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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239 views

How to define a FHE scheme whose plaintext space is infinite using boolean circuits?

There are many kinds of fully homomorphic encryption scheme by using boolean circuits. And the plaintext space $\mathcal{P} = \{ 0,1 \}$. If there is a -bit FHE scheme, we can construct a FHE scheme ...
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Is there some function of $n$ that is a multiple of $\phi(n^2)$?

Not sure which forum to post this question so here is a link to it from MSE. This is to adapt the approach of Fermat's Little Theorem to the Paillier encryption system. I understand that this will ...
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74 views

Does asymmetric order-preserving encryption exist?

As I understand from this post, mapping from plaintext space to ciphertext space is the fundamental point of all order-preserving encryption. So the only way that we let someone encrypt an arbitrary ...
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Advantages of Paillier vs Goldwasser-Micali

It is easy to see that both Paillier and Goldwasser-Micali are homomorphic addition schemes and are secure, but what would be the advantages of choosing one over the other?
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SS/HE/GC/OT secure integer comparison

I have been reading some papers to find a 'faster' way to compare two integers without revealing their real values. But I think I'm a bit lost in those papers due to my limited knowledge in ...
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FHE over the integers - Is that paper's scheme known to be insecure against quantum adversaries?

I was reading the paper Fully Homomorphic Encryption over the Integers, and started wondering if there is a known quantum attack on their main scheme, because There is an efficient quantum attack on ...
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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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167 views

zeroing out slots in SEAL ciphertext

I've been messing around with SEAL library for a few days and I've got a following question. I've got a bunch of datapoints [x_1, ..., x_n], n < poly_mod_deg of type 'double' and I use batch ...
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Simple question about BGV scheme

While I'm trying to implement BGV scheme myself, I found that I'm really confusing about the encryption and decryption of the scheme. Here's my understanding: Let $p$ be a plaintext modulus and $q$ be ...
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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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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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SEAL-CKKS max multiplication depth

I am trying to understand how SEAL-CKKS scheme works and I wonder what multiplication level can we achieve using this scheme? Like 100 possible?
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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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1answer
137 views

Verification of data on an untrusted remote storage server

I was looking at tahoe-lafs which accepts a file, encrypts it, does erasure coding on it which generates n shares and then distributes it over the storage servers. The distribution is Share 1 = Server ...
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How does bootstrapping work?

I have read FHE lately. In Fully Homomorphic encryption using ideal lattice[Gen09], I noticed his recrypt algorithms: We have a ciphertext $\phi_1$ which is encrypted by public key $pk_1$, and can be ...
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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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Homomorphic encryption key switching

I understand the general idea of key switching, but I would like to know when it is used. Sometimes it is referred to as same thing as relinearisation(after multiplication), but is key switching also ...
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1answer
149 views

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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1answer
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Bitwise operations in FHE

Im reading about FHE and the libraries implementing it (SEAL, HELib). I saw that SEAL doesn't support bitwise operations but I wondered if its theoretically feasible. For example, bitwise-ing XOR an ...
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RLWE like problem

Assume we have the polynomial space $R_q$ defined as $R_q = Z_q/(X^n + 1)$. Additionally, we define the error distribution $\chi$ as a discrete centred Gaussian bounded by $B$. Let $s \gets R_q$ be a ...
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An implementation about multi thread TFHE

recently I'm trying to use TFHE library for project(https://tfhe.github.io/tfhe/). In order to accelerate the whole program, I use pthread to make multi thread computation. However, I find that the ...
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Joint distribution of RLWE samples

Assume we have the polynomial space $R_q$ defined as $R_q = Z_q/(X^n + 1)$. We draw samples $s_i \gets R_q$ uniformly at random. Additionally, we define the error distribution $\chi$ as a discrete ...
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Role of AND operation in FHE, MPC and ZK

Going through LowMC, one of the main advantage of it seems to be useful in Fully Homomorphic Encryption (FHE), Multi-party Computation (MPC) and Zero Knowledge (ZK) proofs. I have no idea about any of ...
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Proving the security of the public key BGV scheme

The security proof basically comes down to the following based on this paper. We want to show that two distributions are statistically indistinguishable. Say we have that $a,a′,x,x′$ are drawn from an ...
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Why is Approximate GCD a hard problem?

