# Tagged Questions

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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### identifying presence of encryption of zero in additive homomorphic encryption

Lets say the server has corpus of ciphertext contains $enc(a),enc(b),enc(c), \dotsc enc(x)$. The encryption function is an additive homomorphic scheme (like Paillier). The server knows only the public ...
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### paradox on fully homomorphic equality checking

Imagine, a client encrypts a corpus of data (say documents of text) with the public key of a Fully Homomorphic Encryption scheme (FHE) and outsources the data to an untrusted server.Now the client ...
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### Equality checking using additive homomorphic encryption

Given two ciphertexts $c_1 = enc(p_1)$ and $c_2= enc(p_2)$ using any additive homomorphic encryption scheme (or specifically Paillier). Can we find out whether the underlying plaintexts $p_1,p_2$ ...
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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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### Additive homomorphic encryption over small fields

Are there encryption schemes that are additively homomorphic with respect to small fields such as $\mathbb{F}_{2^4}$ or $\mathbb{F}_{2^8}$?
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### Generating random vector for Full Homomorphic Cryptography

The site below explains that part of doing homomorphic encryption, you need to generate a vector of random numbers that have the property that its dot product against a randomly generated bit vector ...
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### Practical multivariate quadratic FHE โ how does it compare to other FHEs?

Came across this startup claiming practical FHE and then their blog post going into some additional details on it. It was my understanding that practical FHE is still years/decades off. They said ...
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### Comparison on Ciphertext with Helib

Is it possible to do a greater than homomorphic comparison in the form ($c_1 < c_2$) on two ciphertexts using Helib? The equal comparison ($c_1 == c_2$) can be done in modulus 2 by adding both ...
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### Sorting over encrypted data with different symmetric keys

I'm working on a security project. I need to perform a sorting on the lists of encrypted integers and strings. The encryption used is symmetric. The clients send the encrypted data in a list to the ...
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### Homomorphic multiplication by a scalar

Few homomorphic encryption schemes like Paillier , Ring-LWE support homomorphic multiplication operation by a scalar apart from additive homomorphic property. Loosely they could be defined as below ...
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### Additive ElGamal cryptosystem using a finite field

I'm trying to implement a modified version of the ElGamal cryptosystem as specified by Cramer et al. in "A secure and optimally efficient multi-authority election scheme", which possesses additive ...
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### Can we do modulus switching for number theoretic encryption?

Can we do modulus switching for number theoretic encryption such as Paillier or ElGamal?
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### How to find the value of a vector modulo a basis in lattice-based cryptography

In Gentry's paper on fully homomorphic encryption using ideal lattices, he finds the values of vectors modulo a certain basis. For instance: $\psi \leftarrow \psi' \mod B$ Taken from page 69 of ...
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### About BGV Scheme Batching Technique

I am reading BGV12 about BGV homomorphic scheme right now.But I am being stuck to understand Batching technique in this paper. In Pack function (page 32),this paper feeds ciphertext $c_i$ and sk $s_1$...
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### Analysis of DGHV Security

I want to know how security of DGHV can be breached using oracle and Binary GCD. As I study this paper : Fully Homomorphic Encryption over the Integers But I am not able to understand Section 4.1: ...
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### What would be a typical value for the security parameter of the Fully Homomorphic Encryption over the Integers scheme?

The parameters of the Fully Homomorphic Encryption scheme by Dijk et.al are chosen according to the value of the security parameter ${\lambda}$, section 3 of the aforementioned article. What is the ...
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### Are there simpler FHE methods than Craig Gentry's original paper?

Craig Gentry's 2010 paper on FHE is very cool, and I'm planning on implementing a basic proof of concept FHE. I was wondering though, are there any simpler methods that have been discovered since ...
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### Can the Smart-Vercauteren Homomorphic Encryption be implemented as a practical fully homomorphic encryption scheme?

Smart and Vercauteren proposed a homomorphic encryption scheme (PKC 2010) following Gentry's principles. โ Though their scheme can achieve fully homomorphism theoretically, they admitted that "for ...
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### Quantifying bit security for smart-vercauteren encryption scheme

I am working on project that requires to compare in terms of security between two encryption schemes, one of them is the SV scheme. However, I dont know what are the steps exactly towards quantifying ...
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### How do voters verify a Helios (v3) election result?

So from my understanding of verification specification version 3, a Helios election proceeds as follows: A voter retrieves the system's public key to encrypt their vote & submit it. The voter ...
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### How to Perform Computation on AES Encrypted Data

I have this code that successfully performs symmetric encryption using AES algorithm. How can I go about performing computation on it to achieve somewhat homomorphic encryption? ...
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### How to prove hardness of approximate-GCD problem?

I am trying to prove the security of my system using the hardness assumption of the approximate-GCD problem using contradiction, i.e. If the attacker is able to break in our scheme, then attacker ...
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### Beavers Triple Vs BGW Multiplication on MPC

Typically MPC protocols that are secure against semi-honest adversaries recommend the use of the revised GMW multiplication protocol by Gennaro et al. This is not the case against Active adversaries ...
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### Confusion about definition of homomorphic encryption

I am trying to better understand homomorphic encryption, but I feel like I keep getting inconsistent information in the papers that I am reading. One of the papers I am reading says the following: ...
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### How does order-preserving encryption work on string?

I have read โHow does order-preserving encryption work?โ. After that, I completed order-preserving encryption on integer data. Now, I have four questions in this subject: Is it possible to apply ...
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### Homomorphic Encryption with Addition and Exponentiation

Is there any homomorphic encryption scheme which supports addition and power over cipher text ? Paillier is close but it supports addition and multiplication with a constant. I am getting an output ...
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### Scalability of homomorphic tallying

Whenever I look at online voting schemes, the idea of homomorphic encryption being a key concept, specially in the form of homomorphic tallying, appears to be universally accepted. The accepted answer ...
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### How to make the range of modulo $p$ to $[-\frac{p}{2};\frac{p}{2}]$?

I am using NTL (A Library for doing Number Theory) to implement a FHE (Fully Homomorphic Encryption) scheme. In general, the range of modulo p is $[-\frac{p}{2};\frac{p}{2}]$ in FHE scheme. However, ...
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### Performance of Fully homomorphic encryption VS Paillier encryption in Practice

Consider two schemes both have computation complexity linear to the input size (i.e. number of inputs). One scheme is based on Paillier encryption and the other one is based on fully homomorphic ...
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### Why doesn't this operation reveal the voter's message?

I am working my way through this paper. I am trying to figure out the OR zero knowledge proof in figure 2. The prover is verifying that she has correctly voted, and that her input satisfies \log_gx=\...
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