Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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 *).

0
votes
0answers
42 views

MPC using homomorphic encryption

Is there a way to implement secure square root protocol between two parties (using homomorphic encryption)? I couldn't find existing solutions in literature. My desired protocol is as follows: ...
1
vote
1answer
53 views

How does the polynomial modulus work in the Fan-Vercauteren scheme?

I'm reading this introductory blog on the Fan-Vercauteren scheme and there are a few things I don't understand about polynomial moduli. The author uses practical examples: Because we are ...
0
votes
0answers
16 views

Are there protocols do Homomorphic cryptography set difference?

I am thinking of experimenting with a small voting system that allows users to delegate their votes to other users or retract them before they are counted. For this, I wanted to model users as a set ...
3
votes
0answers
43 views

Using error-correcting codes for the bootstrapping procedure of Fully Homomorphic Schemes

In the context of Fully Homomorphic Schemes, we use a technique called "bootstrapping" to refresh the ciphertext, by evaluating homomorphically the decryption circuit with an encrypted version of the ...
4
votes
1answer
434 views

Is there a way of maintaining malleability in a homomorphic encryption system while making it infeasible to perform chosen ciphertext attacks?

Is there a way of maintaining malleability in a homomorphic encryption system while making it infeasible to perform chosen ciphertext attacks? I have been reading about homomorphic encryption and ...
3
votes
0answers
68 views

Two plaintexts map to the same ciphertext in fully homomorphic encryption?

In standard symmetric encryption, we can create an encryption scheme, in which two plaintexts $x_1, x_2$ map to the same ciphertext $y$, by choosing appropriate keys $k_1,k_2$ (!). The most simple ...
2
votes
0answers
43 views

Is there a partially homomorphic cryptosystem without an inverse (addition without subtraction, multiplication without division)?

I am learning about partially homomorphic cryptography, and was interested to see if there was a system such that one operation was homomorphic, but its inverse was not. For example, if I have two ...
9
votes
3answers
2k views

Re-encrypting a message and proving that the message has not changed

Is there a method that allows for re-encryption of a message in a way that allows observers who only have access to the two cipher texts to prove that the plain text message is the same in each? More ...
1
vote
1answer
91 views

Interactive Homomorphic Encryption

Let's say that I have a plain computational process that consists of several divisions and I do not want to do it with non-interactive homomorphic encryption. I would like to ask how can I call this ...
2
votes
2answers
78 views

Homomorphic properties of Paillier

I'm curious about the homomorphic properties of Paillier. So, basically if I have $\textsf{Dec}(\textsf{sk}, \textsf{Enc}(\textsf{pk}, \alpha) \cdot \textsf{Enc}(\textsf{pk}, \alpha^{-1}))$, I will ...
0
votes
1answer
56 views

Binary representation of the inverse of a big number [closed]

In one of the first FHE schemes by Gentry, the KeyGen algorithm is defined as follow: For a security parameter $\lambda$, set $N = \lambda ^ 2, P = \lambda ^ 2, Q = \lambda ^ 5$. KeyGen$(\lambda)$: ...
6
votes
1answer
118 views

Representing a function as FHE circuit

I am actually trying to study homomorphic encryption (on lattices) but I'm facing a problem. Every paper that I have read so far talk about writing the function to evaluate on ciphertexts as a circuit,...
1
vote
0answers
49 views

How HomNAND has been computed in Leo Ducas and Daniele Micciancio's FHEW?

In section 4.1 of Leo Ducas and Daniele Micciancio's paper FHE Bootstrapping in less than a second, HomNAND has been computed as follows: $$ (\textbf{a}, b) = HomNAND((\textbf{a}_0, b_0),(\textbf{a}_1,...
0
votes
0answers
43 views

How to ensure a trusted computing of a function in untrusted Cloud server?