There are many Fully Homomorphic Encryption over the Integers schemes whose security is based on the intractability of the Approximate GCD (AGCD) problem. The paper Algorithms for the Approximate ...
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Can I alter encrypted data without decrypting it? [duplicate]

I didn't find a direct solution for it. Can I modify encrypted data without accessing it? If there is an example, I would appreciate it.
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CKKS : Ciphertext extension

I have a CKKS ciphertext containing [a, b, c, d] and I want to get these 4 ciphertexts : [a, a, a, a]; [b, b, b, b]; [c, c, c, c]; [d, d, d, d]. Is there a more efficient way than repeating the ...
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1answer
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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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1answer
139 views

Gentry-Halevi’s Fully-Homomorphic Encryption and hermite factor

In section 7.2, page 18 in Chen-Nguyen paper regarding BKZ 2.0, they point out different Hermite factors related to Gentry-Halevi FHE. More precisely, it is said that the critical Hermite factor for ...
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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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What is the evaluation step in an HE scheme? [duplicate]

I quote: By homomorphic encryption, we mean the family of encryption schemes being able to perform homomorphic operations on ciphertexts, without decrypting them. The first time someone introduced ...
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Palisade: EvalMult between plaintext and ciphertext resulting in tower size mismatch

I hope someone can help me understand an error I get when using Palisades. I want to only use the first 329 slots of a BGV ciphertext, and zero out the rest (which at some point contains some '...
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1answer
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How to understand why an algorithm uses additive or multiplicative homomorphic

If we take the example of LWE (Learning With Errors) how does one know if it's homomorphic by addition or multiplication?
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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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Comparison of SNARK-friendly hash algorithms MiMC7, Poseidon, Pederson?

There are some cryptographically secure hash algorithms designed to be efficient for SNARKs, STARKs and FHE. Some of them already implemented in Zcash, Zokrates and circom. The ones that I know of are:...
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1answer
35 views

Paillier estimate attack costs on short keys

I was thinking about how to use the homeomorphic property of that cryptosystem to achieve not a "semantic security" but a less ambitous obfuscation of the source code (an ipotetical scenario ...
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2answers
178 views

How to get exact number of slots in HElib? Such as 256, 4096

In the Homomorphic Encryption Library, HElib (https://github.com/homenc/HElib), we set up a set of parameters before generating the ciphertext. For example: ...
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1answer
53 views

AES (or otherwise): can you decrypt concatenated encrypted messages as one?

Say I have 20 distinct encrypted messages. Using AES, I am only getting the correct output if I decrypt each of the 20 messages individually. Is it possible using AES or another method to call my ...
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Secret key generation in the BGV scheme in HElib

This question is about secret key generation, based on section 4.7 in the design document: https://homenc.github.io/HElib/documentation/Design_Document/HElib-design.pdf It seems that if $m$ is not a ...
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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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1answer
253 views

Is there any way to check hash of homomorphic encrypted data?

I need some algorithm that satisfies: H - hash function Enc - encryption function (using public key) M - secret data $Enc(H(M)) = H(Enc(M))$ Let this system exist: the First person has a secret ...
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1answer
124 views

What's the difficulty of using elliptic curves to design homomorphic encryption protocols?

I have recently been very interested in elliptic curves because they are a powerful tool in crypto, ECC, pairing, etc. However, it seems that elliptic curves are not popular in homomorphic encryption. ...
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448 views

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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1answer
48 views

What is the difference between Paillier additive homomorphic property and addition of two paillier ciphers

Paillier has additive homomorphic property that states: if two ciphers c1 and c2, are multiplied, and the result is decrypted, it is equal to addition of the two plaintexts. D(c1*c2)= m1+m2 ...
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35 views

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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1answer
101 views

How expensive would running a practical application on full homomorphic encryption be?

This is a multidisciplinary question, hopefully I can stay on topic. It has been published that we can now use (try?) fully homomorphic encryption computation on cipher text inputs. But I'd like to ...

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