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 (+ and * at the same time).

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Perform general computation using a crypto algorithm as a building block

I have a somewhat special question. In our software we use a existing dongle which got cracked by our customers. The protection offered by the dongle isn't very sophisticated. For the moment I can't ...
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36 views

Partial Homomorphic Schemes with padding

As mentioned in wikipedia there are many Partial Homomorphic Encryption(PHE) scheme like RSA, Elgamal, Pailler etc. But out of them only unpadded RSA scheme seems to be partial(multiplicative) ...
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478 views

breaking fully homomorphic encryption schemes

Fully homomorphic encryption schemes allow one to evaluate any arbitrary computation over encrypted data. Intuitively this seems to be too weak, irrespective of how we achieve this. An adversary who ...
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49 views

Privacy-Preserving Protocols and Proofs of Security

While dabbling in privacy-preserving protocols (mainly using Semi-Homomorphic Encryption) and coming up with miscellaneous ideas for comparison tests or other similar primitives, based on obfuscation ...
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85 views

“Practical” operations supported by functional encryption?

I'm curious about what operations have been developed into functional encryption schemes. What I mean by that is: what operations can be performed over encrypted ciphertexts? Obviously homomorphic ...
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why should one use lattice-based systems in travel documents or epassports in post- quantum computers era? [duplicate]

What are the attack algos and complexities to break lattice based systems? What is the motivation for using lattice crypto? why it has not been used extensively? what is fully homomorphic ...
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2answers
113 views

Homomorphic Encryption: how does the equality test on ciphertexts work?

Let's suppose we have a asymmetric crypto-system $H$ which is homomorphic with respect to some function $F$. Alice encrypts a message $m$ with her private key $e$ in the crypto-system $H$ and ...
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1answer
51 views

Size of Fresh Ciphertext's Noise in FHE over the integers

I'm studying FHE over the Integer which is https://eprint.iacr.org/2009/616.pdf In the remark 3.4, it says that the fresh ciphertexts have noise at most $2^{\rho'+2}$. I don't know why that ...
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1answer
100 views

Public key in fully homomorphic encryption over the integers

I'm reading “Fully Homomorphic Encryption over the Integers” by van Dijk et al. I wonder why $x_0$, which is a component of the public key, should be an odd number?
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1answer
90 views

Questions on FHE over the Integers - the question modified!

I modified my question since it is not as specific as I wanted. I'm studying FHE over the Integer which is https://eprint.iacr.org/2009/616.pdf I got questions about the proof of Lemma A.1. In page ...
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109 views

Lowest number challenge scheme

Suppose Alice knows a secret number $a$, and Bob knows a secret number $b$. Is there a simple way for Alice and Bob to know who has the lowest number, without Alice & Bob exchanging their numbers ...
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1answer
98 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 ...
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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 ...
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344 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, ...
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1answer
86 views

Multiplication-homomorphic schemes

I'm looking into multiplication-homomorphic schemes now and basically I see that there are 3 options: RSA, Boneh-Goh-Nissim and ElGamal. RSA was proved to be insecure unless message is randomly ...
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1answer
105 views

Pailler and Gentry - homomorphic encryption

Paillier cryptosystem is a probabilistic asymmetric algorithm for public key cryptography. Doesn't homomorphic encryption schemes have regular effects on the plaintext, and does that mean Pailliers ...
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2answers
105 views

How can I perform matching on an “encrypted- fingerprint feature matrix” using Fully Homomorphic Encryption?

I am doing a finger-print authentication process. The feature-extraction using minutiae has been done and I get an N x 6 matrix, where the 6 columns are {$x_i$ ...
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84 views

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 ...
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1answer
114 views

FHE over the Integers - reduction to approximate gcd problem

I have three quick questions concerning the reduction of the scheme to the approximate gcd problem: What exactly do the authors mean by $q_p(z_1')$ being the odd part of the gcd? (last line of step ...
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1answer
68 views

difference between leveled FHE and normal FHE scheme

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

Which homomorphic encryption scheme has the same size of plaintext space and ciphertext space?

I want to pre-compute the result for all possible ciphertext of a homomorphic encryption. Is it acheivable? Is there a fully homomorphic encryption scheme that has the same size of plaintext space ...
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1answer
220 views

How to select $g$ in Paillier Cryptosystem

For my cryptography class project in university I have selected Paillier Cryptosystem as a course project ...
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2answers
154 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 ...
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1answer
98 views

Homomorphic Encryption - Smart Vercauteren Batching

I'm going through Smart and Vercauteren's paper "Fully Homomorphic SIMD operations" and had a question about some notation used in the paper. In section 2 of the above it is stated that for each ...
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2answers
124 views

secure integer comparison

I have been going through a huge amount of papers to find a simple and a practical method to compare integer numbers without revealing their original values. I know that this falls within the area of ...
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1answer
96 views

Why do we apply the concept of circuit in homomorphic encryption schemes?