Could you please let me know the latest practical techniques and cryptographic schemes that allow hiding function execution in an untrusted Cloud?
0
votes
1answer
45 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 ...
2
votes
0answers
53 views

Verifiable secret sharing - Benaloh scheme; some doubts not answered earlier

I reviewed the paper "Secret sharing homomorphisms: keeping shares of a secret secret" by J.C. Benaloh yesterday and I had some difficulty understanding his version of verifiable secret sharing to ...
0
votes
0answers
114 views

Modifying password-encrypted values to generate new password-encrypted values

Do there exist four functions f, g, Enc, Dec such that: $$f(Enc(x, p), i) = Enc(g(x, i), p)$$ $$Dec(Enc(x, p), p) = x$$ where Enc and Dec are a secure encryption/decryption algorithm (such as AES)? ...
0
votes
1answer
47 views

Bitwise homomorphic encryption

I am fairly new to HE and would like a short clarification on how exactly integers are securely encrypted using bits. The main idea is that one encrypts each bit value and represents the n bit number ...
0
votes
2answers
107 views

How to compute secure sum using secure multparty computation?

Suppose there are three voters $P$, $Q$ and $R$, and each will vote only on one candidate out of $X$, $Y$ or $Z$, with a 6 bit vote vector corresponding to $X $, $Y$ and $Z$ respectively (with 2 bits ...
4
votes
1answer
99 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 ...
2
votes
0answers
75 views

Chinese Remainder Theorem and Elgamal

I am studying an encryption scheme which is Elgamal-like where I think CRT can help optimise the encryption and decryption but I am not sure if I am applying CRT the correct way. I have a cyclic ...
4
votes
1answer
83 views

Random Masking of Padded RSA Ciphertext through homomorphism

I had asked a question related to this before: Oblivious Decryption: Decrypting with a private key, without knowing the message @rikhavshah has an answer, which I would like to discuss the security ...
7
votes
1answer
198 views

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 ...
1
vote
2answers
88 views

Oblivious Decryption: Decrypting with a private key, without knowing the message

I’m trying to devise a protocol, complimentary to a private-set-intersection, involving three parties, namely Alice, Bob and Charlie. Alice has a public and a private key. And receives website logs ...
1
vote
0answers
41 views

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 ...
1
vote
1answer
39 views

In Multi-party communication, how can I find that one encrypted value is negative or not?

I'm using Pailier Cryptosystem as an additive homomorphic system in my scenario. I have two parties: Alice and Bob. Alice has one pair of (SK, Pk) keys. She encryptes one value using her public key ...
4
votes
3answers
522 views

What is the purpose of Homomorphic encryption? [closed]

Homomorphic cryptography is a kind of cryptography that allows you to do special math operations on the ciphertext, and the maths performed are identical to the obvious ones. For example, one person ...
2
votes
1answer
42 views

Paillier encryption problem when q or p divides r

I am having a problem with Paillier encryption as described on Wikipedia. It says to pick $0 < r < n$, where $n=pq$ for large, equally sized primes $p$ and $q$. However, I've been testing ...
2
votes
2answers
64 views

Bijective encryption function in Paillier cryptoststem

In Paillier cryptoststem many ciphertexts can correspond to the same plaintext. How can I modify the scheme so to make the correspondence between ciphertexts and plaintexts a one to one correspondece? ...
1
vote
0answers
14 views

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 ...
4
votes
0answers
44 views

Threshold homomorphic

Quite a specific question, but are there any threshold signatures that are also homomorphic? Preferably ones that work in the discrete log setting and don't require any pairings.
1
vote
1answer
42 views

Additive homomorphic encryption: strict equality - handling congruence

Is there an additive homomorphic encryption scheme which guarantees that if provided with $E(v)$, $E(m_1)$ and $E(m_2)$ and $E(v)=E(m_1).E(m_2)$ then $v=m_1+m_2$ Please note this is not $v \equiv ...
1
vote
1answer
56 views

For ElGamal-based key encapsulation, is it necessary to hash before using as AES key?

