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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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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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Security of somewhat homomorphic encryption via LSB encoding?

I'm reading this paper https://eprint.iacr.org/2011/344.pdf It says that "The secret-key encryption scheme whose security is based on the LWE assumption is rather straightforward. To encrypt a bit, $...
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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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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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Is there a way to perform a one way function on encrypted data?

Does the following scheme exist? Let f be a one-way function (say, an encryption scheme). Let $Enc_{sk}(x)$ be an encryption of x. We then have $Eval_{pk}(f, Enc_{sk}(x)) = f(x)$. Note that this is ...
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Guaranteeing uniqueness of a string, irrespective of its characters position when generating LtHash-like sum [migrated]

I'm trying to accomplish what LtHash offers as functionality, leaving the secure concept alone: compute a sum from a list of items, irrespective of their order to then hash it and use it as an ...
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Multi-party computation with only 1 party?

MPC is $f(E_1(a), E_2(b)) = c$, where $E$ is encryption by different keys $k_1$ and $k_2$. Homomorphic encryption is $f(E_1(a)) = E_1(c)$, where the input and output are encrypted. I want $f(E_1(a)) ...
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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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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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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 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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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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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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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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Meaning of “integers modulo 4 ” in “Fully homomorphic encryption modulo Fermat numbers” scheme

My question refers to the paper "Fully homomorphic encryption modulo Fermat numbers" by Antoine Joux. On page 3, the author describes a basic concept of the system: As many FHE systems, we deal ...
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Is there any implementation of threshold BGN homomorphic encryption?

The BGN paper (Evaluating 2-DNF Formulas on Ciphertexts) used a threshold variant of BGN. I also want to use this cryptosystem, however, I cannot find any open-source implementation. Is there any such ...
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Key derivation scheme with shared secrets?

I want to derive a list of sub-keys derived[t] from a master key mk by a key derivation function ...
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Retrieving correct ciphertext from additive ElGamal

I have been studying additive ElGamal and I think I have the hang of it except the part where the message $M$ must be retrieved by computing the discrete log of $g^M$. From what I've read, the ...
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Is there a cryptosystem which allows slicing and concatenating strings without decryption?

I want a cryptosystem with the following four functions: ...
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One-way Functions for Floating Points

Are there any commutative one-way functions for floating points? I tried to explain why I need these functions. First, I describe the problem on a high level and then I further formalize it; There ...
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Sum vector elements homorphically

I'm looking for the homomorphic version of the following (I'm using Python here): $ a = [1,2,3] $ s = sum(a) $ print(s) 6 Is there an open source fully ...
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Reference for the Security Analysis of Ring-LWE

Can someone please share a link of any research paper or web-page analyzing the security of Ring-LWE? Essentially, how should I choose my parameters to get security equivalent to 128-bit or 256-bit?
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Homomorphic Public/Private Key Encryption Scheme for Floating Numbers

Is there any public/private homomorphic encryption scheme that directly works on floating numbers or vectors of floating numbers? In our application, we want to find out if $$v_1 \approx v_2, \qquad\...
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Is it possible to sample HE ciphertexts using pseudo-random generator?

I'm trying to sample HE ciphertexts which serve as ciphertexts encrypting some random values. I have realized a example program using Microsoft SEAL, which implements a variant of BFV scheme. ...
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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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Can homomorphic encryption be used to exchange keys?

Fully Homomorphic Encryption (FHE) allows computations be done on ciphertexts. Can this technique be used to exchange keys? For example, Alice and Bob need to agree on a 4-bit secret key. Alice sends ...
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Why is the Paillier cryptosystem not considered fully homomorphic encryption? [duplicate]

Paillier is an additive homomorphic encryption system that can achieve the encrypted version of its sums. However, we can calculate the encrypted version of their multiplications by raising an ...
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Is there a standard benchmark data set for “Homomorphic Encryption” implementations?

