homomorphic encryption using only integers. The basic idea is that a bit m is encoded as a large integer c. ...
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Homomorphic Encryption with Addition and Exponentiation

Is there any homomorphic encryption scheme which supports addition and power over cipher text ? Paillier is close but it supports addition and multiplication with a constant. I am getting an output ...
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1answer
132 views

What is scale-invariance notion of a fully homomorphic encryption scheme?

I read this paper https://eprint.iacr.org/2012/078.pdf and I didn't understand what does the author mean with scale-invariance perspective. The perspective in which we view the ciphertext is ...
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What is the bound for the probability distribution for ATV-FHE scheme?

I try to implement the ATV-FHE scheme as described in this paper https://eprint.iacr.org/2014/039.pdf. How do I choose the bound for the probability distribution chi? How do I choose standard ...
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How to choose moduli ladder for ATV-FHE scheme?

I try to implement the ATV-FHE scheme as mentioned in section 2 in this paper https://eprint.iacr.org/2014/039.pdf. In this paper, authors say this "For example, given a 256-bit prime q ..." in ...
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33 views

How to generate public key for ATV-FHE scheme?

I want to implement the ATV-FHE scheme as it is described here https://eprint.iacr.org/2014/039.pdf. How to generate the public key? Should I compute it as indicated in section 2 : $h(i) = 2g(i)*...
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498 views

Which is/are the strongest known Fully Homomorphic Encryption scheme(s)?

As it is discussed here that the highest security any homomorphic encryption scheme is at most IND-CCA1, Is there any known fully homomorphic encryption scheme that achieves this security level? Out ...
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Can I expand the modular of an encryption scheme?

Take the lifted ElGamal as an example: suppose the original ciphertext is $<g^y ~mod~q,~g^m~mod~q>$. After some calculations, $m$ could be large enough to do modular. But I don't want $m$ to be ...
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How to test a FHE implementation?

I want to implement a FHE scheme based on NTRU, namely the scheme described here https://eprint.iacr.org/2014/039.pdf . How to test the security of my implementation ? Do I have to implement the ...
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What about using only XOR gates in homomorphic encryption?

What if we were substitute the ANDs with XORs in some homomorphic encryption scheme like BGV(https://eprint.iacr.org/2011/277.pdf), LTV ( https://eprint.iacr.org/2013/094.pdf) ? It may be more ...
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How to use this homNAND gate?

I was reading this paper https://eprint.iacr.org/2014/816.pdf "Bootstratpping in less than one second" but I didn't understand it throughly. What's the point to build a cheap NAND gate ? Maybe to ...
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How to toggle a bit homomorphically ?

Suppose I want to use LTV scheme from this paper https://eprint.iacr.org/2013/094.pdf to compute homomorphically a function. But the multiplication operation is more expensive than the additive one. ...