I'm working with SJCL, specifically using ElGamal to encrypt messages. Behind the scenes, this is doing something similar to what's described in this SO post (emphasis mine): Regardless how big ...
2
votes
1answer
48 views

Bitwise operation on secret values revealing the result only to the participants

Given the following situation, what sort of cryptographic construction am I looking for? Alice has a bitfield (vector, polynomial representation, etc.) Bob has a different bitfield of the same length ...
5
votes
1answer
123 views

“Power of one” as input to functions of a cryptosystem

What does $1^\lambda$ mean when you pass it as a parameter to the functions of a cryptosystem. The cryptosystem in question is this and a picture reference is this. I have been told it signifies the ...
1
vote
0answers
38 views

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 ...
4
votes
1answer
87 views

How can one turn a malleable encryption to not malleable

An encryption algorithm is "malleable" if it is possible to transform a ciphertext into another ciphertext which decrypts to a related plaintext. That is, given an encryption of a plaintext m, it is ...
1
vote
0answers
41 views

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)?
1
vote
0answers
34 views

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 ...
3
votes
2answers
158 views

How to use Homomorphic encryption for secure computing Arctan() function?

In the multi-party communication(MPC), if partyA has the coordinate(x1 y1) and partyB has the coordiante(x2,y2), how two parties can securely compute Arctan((y1-y2)/(x1-x2)) without revealing their ...
8
votes
0answers
102 views

Why is fully homomorphic encryption so slow? [duplicate]

What are the reasons that FHE is so slow? Is it possible to make the FHE algorithm so fast that it can be used in practice (say, the practical FHE algorithm should be slower no more than 10 times ...
1
vote
1answer
75 views

Can homomorphic encryption achieve program integrity (verification) in the cloud?

As I understand it, homomorphic encryption can be used to keep data confidential while still allowing computations over the data. From another question, I found out that one can also verify the ...
3
votes
3answers
2k views

Can multiplication of two primes be seen as a strong cipher?

If we were define such a cipher: A reversible function that would accept a message $M$ and an initialization vector $\text{IV}_1$ $\operatorname{map}(\text{IV}_1, M)$ which can map an input $M$ to a ...
0
votes
1answer
62 views

How can a fully encrypted homomorphic program resist copying?

Let's say that we have an original homomorphically encrypted program with any possible code inside. What methods can it use to ensure that it is impossible to create an exact copy of it? Are there ...
2
votes
2answers
82 views

Limiting how many key pairs someone can generate without compromising their keys

Is there any way to assign someone a limited quota for how many cryptographic key pairs they can generate (ECC, RSA, any algorithm), and preferably non-interactively? By non-interactively I mean there ...
1
vote
0answers
42 views

Is there a hash function h(M + t1) = c1 that relates to h(M + t2) = c2 in a way that can be verified without knowing M? [duplicate]

Is there a hash function h(M + t1) = c1 that relates to h(M + t2) = c2 in a way that, knowing t1, t2, c1, c2, and with no knowledge of M, it can be verified whether both use the same M?
1
vote
2answers
78 views

Can homomorphic encryption offer program integrity and program obfuscation?

By program integrity, I mean the (encrypted) result I receive is indeed the expected result and not, say, an intermediate result or a result affected by an adversary. Can homomorphic encryption defend ...
5
votes
1answer
167 views

How can homomorphic encryption be probabilistic while allowing for math to be conducted?

I've been playing with some homomorphic encryption libraries. It's given me a greater appreciation for probabilistic encryption. These two answers were instrumental in leading to this question, but ...
4
votes
2answers
81 views

Are there any additively homomorphic encryption schemes over $\Bbb Z_2$ besides Goldwasser-Micali?

I am aware of Goldwasser-Micali cryptosystem, which is additively homomorphic over $\Bbb Z_2$. Are there other schemes that satisfy this property? Note: If one is willing to involve advanced tools ...
4
votes
3answers
146 views

Homomorphic & Functional encryption: Mapping unencrypted outputs to encrypted outputs using existing data

Let's assume I have datapiece A which, after being put through a model or neural network, has a known output X in the unencrypted space. When I move datapiece A into an encrypted space, and put it ...