Questions tagged [homomorphic-encryption]

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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elliptic curve scalar addition

say there is an homomorphic cryptosystem on elliptic which allows unlimited addition and only one multiplication. So in order to same the mult operation for a later functionality, I need to add a ...
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Paillier scheme : Encoding floats into integers impact on computations

In Privacy Preserving Processing Over Encrypted Images, I could understand that appropriate encoding of floats into integers (required in Paillier) only incur negligible error in computations. Any ...
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GSW and homomorphic addition on integers

Is it possible to use the GSW scheme (Gentry, Sahai, Waters) also on integer values and not just single bits? If not, are there any schemes that support integer arithmetic with the same nice property ...
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GSW13 scheme and integer arithmetic

I'm new to lattice-based cryptography and have trouble understanding if the GSW13 (Gentry, Sahai, Waters) scheme works only on single bits. But is it also possible to encrypt integers with this scheme ...
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Homomorphic encryption in social networks

I want to gain some experience with homomorphic encryption, specifically possible applications in social networks. I am thinking about using a HE library (such as Microsoft SEAL) with a graph database ...
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Is overflow-ing possible in CKKS FHE scheme?

I'm using the CKKS Fully homomorphic scheme using Microsoft SEAL, and wonder what will be the result of overflowing a certain floating point variable? Is it even possible to do so? I found a statement ...
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How to count the number of selected element in each slot within the packed ciphertext

Given an encrypted ciphertext (n slots, packed n elements into a single ciphertext), such as 𝑐𝑡={(2,0,1,2),(3,2,1,3),(3,4,0,4),(5,1,4,2)}. Formally, 𝑛 slots can be expressed as 𝑚 blocks, each ...
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Using two or more encryption algorithms together, how do we compute the strength of the final encryption?

If two or more encryption algorithms are used together, how do we compute the strength of the final encryption? And how would the application perform against quantum computers? The first two tables ...
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Homomorphic encryption watermarking identity

I've been doing some research on FHE and SWHE schemes, most specifically on watermarking. As far as I've understood, you take as the merchant, take the buyer information encrypted and his public key ...
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Autonomous homomorphic encryption

So, my understanding of homomorphic encryption is that Alice has a private key and an algorithm, gives an encrypted copy of the algorithm to Bob, Bob runs the algorithm without understanding it, and ...
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Zero knowledge proof of Paillier cryptosystem

I have read the paper recently and I am curious about part 3. According to part 3, Bob sends a zero-knowledge proof such that $c_B=b\times_{E}c_A+_E E_A(\beta')$. Then Alice should first decrypt the ...
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Security analysis of encrypting a matrix after homomorphic encryption by the random mask

Problem Definition Alice has two private matrices $M_A$ ($N*M$), $M_a$, where $M_a$ is the binary matrix of $M_A$ Bob has a private matrix $M_B$($N*M$) Alice and Bob are semi-honest server and ...
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Is there anyone intrested in quantum fully homomorphic encryption?

Recently, I have read a paper named "Classical Homomorphic Encryption for Quantum Circuits". The author claims a quantum scheme that can apply an encrypted (like GSW encryption) bit to ...
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AES homomorphic updates

I am looking for some help regarding something I am trying to do and I think to solution might be in Homomorphic encryption. Person A and B encrypt the same number(unsinged long) N using AES with ...
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How many known plaintexts are required to break a system with this property?

Suppose we have an $n$ bit block cipher $E$ with a key $k$ that has the following property $$E(k; m_1⊕m_2) = E(k;m_1) ⊕E(k; m_2).$$ How many minimum number of chosen plaintexts are required to ...
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Bitwise operations in FHE

Im reading about FHE and the libraries implementing it (SEAL, HELib). I saw that SEAL doesn't support bitwise operations but I wondered if its theoretically feasible. For example, bitwise-ing XOR an ...
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Privacy preserving aggregation of encrypted data

I have the following problem: I have $t$ servers $S_1, S_2, S_3, \ldots, S_t$, each of them storing some $key : value$ list. They have to upload this data into a big dropbox server $D$, but in such a ...
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What is the key generation and management process of a fully homomorphic encryption system?

I've been very interested in fully homomorphic encryption lately, and I understand the concept well enough, but there is one thing that I don't understand... What is the key creation and, more ...
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How is it that homomorphic encryption can encrypt program code and run it without decryption?

In my journey of interest in the world of homomorphic encryption has led me to a concept floating around the internet where they describe homomorphic encryption being used with "mobile agents&...
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Hash chain based secret revealing using homorphic princples?

I have recently been looking into Homomorphic encryption and I am looking for a specific hash-based encryption/decryption scheme. I don't need a full implementation but I am not sure if what I want ...
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CKKS Encoding scheme explanation

I have been going over the CKKS Homomorphic Encryption scheme but I can't seem to understand how the mapping takes place while encoding. I don't get what the line below is trying to convey. I saw this ...
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Retrofitting software: the biggest problem with Homomorphic Encryption?

