# 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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### How to combine homomorphic encryption with secure multi-party computing?

I admit that I am a novice in cryptography, and I temporarily received a project that requires the use of homomorphic encryption technology and secure multiparty computing technology. Our team plans ...
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### Representing a function as FHE circuit

I am actually trying to study homomorphic encryption (on lattices) but I'm facing a problem. Every paper that I have read so far talk about writing the function to evaluate on ciphertexts as a circuit,...
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### Bootstrapping vs Recryption

In the context of fully homomorphic encryption, what is the difference between bootstrapping and recryption, since both offer the same result which is trying to eliminate/decrease the noise budget. ...
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### Bubble sort in Fully Homomorphic Encryption [duplicate]

I've read in a pdf written by Ayantika Chatterjee and Khin Mi Mi Aung whose title is "Fully Homomorphic Encryption in Real World Applications" that it is possible to implement a bubble sort algorithm ...
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### Vector dot product in Microsoft SEAL using the CKKS scheme

I'm trying to use the Microsoft SEAL library in order to do Matrix multiplication. That's why I'm trying to find a way to compute the Dot Product of 2 vectors. My issue is that the CKKS encoder in ...
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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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### 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 guess, that they are called circuits because the holy grail is to realize a ...
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### How do I prove that a user encrypted the data?

I am using homomorphic encryption, and I need to check whether or not a user's data is actually encrypted. For example, an eCommerce website pulls data from a user called Alice and wants to prove to ...
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### Does Goldwasser-Micali only encrypts only 1-bit or multiple?

I've read online that the Goldwasser-Micali scheme can only encrypt 1-bit then I read that in another pdf that that scheme can encrypt a message of multiple bits so I'm confused. Can anyone clarify ...
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### Advantages of Pallier vs Goldwasser-Micali

It is easy to see that both Pallier and Goldwasser-Micali are homomorphic addition schemes and are secure but what would be the advantages of choosing one over the other?
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### how to get top 10 numbers after using Pallier cryptosystem

Assume I encrypted 1000 Integers using the pallier cryptosystem. Since each time I encrypt a number using pallier I'm using a random ...
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### BGV for three multiplication level/depth

Can BGV homomorphic encryption scheme support three multiplication level/depth with the help of key switching and modulus switching? If Yes, how does one set up the parameter to achieve that?
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### Complexity of computing zk-SNARK Proofs

Disclaimer: I have no background in cryptography, and everything I'm asking about is what I've learnt from last couple of days of frantic reading on this topic. Any help is much appreciated. Q: What ...
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### Proving the right encrypted message was sent

Total amateur to crypto here but I've searched and searched and am at the extent of my knowledge. I've gone down several avenues to satisfy what I'm looking for but I'm just going to describe what I'd ...
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### How does the 'Flatten' function reduce the coefficients of a vector/matrix?

Seen here, at the bottom of page 5, $\operatorname{Flatten}(\vec{a})$ is defined as: $\operatorname{Flatten}(\vec{a})=\operatorname{BitDecomp}(\operatorname{BitDecomp}^{-1}(\vec{a}))$ For an n-...
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### How does Flatten really make the coefficients of a vector matrix small in LWE

In Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based, Gentry et. al defined Flattening as follows; Let $\vec{a},\vec{b}$ be vectors of ...
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### Is it possible to derive a homomorphic signature from homomorphic encryption

At the moment I am trying to find a practical way to implement a linearly homomorphic signature. Background: "In a homomorphic signature scheme, a user Alice signs some large dataset x using her ...
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### Does the relationship between plaintext and ciphertext moduli affect the security of BGV/BV SwHE?

The SwHE schemes due to Brakerski and Vaikuntanathan (BV) and Brakerski-Gentry-Vaikuntanathan (BGV) have common concept in which the message bit is put in the least significant bit of the ciphertext. ...
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I'm looking for some suggestions on what to read (papers, notes, book chapters?) on homomorphic encryption in order to understand the most recent (more optimal) schemes, as well as optimized use cases ...
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### Threshold decryption in multi-key homomorphic encryption

I have a problem understanding the security of threshold decryption in multi-key homomorphic encryption (MKHE) with so called "noise flooding". In particular I think that it is not secure, so probably ...
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### Gentry-Halevi’s Fully-Homomorphic Encryption and hermite factor

In section 7.2, page 18 in Chen-Nguyen paper regarding BKZ 2.0, they point out different Hermite factors related to Gentry-Halevi FHE. More precisely, it is said that the critical Hermite factor for ...
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### Complexity of computing homomorphic encrypted matrix multiplication

Given two players $P_1 , P_2$ . In our setting $P_1$ poses two encrypted matrices $M_{1_{k \times k}},M_{2_{k \times k}}$ over field $F$, and the encryption has additive homomorphic property, over ...
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### How to implement GSW13 using Helib or SEAL?