I am a beginner to the concept of homomorphic encryption. One thing that makes me very confused is why we use the circuit concept or approach to homomorphic encryption. Gentry's paper does not discuss ...
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59 views

Obfuscating point-like functions

There are standard schemes for obfuscating a point function; I'm wondering if we know how to obfuscate a slight generalization of a point function. I'll elaborate more precisely. Definition 1. A ...
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1answer
97 views

Homomorphic crypto allowing anonymous yes/no votes?

I'd need a crypto system allowing online yes/no votes but without revealing who voted what. Is a "partial" homomorphic crypto system what I'm after? Would, for example, Damgard-Jurik work in my case? ...
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1answer
200 views

Homomorphic encryption for vector addition

Building on the question and answer from Addition-only PHE in F# which ponders homomorphic cryptosystems to navigate, relatively, a single dimension without revealing absolute position (an encrypted ...
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1answer
67 views

Addition-only PHE in F#

Using homomorphic encryption, I would like to be able to take an encrypted integer and either add 1 or -1 for a new encrypted value. I do not want the encrypted value to be recoverable - just the ...
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ElGamal Homomorphic Encryption Formula Question [duplicate]

With Pubic Key $(G, q, g, h)$ where $G$ is a group, $q$ prime, $g$ a generator of $G$, Am I right in thinking that: $$\mathrm{Enc}(m;r) := (g^r, h^r \cdot g^m)$$
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120 views

Homomorphic Encryption Notation Question

What does the following notation mean in a homomorphic encryption scheme? ENC(x;r) What does x and ...
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2answers
83 views

What is the difference between homomorphic encryption and homomorphic signature? [closed]

I want to apply homomorphic signature instead of homomorphic encryption in Provable data possession. So I want to know about homomorphic signature and homomorphic encryption.
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1answer
168 views

Outsourcing arbitrary computations securely

Consider the following scheme. Alice wants Bob to make some computations for her, but she doesn't want to reveal the data on which he's going to do it. So, she encrypts the data, sends them to Bob, he ...
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1answer
102 views

Logical OR operation in a homomorphic additive cryptosystem

Suppose we have a cryptosystem homomorphic for addition (say Paillier's). Is there a way to perform a logical OR operation between two binary values (with a binary result). We can, of course, obtain ...
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127 views

Is a simple stream cipher “partially homomorphic” if no integrity check is applied?

My understanding is that, simply put, a stream cipher is just a CSPRNG such that $R(i,k)$ will produce a deterministic but statistically random sequence, where $i$ is an IV, and $k$ is the session ...
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1answer
146 views

Can homomorphic encryption filter?

Often in articles homomorphic encryption is praised as the holy grail of encryption for cloud storage. This is done by suggesting that it can do any computation, and as such could be used for ...
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1answer
162 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 ...
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1answer
69 views

How do you prevent the risk of damage to the security of Fully Homomorphic Encryption?

In this paper on pg. 1248 in the "preprocessing phase" section the authors say: In the preprocessing phase, the parties run a (standard) MPC to collectively generate a key pair (pk,sk) for the ...
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96 views

What scheme will allow merging and splitting the result of a function?

I am wondering if it's possible to have a scheme as follows. Here is the scenario: we have a set of objects (e.g. strings) {O1, O2, ..., On} we have a set of users {U1, U2, ..., Um} each user asks ...
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1answer
141 views

Homomorphic Encryption, LWE, and Practical Applications

I've been reading Brakerski and Vaikuntanathan's Efficient Fully Homomorphic Encryption from (Standard) LWE. When the authors discuss a small modulus p used for the transition from (n, log q) to (k, ...
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70 views

Is the following aggregation scheme private?

Is the following scheme private? By private i mean an untrusted aggregator (UA) cannot reveal anything other then an aggregate function output on plaintext data Each party holds a secret key $k_i$ ...
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1answer
545 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 ...
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1answer
197 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 ...
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1answer
228 views

FHE - Brakerski's “Scale Invariant” Scheme

I thought the current state of the art for fully homomorphic encryption was Brakerski, Gentry and Vaikuntanathan's scheme (BGV) based on standard/ring LWE employing modulus switching for noise ...
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1answer
118 views

Verifying encrypted addition

Alice has two secret numbers, a and b. She publishes c1=E(a), c2=E(b) and c3=E(a+b). Is there an encryption system E such that anyone would be able to prove that the c3 as published by Alice is ...
4
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2answers
208 views

Is there an encyption scheme that combines additive homomorphism with ability to proxy re-encrypt?

Is there an encyption scheme that combines additive homomorphism with ability to proxy re-encrypt? I've tried digging around on the Internet but haven't found anything conclusive on the topic.
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353 views

garbled circuit vs fully homomorphic encryption

Consider an outsourced database to an untrusted cloud (think CryptDb), the question is how to compute a function $f(.)$ on the data. I think I understand how (fully or partially) homomorphic ...
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2answers
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How to get the same calculation result on an untrusted computer, while withholding some information?

Consider this command on a trusted computer: result = function(public data, secret data) or shorter: r = f(p,s). How could a ...
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2answers
154 views

Privately Sum Values without Dealers, MPC

Suppose $n$ actors each hold a plaintext $p_i$. We wish to find $\sum p_i$, without leaking any information about individual $p_i$. Any actor (or any link in the network) could be controlled by an ...