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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Can the hash of the ciphertext be derived from the hash of the plaintext

Let $C$ be a symmetric cipher $H$ a hash function. Alice uses $C$ with a key $k$ to encrypt plaintext message $m$ yielding ciphertext $c$. She then calculates the hash of the message $h_m = H(m)$ and ...
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How to count the number of selected element in each slot within the packed ciphertext

Given an encrypted ciphertext (n slots, packed n elements into a single ciphertext), such as 𝑐𝑡={(2,0,1,2),(3,2,1,3),(3,4,0,4),(5,1,4,2)}. Formally, 𝑛 slots can be expressed as 𝑚 blocks, each ...
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CRT decomposition in NTT for BFV

AS explained in section 4.5, decomposition for relinearization (2nd step of ciphertext multiplication in bfv) can be done using RNS components of ciphertext. In other words, they proposed a way to do ...
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Decrypting message as MSB in regev scheme

I was watching this FHE video and it define Regev encryption scheme as fallow : kyegen: sk : choose $t = (1,s)^t \in \mathbb{Z}_q^{n+1}$ pk = $A \in \mathbb{Z}_q^{m*(n+1)}$ random except $[A * t]_q$ ...
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How to generate a collinear point without revealing one of the existed two points?

Assume we have point $A(x_A,y_A)$ and point $B(x_B,y_B)$, and now we want to generate a point $C(x_C,y_C)$ so that $A,B,C$ are on the same straight line. All mod $p$. If $A$ or $B$ could not be ...
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Can I alter encrypted data without decrypting it?

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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cascade encryption - If I encrypt my data using many different encryption algorithms

If I encrypt my data using many different encryption algorithms (using different passwords) how will an adversary be able to decipher the message?
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How is a NAND gate constructed from just addition and (mixed) multiplication in a FHE circuit? [duplicate]

From what I've read I know that FHE requires "circuits" to construct functions and gates to operate on the FHE encrypted data. I've also read that these circuits are constructed from just ...
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Using two or more encryption algorithms together, how do we compute the strength of the final encryption?

If two or more encryption algorithms are used together, how do we compute the strength of the final encryption? And how would the application perform against quantum computers? The first two tables ...
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Homomorphic encryption watermarking identity

I've been doing some research on FHE and SWHE schemes, most specifically on watermarking. As far as I've understood, you take as the merchant, take the buyer information encrypted and his public key ...
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Threshold Encryption Scheme for Multiple Messages

In a threshold encryption scheme, a dealer generates $(PK,SK1,…,SKn)$ and distributes the secret keys to users indexed by $1,…,n$, and if a combiner obtains $t+1$ partially-decrypted ciphertexts, it ...
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CKKS security estimation for Palisade

My question is rather practical and specific. I am trying to setup an efficient CKKS scheme in Palisade. To this end, the automatic choice for secure parameters has to be turned off and I rely on the ...
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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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What is batching in homomorphic encryption?

I have been reading journals about FHE schemes and I keep encountering the term "batching". What does it mean to batch in homomorphic encryption in a simple way?
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Autonomous homomorphic encryption

So, my understanding of homomorphic encryption is that Alice has a private key and an algorithm, gives an encrypted copy of the algorithm to Bob, Bob runs the algorithm without understanding it, and ...
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Zero knowledge proof of Paillier cryptosystem

I have read the paper recently and I am curious about part 3. According to part 3, Bob sends a zero-knowledge proof such that $c_B=b\times_{E}c_A+_E E_A(\beta')$. Then Alice should first decrypt the ...
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Predicting with a machine learning model while preserving the privacy

Imagine Alice has trained a machine learning model. She wants to store her model in a blockchain so that everyone can use it; however, she wants her model to be private so that no one can steal her ...
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can we know the sign of a ciphertext (homomorphic)

Is it possible to know the sign (positive or negative) of an homomorphic ciphertext particularly under paillier scheme ?
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What schemes support atomic decryption+reencryption

What encryption schemes support this workflow? Vendor encrypts and publishes information for the client Client generates public and private key Vendor encrypts private information Vendor publishes ...
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functional encryption over homomorphic encryption

I recently read about "functional encryption" which seems interesting, although I didn't understand yet how it works ... but is it possible to combine it or adapt it with homomorphic ...
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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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Are all homomorphic encryption schemes based on latticed-based schemes?

PALISADE offers a pool of Homomorphic Encryption schemes and it is stated that "PALISADE is a general lattice cryptography library ...". My question is rather simple: are all homomorphic ...
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Security analysis of encrypting a matrix after homomorphic encryption by the random mask

Problem Definition Alice has two private matrices $M_A$ ($N*M$), $M_a$, where $M_a$ is the binary matrix of $M_A$ Bob has a private matrix $M_B$($N*M$) Alice and Bob are semi-honest server and ...
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Is there anyone intrested in quantum fully homomorphic encryption?

Recently, I have read a paper named "Classical Homomorphic Encryption for Quantum Circuits". The author claims a quantum scheme that can apply an encrypted (like GSW encryption) bit to ...
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AES homomorphic updates

I am looking for some help regarding something I am trying to do and I think to solution might be in Homomorphic encryption. Person A and B encrypt the same number(unsinged long) N using AES with ...
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How many known plaintexts are required to break a system with this property?

