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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88
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8answers
26k views

How is CipherCloud doing homomorphic encryption?

Much of the literature and latest papers suggest that homomorphic encryption is still not practical yet. How is CipherCloud able to achieve this? Does anyone have an idea? Their website does not ...
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2answers
5k views

What is the most practical fully homomorphic cryptosystem?

Craig Gentry recently gave the first fully homomorphic cryptosystem. Quite a bit of work has been done since extending his work. It seems, however, that no system is practical for real world use. ...
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3answers
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Chinese Remainder Theorem and RSA

Wikipedia has a nice section regarding the speedup of the RSA decryption using the Chinese Remainder Theorem here. I need to understand the implementation of a similar speedup for the encryption ...
13
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5answers
613 views

Choose a random number that is different from a bunch of other secret numbers

I'm looking for an algorithm where n participants each have a different secret number between $[0..x]$ (and where $x$ is known) and where the participants then select randomly another, non-secret, ...
12
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1answer
2k views

What exactly is bootstrapping in FHE?

I have been reading about FHE lately, and it seems that bootstrapping is the core concept in order to develop FHE schemes. But, I don't exactly understand the idea behind it. I know that the schemes ...
12
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1answer
2k views

Applying machine learning algorithms to homomorphic encrypted data

I have a basic understanding of encryption and I got back to the topic because of an interesting site that encrypts financial data using homomorphic encryption (HE) and I would be happy for any input ...
11
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1answer
5k views

Can Elgamal be made additively homomorphic and how could it be used for E-voting?

Elgamal is a cryptosystem that is homomorphic over multiplication. How can I convert it to an additive homomorphic cryptosystem? How can I use this additive homomorphic Elgamal cryptosystem for E-...
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2answers
3k views

What does “circuits” mean in Cryptography?

I am not a hardcore cryptographer so this might be a really stupid question. I am looking through some papers in homomorphic encryption and discovered they describe computation as "circuits", why do ...
10
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3answers
8k views

What are some disadvantages of homomorphic encryption schemes?

I'm doing some self-teaching / research for my own benefit in homomorphic cryptography. I've studied both additive and multiplicative schemes (Pallier and RSA respectively), but all I can seem to ...
10
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3answers
2k views

Division in paillier cryptosystem

Is division possible in the Paillier Cryptosystem? i.e. given a the cipher-text $C$ of an integer $M$ the plain-text divisor $D$, and only the public key, can one compute the cipher-text of $M/D$ ?
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Key Size for Symmetric Homomorphic Encryption Over the Integers

In the paper Fully Homomorphic Encryption over the Integers, it mentions a symmetric key scheme on page 1 and 2. Key Generation: Pick a random odd number $p \epsilon [2^{N-1},2^N)$ Encrypt A Bit m: $...
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2answers
1k views

Is full Homomorphic encryption quantum resistant?

Since most of our asymmetric encryption algorithms are going to be out-of-date in a couple of year due to Shor's algorithm, I was wondering about the future of FHE schemes. I have found this paper, ...
10
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1answer
4k views

Homomorphic (encrypted) comparison to an integer

When working with an additive homomorphic encryption scheme (say Pallier's), is there an efficient way to get the encrypted value of a comparison test to an integer value (I realise that an ...
10
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1answer
260 views

IND-CPA secure RSA padding with a partial homomorphic property

A while ago, I asked for an IND-CCA1 secure padding for RSA that still allows for the multiplicative homomorphic property of RSA and got no answers (yet). Now I've seen fgrieu's answer about standard ...
10
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1answer
294 views

Computing Logarithm using homomorphic encryption

Let's say we have $Enc_{pub}(a)$, the encryption of an integer $a \in \mathbb{Z}^*$ under the public key pub with a Homomorphic encryption scheme that supports both ...
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3answers
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Homomorphic encryption - Why does addition not imply multiplication?

As far as I know: There are some partially homomorphic encryption (PHE) systems that support either addition or multiplication. A fully homomorphic encryption (FHE) system can do addition as well as ...
9
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3answers
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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 ...
9
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1answer
603 views

Difference between somewhat homomorphic encryption and leveled homomorphic encryption?

Is there any difference between somewhat homomorphic encryption and leveled homomorphic encryption? I heard that leveled homomorphic encryption supports computing circuits of bounded depth on cipher ...
9
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1answer
411 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,...
9
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1answer
2k views

Can a homomorphic encryption scheme be made CCA2 Secure?

Is it possible to modify a homomorphic encryption scheme so that it can be CCA2 secure? From the definition of a homomorphic scheme, it seems that it is malleable, which would result in lack of CCA2 ...
9
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1answer
384 views

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 ...
9
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2answers
428 views

What math makes it safe to offer a stolen-password check service?

The database provider HIBP has 4 billion stolen passwords, and wishes to offer an API for websites to use during new-user signup (and password change) operations, so they can refuse to allow users to ...
8
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3answers
211 views

Homomorphic OR operations

Is there an encryption scheme that provides efficient homomorphic OR operations at the ciphertext space? Of course any fully homomorphic encryption can be used but I do not require or want additional ...
8
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1answer
1k views

Noise in Homomorphic encryption

What is the noise in homomorphic encryption schemes? (or where does the noise come from, I see that its inbuilt in the scheme and is not a side channel or disturbance noise) Is it also due to the ...
8
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1answer
200 views

Obfuscating functions that are mostly zero

Let $f_k(x)$ be a boolean function of two arguments with two properties: The function $f$ can be efficiently computed. The output is always 0 or 1, and for any fixed $k$, if we choose $x$ randomly, $\...
8
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2answers
642 views

How could Fully Homomorphic Encryption support power operations?