In my experience, conversations around Homomorphic Encryption tend to focus on the narrative "HE is the holy grail of secure computations, but it's still too computational intensive to be practical". ...
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Whether there is a public key encryption system based on elliptic curve with the property of multiplication and addition homomorphism。

I want to implement it on the intelligent contract and then do the development,because use paillier i cant genereate 1024bits key,so i try to find if there is exit a public key encryption system based ...
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Noise budget stops decreasing further, while running simple additions

I'm experimenting with Microsoft SEAL 3.4.5. I've a simple addition, which I run within a for-loop. ...
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Confidential data encryption on ethereum

I already built a supply chain that is able to collect product information on Ethereum. Now, that data can be confidential, but I still want to do Matrix calculations on it. I came across homomorphic ...
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Is it possible using homomorphic encryption (or some other technique)

Is the following possible with homomorphic encryption (or some other technique)? Suppose the cloud server keeps a key-value list for a user with each value field encrypted (prv key with user). Now, ...
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How to implement division operation on ciphertext by using HElib or SEAL?

HElib has no general purpose API for number operations such as comparison or division. How can we implement division operation on ciphertext?How to encrypt floating numbers of any length in ...
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What's the deal with conditional and jump operations in homomorphic encryption?

I'm doing some research about full homomorphic encryption (FHE). As I figured out, algorithms are implemented in circuits. I suppose that they are called circuits because the Holy Grail is to realize ...
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Homomorphic Encryption Verification

How much is it possibile to devide $E(m_1+m_2)$ by $E (m_1)$ to obtain $E (m_2)$ based on the fully Homomorphic-encryption property which says; $$E (m_1) * E (m_2) = E (m_1 + m_2)$$. And if yes what ...
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Question about Gentry's “Computing Arbitrary Functions of Encrypted Data”

I am working through the "Computing Arbitrary Functions of Encrypted Data" by Gentry, trying to understand more about Fully Homomorphic Encryption. I'm stuck trying to understand why his "Somewhat ...
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Difference between function $f$ in eval and dec of homomorphic authenticated encryption

In the homomorphic authenticated encryption, as described 1, there are Eval and Dec PPT algorithms: In Eval, f is the function to be performed on the encrypted data. However, I need to know why it ...
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Hash function over numbers that preserve addition and multiplication

I wonder if there is a known hash function that for any $x$, $y$ which are numbers in a certain range with certain accuracy (I guess one can think of them as integers?), you can define two functions ...
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homomorphic encryption function representation

As it known, Homomorphic encryption can be used for privacy-preserving outsourced storage and computation. In various constructions, the computations are represented as either Boolean or arithmetic ...
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What is the main purpose of using Boolean Circuit Model in Homomorphic Encryption?

Why do we use or have Boolean Circuit Model is it because since it uses gates and bits we could adapt it into a hardware model?
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In using Boolean Circuits model of Computation in Homomorphic Encryption why is is considered fast?

I am currently doing some reading on Homomorphic Encryption for research purposes and based on my reading using the Boolean Circuit Model of Computation specifically in regards to Fast Fully ...
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Does such cryptographic scheme exists?

Is there any multi-key additive homomorphic encryption scheme based on elliptic curve cryptography? Meaning adding encrypted values encrypted with different public keys and decrypt the total sum with ...
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SEAL-CKKS max multiplication depth

I am trying to understand how SEAL-CKKS scheme works and I wonder what multiplication level can we achieve using this scheme? Like 100 possible?
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How can a node establish pairwise shared key with other nodes using its own polynomial share together with other's public values?

A server has a symmetric bivariate polynomial $ F(x, y) = \sum_{{i,j}=0}^{t-1}a_{i,j}x^iy^j$ $\in GF(p)[X, Y] $ of degree $t-1$. For simpliciy, $ F(x, y) = a_{0,0}+a_{1,0} x+a_{0,1}y+ a_{1,1}xy$ mod ...
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Blinding factor SEAL

For a protocol, I need to blind a ciphertext. I am not sure how to choose the blinding factor. How should I choose the range? What should I consider to offer security? I am using CKKS scheme, the one ...
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homomorphic division with scaling/Paillier

Let's say that I have to use fractions instead of integers and I am using Paillier cryptosystem. So, I use scaling to obtain integers. Assume that I have a secure division protocol. What happens if ...
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Verification of data on an untrusted remote storage server

I was looking at tahoe-lafs which accepts a file, encrypts it, does erasure coding on it which generates n shares and then distributes it over the storage servers. The distribution is Share 1 = Server ...
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How is the security of a plaintext of Ring-LWE without an error term?

I think until public key $\mathsf{pk}=(b=-[as + e]_q,a) $ is broken, Ring-LWE is secure where $a$ is uniformaly random polynomial, $e$ is an error sampled from gaussian distribution with std=$\sigma$ ...
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How to authenticate indivisual value after applying homomorphic encryption using Paillier homomorphic

Assuming I have three parties in a system: Alice, Bob, and a Server. Alice and Bob needs to aggregate some messages $m1$ for Alice, and $m2$ for Bob. And send the aggregate $m1+m2$ to the Server. I ...
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Automorphism in Cryptography

I read a research paper in which the writer again and again writes about norm preserving automorphism such as $\left \| \phi(a) \right \|$ =$\left \| a\right \|$ and determinant preserving ...
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Recryption of ciphertext with a different key

Let's have $P$ some sensitive piece of data and $K_1$a secret value, both known to Alice, but not to Bob. $K_1(P)$ means $P$ encrypted using $K_1$. Alice sends $K_1(P)$ to Bob. Bob keeps the value of ...
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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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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 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. ...

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