Both in terms of statistical analysis (mean/variance, histograms, contingency tables, etc) and machine learning data sets. The question has also been asked here.
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Why is the Domingo-Ferrer cryptosystem not used in practice?

The Domingo-Ferrer cryptosystem is a fully homomorphic cryptosystem. It works fast enough. I have only seen known-plaintext attacks. Is this a reason not to use it in practice? Or are there more ...
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Are biases narrowed towards the provenance of hard NP complete problems relevant?

I hear of randomized reduction, deterministic reduction and non-deterministic reduction of complexity from A to B problems. This could make things impossible for polynomial time adversary prying into ...
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Do I need to use a matrix of size N x n for the public key in the BGV scheme when using Ring-LWE?

I'm going through the BGV paper and trying to make a toy implementation, but I just want to focus on Ring-LWE. In the paper, they set $N = \lceil{(2n + 1)\log_2(q)\rceil}$, and generate $A'$ uniformly ...
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Maintaining validity of ZKP throughout re-randomization of homomorphic ciphertext without linkability to previous ciphertext

Question: How is it possible to adapt a ZKP for a homomorphic ciphertext to still be valid after said ciphertext has been re-randomized? Context: In a lot of e-voting systems homomorphic encryption ...
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Compute ln function of a Paillier encrypted value [closed]

If I have an encrypted value $Enc(x)$ with Paillier cryptosystem, is it feasible to compute an encryption form of $\ln(x)$ or its approximation using homomorphic properties? The input $x$ is always ...
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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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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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Why FHE only needs support for addition and multiplication

For example, given $E(m_1)$ and $E(m_2)$ to the cloud. How does it calculate $E(m{_1}^{m_2})$? Is it related to the claim that any computable function can be represented as a circuit containing or <...
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What is Homomorphic encryption evaluation key

In some homomorphic encryption schemes (e.g Multi-key fully homomorphic encryption report, Computing Blindfolded: New Developments in Fully Homomorphic Encryption), it defines an encryption key, a ...
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What is labeled program

I've been studying homomorphic encryption. From their instantiations, i read Labeled Homomorphic Encryption (labHE) scheme 1 where it combines the notion of homomorphic encryption with labeled ...
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Implementation of addition in the scheme TFHE

I want to implement the addition operation in a fully homomorphic scheme - TFHE. It contains homomorphic operations on bits: AND, OR, NOT, XOR. Found addition algorithms include left and right shift. ...
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An example of calculation of BGV encryption

Can anyone give an example RLWE BGV encryption with numbers? like where m=8 (ring dimension), q=ciphertext modulus = 33=3*11 with level=2 What are COEFFICIENT and EVALUATION representation ?
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Can someone explain Relinearisation process in FV scheme for Homomorphic Encryption?

I am trying to understand the relinearisation process in FV scheme for Homomorphic Encryption based on R-LWE. Can one someone explain how the homomorphism keys are generated? I have worked out an ...
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How to solve a simple case of a RLWE problem

I've been reading up on the Ring Learning with Errors problem and the proposed attacks, in relation to homomorphic encryption. Some of the literature has been quite difficult to understand - what I ...
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FHE: What is the difference between multiplicative depth and multiplicative level?

I have seen the terms multiplicative depth and multiplicative level while reading Faster homomorphic encryption is not enough: improved heuristic for multiplicative depth minimization of Boolean ...
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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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Is there any relationship between Paillier Cryptosystem's random r and other factors

I want to try run an example of Paillier cryptosystem(Algorithm), So i just started with some basic examples, but cannot obtain correct result/decryption. I just change random factor ...
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Where does bootstrapping occur, client side or server side?

In Fully Homomorphic Encryption, where does the bootstrapping procedure performed, in the client-side or the server-side? Also, which side holds the secret key and the public key?
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What are the advantages of using Leveled Homomorphic Encryption over Somewhat Homomorphic Encryption?

Is there a point in using LHE over SHE? From what I understand, SHE is like an extended version of LHE, the only difference is that you limit the depth of circuits that can be evaluated. Therefore, I ...