# 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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### I'm wondering if using the same one public key does not guarantee privacy in the computation of multiple data owners

Participating entity: multiple data owners, computing clouds Protocol: The multiple data owners send their data to the computing clouds, which perform the computation of the data. Privacy protection:...
1 vote
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### Understanding Gentry's initial FHE construction based on ideal lattices

I am trying to understand the encryption procedure in Craig Gentry's initial construction for FHE described in Fully Homomorphic Encryption Using Ideal Lattices. Unfortunately after repeated attempts ...
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### convert from integer to polynomial ring in BFV homomorphic algorithm

BFV algorithm is one type of fully homomorphic encryption algorithms, how can I encoding integer to polynomial ring by using batch encoder based on Rt:=Zt[X]/⟨(X^n)+1⟩, the plaintext space (R mod t) ...
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### [error reducing techinique in lattice based commitment]

I am aware there are many techniques to reduce the error of lattice-based homomorphic encryption. But is there any technique to deal with lattice-based homomorphic commitment, e.g., More Efficient ...
1 vote
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### Decryption of Naccache–Stern cryptosystem is not guaranteed for large keys

Naccache-Stern cryptosystem is mainly based on Chinese Remainder Theorem. According to its wiki page and Partially Homomorphic encryption book, I generated following keys. 1- Picked a family of k ...
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### Understanding and Implementing fast base conversion (FastBConv, bconv) in Mathematica

According to Section 2.3 of Full-RNS CKKS: More precisely, for a basis $\left\{p_{0}, \ldots, p_{k-1}, q_{0}, \ldots, q_{\ell-1}\right\}$, let $\mathcal{B}=\left\{p_{0}, \ldots, p_{k-1}\right\}$ ...
47 views

### merging structured encrypted data

this is a followup of the post I made there: https://stackoverflow.com/questions/77428690/merging-structured-encrypted-data Essentialy, I'd like to know if there is a way to merge bencoded data (or ...
1 vote
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### Homomorphic encryption with multiple keys that is secure under the assumption of a compromise of the combined key

Is it possible to extend the general concept of homomorphic encryption: $$f(m_1)\cdot f(m_2)=f(m_1+m_2)$$ to: $$f(m_1)\cdot g(m_2)=f\cdot g(m_1+m_2)$$ is it further possible to construct the scheme in ...
1 vote
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### Why the refresh (modulus and key switching) is required in BGV after addition?

I am reading the BGV paper. On page 18, after addition, the protocol will also refresh (modulus and key switching), may I ask why is this required? It seems to me that I can still use the same secret ...
1 vote
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### in Homomorphic Encryption Standard, why in the LWE increasing security level yields smaller ciphertext?

I am currently reading Homomorphic Encryption Standard. May I ask that for table 1 in the link, why increasing the security level will yield a smaller ciphertext size (log q)? I attach a screenshot ...
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### [About choosing params in BGV like ciphertexts]

I am new to lattice-based cryptography, so sorry that this question might seems stupid May I ask that how can I choose the BGV parameter of ciphertext with plain text in mod 128, and error in ...
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### Question about the bootstrap of BFV

The description of bootstrapping in Section 5 of the BFV paper (https://eprint.iacr.org/2012/144) is somewhat challenging to grasp, and I have two specific questions: The author mentions that if the ...
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### Approximate-GCD problem in polynomials

I am trying to understand the two main hard problems that have been explored in the context of homomorphic encryption: Learning with Errors Problem (LWE) and the Approximate-GCD (AGCD) problem. I have ...
1 vote
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### About multiply by constant of LWE

I am new to lattice-based cryptography May I ask that for a lattice-based encryption $$enc(m) = A^{T}R+m \bmod q$$ If I set the $q$ to be able to decrypt to $m$ (and suppose the bound of $q$ is tight ...
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### Metrics for difference/error of output and ideally output

I'm working in some homomorphic encryption for my Ph.D. but I'm not of the field... So I'm possible going to ask a really simple question that I'm struggling to find an answer on the internet. ...
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### Noise of Public Key Ciphertexts in HElib

I would like to get a feeling on how the noise develops in different FHE schemes. So I ran some experiments using HElib for both BGV and CKKS. I wanted to look at the noise of a fresh public key and a ...
112 views

### Statistics-heavy crypto papers

I'm currently taking a course in which we choose a stats-heavy paper and analyse it, summarising our work in the form of a written report and presentation. I have tried to find such a paper in crypto, ...
1 vote
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### Does exist an Elliptic analogue of Benaloh encryption scheme?

The definition of Benaloh encryption scheme can be found here. Does exist an elliptic analogue of this scheme? I want to use this scheme but the length of the key ...
1 vote
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### How does the key generation of a homomorphic secret-sharing protocol works?

I am new to cryptography and do not have sufficient background knowledge, and I am sorry for any possible vagueness in my question. I am reading a paper (https://eprint.iacr.org/2019/129.pdf) about ...
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### What is the meaning of X is of order 2N in blind rotation of TFHE?

Could anyone please help me explain this? I am reading the article about TFHE (Guide to Fully Homomorphic Encryption over the [Discretized] Torus). On page 31: I don't understand why we need to scale ...
1 vote
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### Orthogonal Lock

Is there a cryptographic function that employs two locks: first 'Lock A', and then on top of that 'Lock B' but it permits unlocking 'Lock A' before 'Lock B' to read the message?
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### Is it possible to perform an unlimited amount of multiplications on the same ciphertext in fully homomorphic encryption?

I am currently playing around with some of the Python FHE libraries and found out that, e.g. TenSeal (SEAL) is able to perform "only" 8 ciphertext-ciphertext multiplications on the same ...
1 vote
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### Homomorphic Encryption CKKS scheme, Encoding: canonical embeding discretization

I'm trying to understand CKKS (non bootstrappable) and I'm struggling with the encoding part. I'm using the original paper , "Homomorphic Encryption for Arithmetic of Approximate Numbers ", ...
1 vote