Fully Homomorphic Encryption (FHE) enables arbitrary functions computed on encrypted data, because it supports both addition and multiplication. But I wonder if FHE supports power operations. For ...
8
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1answer
3k views

Somewhat Homomorphic Encryption versus Fully Homomorphic Encryption?

Is that correct that Somewhat Homomorphic Encryption is more efficient that “Fully Homomorphic Encryption” (FHE) but less efficient than Partially Homomorphic Encryption (e.g Paillier encryption)? Is ...
8
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2answers
490 views

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. ​ Though their scheme can achieve fully homomorphism theoretically, they admitted that "for ...
8
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1answer
499 views

Homomorphic decryption circuit in integer-based scheme

I'm reading this excellent paper by Gentry as a smooth introduction to Fully Homomorphic Encryption. Most things are clear to me except from the way the homomorphic evaluation of the decryption ...
8
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0answers
130 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 ...
8
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0answers
488 views

LT codes with Homomorphic hashing

I have been working on a project implementing LT codes with Homomorphic hashing (inspired from http://blog.notdot.net/2012/08/Damn-Cool-Algorithms-Homomorphic-Hashing and http://blog.notdot.net/2012/...
7
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3answers
1k views

How is Homomorphic Encryption secure (over integers)?

I have been reading a bit about homomorphic encryption, and have been intrigued by its properties. If I have some cryptosystem that is homomorphic and supports addition, from my understanding, I can ...
7
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2answers
190 views

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: ...
7
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3answers
1k views

Can we proxy-re-encrypt using homomorphic encryption schemes?

Homomorphic encryption schemes are PKE schemes with an additional special method Evaluate. The Evaluate method takes input any function (as boolean circuit) and encrypted inputs of the function and ...
7
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1answer
395 views

What is scale-invariance notion of a fully homomorphic encryption scheme?

I read this paper https://eprint.iacr.org/2012/078.pdf and I didn't understand what does the author mean with scale-invariance perspective. The perspective in which we view the ciphertext is ...
7
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2answers
867 views

Fast attack on approximate GCD problem?

This question is about the approximate GCD problem which is defined as follows: Given any number of the approximate multiples $a_i = p \cdot q_i + r_i$ of $p$, where $p$, $q_i$ and $r_i$ are integers, ...
7
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3answers
1k views

difference between leveled FHE and normal FHE scheme

What is/are difference/s between leveled Fully Homomorphic Encryption and normal Fully Homomorphic Encryption?
7
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1answer
879 views

Fully Homomorphic Encryption over the Integers - Runtime Question

I have a question regarding the paper "Fully Homomorphic Encryption over the Integers" (http://eprint.iacr.org/2009/616.pdf): On page 6 after they set their parameters, it says "This setting results ...
7
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1answer
3k views

Paillier can add and multiply, why is it only partially homomorphic?

I've seen that it's widely accepted that before Gentry's breakthrough (which is not practical yet) in 2009 there were no known full homomorphic encryption scheme. I've read here in another answer ...
7
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1answer
470 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 ...
7
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1answer
353 views

Looking For Additively Homomorphic Encryption

I have a construction that requires as primitive an Additively Homomorphic Encryption scheme that does not rely on hidden group order, meaning I can't use Paillier. I now have two different ...
7
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1answer
135 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 ...
6
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1answer
3k views

Why is “semantically secure” important for cryptosystems?

The first question: what is the exact definition of semantically secure? Basically, a cryptosystem is semantically secure if given the public key and the ciphertext, an adversary cannot learn any ...
6
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1answer
449 views

Homomorphic Encryption and Semantic Security using Lattices?

I've been reading Brakerski and Vaikuntanathan's "Efficient Fully Homomorphic Encryption from (Standard) LWE" and I'm still digesting pieces at a time. Under section 1.1, "Re-Linearization: Somewhat ...
6
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3answers
143 views

How to compute the inner product on encrypted vector by using a third party?

I want to compute the inner product of two vectors on a third party, i.e. $f(x) \cdot f(y) = x \cdot y$ where $x$ and $y$ are two vectors. However, I do not want the third party knows the real value ...
6
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2answers
5k views

Homomorphic cryptosystems in RSA

Hopefully, Crypto can help me understand homomorphic cryptosystems. I'm designing a high score server for a game I made, and because of facets in the language I'm using, the player would be able to ...
6
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1answer
2k views

If you had to implement the BGN Cryptosystem, how would you do it?

If you had to implement BGN, how would you do it? I'm looking for an implementation of the public-key cryptosystem due to Boneh, Goh, and Nissim (aka BGN), or at least some suggestions on ...
6
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1answer
463 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 ...
6
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2answers
878 views

Paillier Homomorphic encryption to calculate the means

Paillier Homomorphic encryption supports addition and multiplication with plaintext value. Can I use these properties to calculate the means of cipher-text values? I try to use the following steps: ...
6
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1answer
555 views

Difference between a circuit and a normal function

I've seen the word circuit used in many crypto contexts (for example, regarding FHE in this pdf). I've always thought of a circuit as another word for a program or function. But is there a difference -...