I want to implement the homomorphic encryption scheme proposed in GSW13, and make some changes to it, but seems that there is no library that has already been implemented it. Since this is a ...
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### ElGamal Homomorphic Encryption Formula Question

With Public Key $(G, q, g, h)$ where $G$ is a group, $q$ prime, $g$ a generator of $G$, Am I right in thinking that: $$\mathrm{Enc}(m;r) := (g^r, h^r \cdot g^m)$$
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### Fully Homomorphic Encryption - state of the art

What are the latest advances in fully homomorphic encryption? First of all, I am interested in cryptosystems based on LWE / RLWE and NTRU problems.
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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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### Paillier's Cryptosystem - Homomorphism

I'm lacking quite some mathematical knowledge here, but could anyone please explain to me why the Paillier cryptosystem is still (additive/multiplicative) homomorphic despite introducing a random ...
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### Noise of ciphertexts in LWE/RLWE based FHE

Often times $[\langle \textbf{c}, \textbf{s} \rangle]_q$ is referred to as the noise associated to the ciphertext $\textbf{c}$, and that decryption is correct when the norm of the noise is $< q/2$. ...
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### Bit decomposing a polynomial in BGV cryptosystem

I'm having trouble with the BitDecomp subroutine on page 9 of the BGV cryptosystem. I'm focusing on the RLWE instantiation so $R_q = \mathbb{Z}[x]/(x^d+1,q)$. I can't see how BitDecomp works for a ...
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### SEAL Homomorphic multiplication

In SEAL homomorphic encryption library, there is an internal procedure to decompose a polynomial with large coefficients into a vector of polynomials with smaller coefficients. The procedure is ...
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### Range query on array of encrypted data using homomorphic encryption

Given an array or database entries of encrypted data is it possible given a min/mix value to get a range of encrypted entries? The min and max values would also be encrypted.
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### What is the current state-of-the-art of function-private functional encryption?

Are there any known constructions of functional encryption with function-privacy for arbitrary functions (e.g. not just inner-product)? If so, are these constructions currently feasible or for now ...
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### How is CipherCloud doing homomorphic encryption?

Much of the literature and latest papers suggest that homomorphic encryption is still not practical yet. How is CipherCloud able to achieve this? Does anyone have an idea? Their website does not ...
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### How to define a FHE scheme whose plaintext space is infinite using boolean circuits?

There are many kinds of fully homomorphic encryption scheme by using boolean circuits. And the plaintext space $\mathcal{P} = \{ 0,1 \}$. If there is a -bit FHE scheme, we can construct a FHE scheme ...
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### Can we proxy-re-encrypt using homomorphic encryption schemes?

Homomorphic encryption schemes are PKE schemes with an additional special method Evaluate. The Evaluate method takes input any function (as boolean circuit) and encrypted inputs of the function and ...
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### How the FHE encrypts a k-bit message just with one-bit encryption scheme?

I'm reading "Fully Homomorphic Encryption over the Integers"——the first generation of FHE. However, this paper seems to detail a scheme to encrypt each bit in a message. I'm very confused about how to ...
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### Homomorphic Modular Reduction for Secure Storage

My question is quite similar to Homomorphic modulo, but I want to give a context where the operation is carried in an outsourced environment. Are there any specific homomorphic cryptographic schemes ...
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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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### Does homomorphic encryption hide the algorithm itself?

The question is rather simple, but finding resources and answers quite tricky. Homomorphic encryption should enable us to compute over encrypted data. What if the algorithm for computing should be ...
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### Do any NIST PQC have “homomorphic” public keys, in the sense that any two pubkeys derive a combination pubkey?

Background: The MathMesh crypto platform (refs at the bottom) is a newly-proposed technology stack which has been somewhat cheekily called a "Grand Unified Theory of Security on the Internet". Its "...
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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?
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 ...