Suppose we have an $n$ bit block cipher $E$ with a key $k$ that has the following property $$E(k; m_1⊕m_2) = E(k;m_1) ⊕E(k; m_2).$$ How many minimum number of chosen plaintexts are required to ...
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Is there a way to confirm that a homomorphic division (multiplication with inverse) using ElGamal produced the correct result?

By running some tests I observed that if I perform a homomorphic division (multiplication with the multiplicative inverse) between two values using the ElGamal scheme, I get the correct result when ...
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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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Proving LWE inversion in Micciancio-Peikert-2012 lattice trapdoors

I'm looking through the lattice trapdoor construction in https://eprint.iacr.org/2011/501. To summarize, assume we have a matrix $G$ where, on input $b$, we can efficiently find $(s,e)$ such that $s^...
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How to add ciphered numbers under benaloh's scheme?

In the answer for Is it possible to subtract/multiply numbers using homomorphic encryption? it says: To add two encrypted numbers, one could use Benaloh, Damgård–Jurik, or several other known ...
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Privacy preserving aggregation of encrypted data

I have the following problem: I have $t$ servers $S_1, S_2, S_3, \ldots, S_t$, each of them storing some $key : value$ list. They have to upload this data into a big dropbox server $D$, but in such a ...
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How can I use two different public keys with the same private key for fully homomorphic encryption?

I am pretty new to cryptography. Recently I run into this question where I have two different public keys with the same private key, and I need them for fully homomorphic encryption. Let's say ...
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What is the key generation and management process of a fully homomorphic encryption system?

I've been very interested in fully homomorphic encryption lately, and I understand the concept well enough, but there is one thing that I don't understand... What is the key creation and, more ...
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How is a non-interactive zero-knowlege proof constructed using homomorphic encryption?

I've been reading too much, and I still haven't found the explaination I so crave. I'm looking specifically at zk-SNARKs, as implemented by ZCash. They say they use homomorphic encryption in their non-...
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How is it that homomorphic encryption can encrypt program code and run it without decryption?

In my journey of interest in the world of homomorphic encryption has led me to a concept floating around the internet where they describe homomorphic encryption being used with "mobile agents&...
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The existing approaches based on machine learning for cryptography [closed]

i'm working on a paper about Machine learning and Deep Learning and i'm wondring about the uses of this domain in cryptography!! so what are these application of Ml that we use in cryptography and the ...
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Convert homomorphically encrypted decimal number to homomorphically encrypted binary number

I am trying to convert a homomorphically encrypted integer to a homomorphically encrypted binary number (in vector form like {Ciphertext(1),Ciphertext(1),Ciphertext(0),Ciphertext(1)}), which I cannot ...
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Is it possible to trim some encrypted values under fully homomorphic encryption

Suppose we have $N$ encrypted values under homomorphic encryption (BFV/BGV ..), and we know that $M$ of them are below $t$. Is it possible to remove those $M$ values? It is known that some methods (e....
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Can I use RSA as hash function?

My end goal is to have an encryption function $e$ and a hash function $H$ such that for all m we have: $$H(e(m)) = e(H(m))$$ This would work if we use RSA encryption along with RSA "hash", ...
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Homomorphic encryption scheme for modulo reduction

I want to know if there is any Homomorphic encryption scheme that supports modulo reduction, i.e., using $Enc_{pk}(m)$ and a public $w$ to compute $Enc_{pk}(m \mod w)$. Thank you.
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DES decryption of the homomorphic encryption ciphertext

I implemented an application using partial homomorphic encryption for outsourced computations. To get an efficient bandwidth, I am thinking to apply (DES) symmetric algorithm to encrypt the message ...
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Multiplication under different keys in BGV

I have a question about BGV homomorphic encryption. If we have ciphertexts c1 and c2 under the same key s, the tensor product c3 of c1 and c2 can be decrypted by the tensor product of s and s. If c1 ...
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Is there a way to change encryption scheme from AES to FHE without data leakage?

So let's say that we have encrypted some data using symmetric encryption in this case AES. And we want to change it to homomorphic encryption but without decrypting the data and encrypting it again ...
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Which are the current solutions to the illegal values in the homomorphic secret sharing?

There is a usual example about homomorphic secret sharing, focused on e-voting. Supposing we use Shamir's scheme for the Secret Sharing system, a participant generates a polynomial whose a0 is +1 (yes)...
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How to generate Multiple Encryption Keys for use in RSA polymorphic multiplication

I am a long time scroller, first time poster in the crypto stack. I've recently been finding myself leaving the realm of mainstream/standard crypto (imo that consists of symmetric/asymmetric ...
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Proof of lemma 1 Paillier encryption

In the original paper of Paillier, lemma 1 shows why $n$ must divide the order of $g$. What I don't understand in the proof of this lemma is why $g^{x_2-x_1}(y_2/y_1)^n$ implies $g^{\lambda(x_2-x_1)}$....
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Hash chain based secret revealing using homorphic princples?

I have recently been looking into Homomorphic encryption and I am looking for a specific hash-based encryption/decryption scheme. I don't need a full implementation but I am not sure if what I want ...
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Timing attacks on homomorphic encryption

I've been wondering for a long time about programs that could potentially break fully homomorphic encryption schemes: ...
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Implementing BFV Relinearization

I'm currently working on a Python implementation of the BFV[12] cryptosystem. I got to a point where key generation, encryption, addition and decryption works as expected. Where I'm struggling with ...
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Paillier scheme and noise growth

Does the problem of noise growth exist in the Paillier homomorphic scheme ?

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