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 break fully homomorphic encryption over integer algorithm with known cipher of same integer?

If I do encryption and decryption like this: Encryption: $\text{E}(m) = (r \times p_1+m) \bmod N$ Decryption: $\text{D}(\text{E}(m)) = ((r \times p_1 + m) \bmod N) \bmod p_1 = m$ where, $r$ = ...
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SEAL - binary encoded ciphertext

In SEAL, am I able to convert a ciphertext that is encoded with polynomial to a ciphertext that is encoded as binary?
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Cryptographic Counter

Good morning, I state that I am not an expert in cryptography. I'm studying the feasibility of a project which looks like requires a kind of cryptographic counter that behave similarly to the one in ...
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Legendre conditions on the factors of the fundamental negative discriminant to minimize the 2-Sylow subgroup of the class group

If we know the prime factorisation of the fundamental negative discriminant $\Delta_K$, say $\Delta_K=p_1\cdot p_2 \cdots p_n$, then we are guaranteed that at least $2^{n-1}\mid h_K$, the class number ...
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Turn a homomorphic encryption scheme into one that doesn't have the homomorphic property

Homomorphic encryption is a form of encryption that allows computation on cipher-texts, generating an encrypted result which, when decrypted, matches the result of the operations as if they had been ...
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Are software solutions such as FHE, PHE, Garbled Circuits used in practice?

Is Fully Homomorphic Encryption or Partially Homomorphic Encryption or Garbled Circuits used in practice? Or is an alternative used instead (I don't mean encryption just for storage here)?
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Example of an attack on a message exchange which uses the homomorphic property

Can someone give me an example of an attack on a message exchange using this encryption scheme, that uses the homomorphic property? In my opinion, Existential forgery under directed message attack ...
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Security of certain homomorphic encryption scheme

Is the following homomorphic encryption scheme: Ahmed El-Yahyaoui and Mohamed Dafir Ech-Chrif El Kettani, A Verifiable Fully Homomorphic Encryption Scheme for Cloud Computing Security (April 2018, at ...
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Additive homomorphic secret sharing

I am new to cryptography esp, homomorphic encryption. I would like to know if the following is possible using something similiar to additive homomorphic secret sharing. Please apologize me if its too ...
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Homomorphic encryption - addition for more than two parties

I have just found out about the homomorphic encryption and I was wondering how is it possible to perform an addition for more than two parties? More concretely, I want to have several parties $P_i$, ...
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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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Effect of small secret attacks on non homomorphic encryption schemes

The new paper by Albrecht describes a new attack on "unusually" small secrets that are used in homomorphic encryption schemes. In the paper the talk about binary secrets or LWE Normal form i.e $\...
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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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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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How to implement automorphisms technique in SEAL?

In the SEAL homomorphic encryption library, no automorphisms technique to move values between the different slots in a given plaintext vector is provided. How could this technique be implemented in ...
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Homomorphic encryption and approximated GCD 2

This is a further question to the one reached here Homomorphic encryption and approximated GCD. I am now thinking about a symmetric cipher in which the plaintext set is integers, illustrated as ...
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Is it necesary to introduce noise in building fully homomorphic encryption?

Is it necesary to introduce noise in building fully homomorphic encryption? At present, almost all formally published FHE schemes are based on noisy approach. However, there are some noise-free FHE ...
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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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Can a number be encrypted, added to other numbers, and then the sum decrypted?

I imagine there is a class of algorithms for this, but I don't know the name to google for more info. To describe the desired behavior: ...
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Homomorphic Obfuscation vs Fully Homomorphic Encryption?

Let's say that we want an untrusted person do to a calculation on a 32 bit floating point number and send us back the result, without learning what the specific number was that we care about. For the ...
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How to generate 1000 prime number of 1024-bit with much less time?

I am generating thousand prime number of 1024 bit each. But it takes lots of time. My procedure is as follows. Generate prime number using ...
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Why need mapping to slots to embed bytes in AES-homomorphic encryption?

The encoding of each AES bytes $𝛼_𝑖$ is using CRT(Chinese remainder theorem). It means that there is an aggregate plaintext $H$ such that: $H \mod F_0 =𝛼_0(MappingData[0])$ $H \mod F_1 =𝛼_1(...
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Partially homomorphic addition - not all parties present

I often see homomorphic encryption as a solution to a problem where a server wants to know the sum of $n$ users' numbers but can not know each individual users' number plaintexts. My question is: if ...
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Example of FHEI scheme?

I am reading this paper Toward Secure Multikeyword Top-k Retrieval over Encrypted Cloud Data. I am trying to work out an example of the FHEI (Fully homomorphic Encryption over Integers) scheme ...
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How to generate public key for ATV-FHE scheme?

