# 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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### Floating Point Homomorphic Encryption Schemes

Are there any homomorphic schemes that can homomorphically compute addition and/or multiplication of encrypted floating Point data?
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### Isn't fully homomorphic encryption trivial with a complex enough decryption function?

Consider the following exchange: Alice has some plaintext $x$. She sends the encrypted version $\mathcal E(x)$ to Bob. Bob returns $(\mathcal E(x), T)$, where $T$ is a turing machine encoding the ...
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### How can we add real values using GF field?

In GF($2^4$) usinfg primitive polynomial g(x) = $x^4 + x^3 +1$, 2+3 = 1 since 010 + 011 = 001, 2 + 2 = 0 Is there any encoding to get 2 + 3 = 5 and 2 + 2 = 4 in GF.
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### NTRU homomorphic rerandomization

I am currently implementing NTRU, keeping its homomorphic properties. I want to implement rerandomization like this: Encryption: $e = pr * h + m \pmod q$ Rerandomization: $e = e + pr \pmod q$ (...
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### Homomorphic Evaluation of Pseudo Random Function

I'm looking for a special Pseudo Random Function (PRF) $F_k()$ which follows the below. For fully homomorphic encryption (FHE), $\mathit{FHE}(F_k(x)) = F_k(\mathit{FHE}(x))$. Or is there any ...
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### Semantic security IND-CPA of Affine Hill Cipher

The ciphertext,c corresponding to plaintext,m is given by c= mK + w, K is the invertible matrix and w is the uniformly distributed random vector. If w is changed during every encryption, will this ...
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### Sign a plaintext accepted by a secure function without revealing private key

Imagine the following scenario: Alice is a well-respected chef. She is famous for reviewing recipes. Anyone can send her a recipe. If she likes it she'll add her famous line of approval to the end: "...
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### Zero knowledge proof for Paillier addition under multiple keys

Suppose $m_0, m_1, m_2 \in \mathbb{N}$ such that $m_0 = m_1 + m_2$, $m_i > 0$ (none of them can be 0 or lower) Under a Paillier cryptosystem, set $e_0 = E(m_0, r_0)$ for a public key $(g_0, n_0)$ ...
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### Decrypt (homomorphically and symmetrically) encrypted data using (homomorphically) encrypted key?

Is it possible to do the following? Generate symmetric key $K$ Encrypt data $D$ with the symmetric key : $E_k{(D)}$ Encrypt the symmetric key and the encrypted data using homomorphic encryption ...
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### Is there an application of fully homomorphic encryption scheme such that encryption key and evaluation key are different?

I want know if there is an application of FHE contains three kinds of users such that: $A$ is the data owner and she has the secret key. $B$ only has the permissions to encrypt (just like a general ...
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### Paillier Homomorphic encryption to calculate the means

Paillier Homomorphic encryption supports addition and multiplication with plaintext value. Can I use these properties to calculate the means of cipher-text values? I try to use the following steps: ...
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### Partially Homomorphic Cryptographic Schemes - Deterministic vs Probabilistic

While reading this paper I realized that textbook RSA was the only deterministic PHE scheme mentioned. I did cross-check the ones listed in the Wikipedia article also and, quite on the opposite ...
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### In Paillier homomorphic encryption, do we need to take modulo after multiplication of 2 ciphertexts?

The multiplication of 2 ciphertexts generated using Paillier encryption will result in encryption of sum of corresponding plaintexts. I need to do a linear combination operation of N integers in ...
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### NTRU-based threshold encryption system?

I want to implement threshold homomorphic encryption for my project. (encrypt a message using one public key, and decrypt a ciphertext using distributed secret keys) I read a paper "Multiparty ...
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### How does fully homomorphic encryption compare to partially homomorphic encryption in terms of security?

I found some questions and answers about the performance of Fully and Partially homomorphic encryption. I am interested in a comparison in terms of security guarantees (of any kind, formal or informal)...
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### Computing Logarithm using homomorphic encryption

Let's say we have $Enc_{pub}(a)$, the encryption of an integer $a \in \mathbb{Z}^*$ under the public key pub with a Homomorphic encryption scheme that supports both ...
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### What's the advantage of branching program? Why we use branching program to compute the encrypted data?

Branching program is one type of NC1 circuit and can be used to compute encrypted data. So whether there exist other methods in the NC1 circuit to compute encrypted data. What's the advantage of ...
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### Why use Phi(m) divide Order(p, m) to get slot number in HElib?

I am reading HElib source code, and have a confusion about FindM function: ...
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### Is there a public key encryption for permutations which is homomorphic under permutation composition?

I'm brainstorming an idea for extending our Latin square autotopism secret sharing scheme (proposed here [open access]) to a repairable scheme. I seek a cryptographic method, which may or may not ...
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### Is modulus switching feasible for plaintext space larger than $\{ 0, 1 \}$?

I read the proof of modulus switching and realised that it can be extended to integers, but do we actually use it for integer encryption in practice? Consider that we are doing additive and ...
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### A practical algorithm for proof of age

I'm new to the list, a layman in cryptography, but a competent programmer. Seeking your help for a practical algorithm that I can implement please. Problem Let a prover ...
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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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### Does Paillier Homomorphic Encryption Work only with numbers?

Paillier homomorphic encryption enables us to combine two messages such as $D\left(E(m_1,r_1) \cdot E(m_2,r_2) \mod n^2\right) = m_1+m_2 \mod n$ My question is what are the specification of $m_1$ ...
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### How to provide security against malicious adversary in Ring LWE homomorphic encryption scheme?

I was reading Ring LWE homomorphic encryption scheme referred in http://www.wisdom.weizmann.ac.il/~zvikab/localpapers/IdealHom.pdf But this encryption scheme provides security mostly in the semi-...
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### Demystifying homomorphic multiplication in RNS FV variant

I am trying to understand a full RNS FV SWHE variant proposed in this paper. My problem is with the homomorphic multiplication. Original ciphertexts are represented in RNS representation using base (...
I have a similar question to this one: Is an equality test possible when using paillier crypto? However I want to do the following: Given the Paillier Cryptosystem. Given the function $f(input)$, ...