I want to implement the ATV-FHE scheme as it is described here https://eprint.iacr.org/2014/039.pdf. How to generate the public key? Should I compute it as indicated in section 2 : $h(i) = 2g(i)*[...
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Obliviously computing the Least common multiple of two poylnomials

Consider I have two polynomials $f_1$ and $f_2$ of the same degree. I want to secure them (using any kind of encryption except FHE) and outsource them to an untrusted server. I want him to compute the ...
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Privacy-Preserving Protocols and Proofs of Security

While dabbling in privacy-preserving protocols (mainly using Semi-Homomorphic Encryption) and coming up with miscellaneous ideas for comparison tests or other similar primitives, based on obfuscation ...
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What scheme will allow merging and splitting the result of a function?

I am wondering if it's possible to have a scheme as follows. Here is the scenario: we have a set of objects (e.g. strings) {O1, O2, ..., On} we have a set of users {U1, U2, ..., Um} each user asks ...
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For a given security parameter $\kappa$. what does $poly(\kappa)$ mean?

Let ($Gen,Enc,Dec$) be an LHE scheme with security parameter $\kappa$ and message space $M$. Assume that a multiplication operation exists in $M$, i.e., is a finite ring. Let $F : \{0, 1\}^s × L → M$ ...
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HElib: send sk and pk to another party for decryption and encryption

This question is about the serialization of pk, sk, and context in HElib. In my scenario, ...
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How to understand the per-gate computation overhead of the FHE scheme?

In BGV12(Fully Homomorphic Encryption without bootstapping), they investigate the efficiency of a FHE scheme by considering the per-gate computation overhead of the FHE scheme, defined as the ratio ...
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What's the performance of the HElib and SEAL?

HElib contains the CKKS and BGV, SEAL contains the BFV and CKKS, is there some concrete performance data about these two lib?
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Is it possible to allow a user to log in if logged out without identifying them?

I have to verify that the user has registered and is currently logged out without identifying the user. Essentially, I am looking for privacy-oriented authorization mechanisms which prevent ...
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How to know the exact result in Paillier chiper-costant multiplication

The encryption function $E_{k^+}: Z_n \rightarrow Z_{n^2}$. The decryption function $D_{k^-}: Z_{n^2} \rightarrow Z_n$. $m_1 = 42, k = 15, n=77$. After encryption, exponentiation and decryption, I get:...
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Rotation with redundant slots in HElib

As described in another question How to get exact number of slots in HElib?, get the exact number of slots with relative small parameters m and ...
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A question about HElib again

Sorry but I've got a question about HElib again. I'm applying HElib to make a secure logical calculation and I apply bootstrapping as usual. Paras I selected was from "example". However, ...
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How to save keys and other paras in HElib

Recently I'm using HElib for project. Here I hope to init a Client-class,which has pub&pri keys. However when I was building class, I found that I don't know how to save Keys and other paras like ...
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Why doesn't HElib support floating point operations?

NB: what I meant is with implementation of the BGV-cryptosystem, not the CKKS cryptosystem which is designed with floating point arithmetic in mind. HElib as I understand it only supports fixed-point ...
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Why is noise growth from relinearisation ignored in the FV crypto scheme?

I'm going through the FV scheme and SEAL and there are a couple of things I'm not understanding with respect to noise growth of relinearisation. On page 8 they say to choose T so that the noise ...
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How to fix the IND-CPA+ problem in CKKS?

In paper On the Security of Homomorphic Encryption on Approximate Numbers the author gave an attack on CKKS, then how to fix it?
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What distribution is required to ensure the security of the RLWE?

In LWE, the error should be sampled from a discrete Gaussian distribution. Then, in RLWE, the error is a polynomial in $\mathbb{Z}_q[x]/(x^N+1)$, it could be sampled coefficient wise. However, when we ...
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Practicality of dangerous/unsafe content safety proof as follows

Suppose I am building a cloud storage with client side encryption. My policy is that I would not allow anyone to store pornographic, violent or otherwise unsafe content but must ensure full privacy. ...
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PYFHEL - Concatenating two encrypted strings and then decoding them

I'm trying out the PYFHEL (PYthon For Homomorphic Encryption Libraries) library, and was wondering if it was possible to concatenate two strings while encrypted and then decrypt the result. This ...
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Could FHE scheme like BGV could be used many times, or fully homomorphic encryption could be used continuously?

Currently I was working with FHE scheme and used HElib to do homomorphic logical operation like the formal question described Homomorphic encryption methods that could support logical XOR, AND?. But ...
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What does the “scale invariant” mean in some FHE schemes?

In some paper about FHE, the term "scale invariant" often appears. What does it means?
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Why are the fully homomorphic encryption algorithms the commitment?

Is there some references about the commitment scheme based on FHE ? Why could the BFV, CKKS, BGV algorithm be convert to commitment? How ?
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FHE Bootstrapping in FV12

I am trying to understand the bootstrapping step in FV12 cipher to obtain the FHE. I know the basic idea of bootstrapping is to homomorphic calculate decryption on ciphertext to obtain new equivalent ...
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Is the BFV homomorphic encryption scheme a commitment scheme?

The BFV scheme can be described as: Public Key: $(p_0, p_1)$ To encrypt a plaintext $m$, the ciphertext is : $(c_0, c_1) , c_0= up_0+\Delta m + e_0, c_1=up_1 + e_1$