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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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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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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5answers
853 views

Approach towards anonymous e-voting

I want to implement an internet-based e-voting system. Voters shall be able to cast their vote for one out of n possible candidates. Each candidate has his own ballot-box kept by and at a trustworthy ...
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1answer
98 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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446 views

What is the flaw in this model for homomorphic encryption?

Imagine a Field Isomorphism $g : \mathbb F1 \to \mathbb F2$ given by some $g(x)$ Assume a client is planning to outsource his computations to server, translates every possible $x$ as $g(x)$ and ...
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1answer
344 views

What is the strength of unpadded RSA?

I would like to use unpadded RSA for homomorphic encryption in a toy P2P game, for things like fair coin flips and shuffling. How many bits of security does unpadded RSA have, in relation to its key ...
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435 views

additive ElGamal encryption algorithm

I'm performing ElGamal encryption algorithm and using the additive homomorphic property so the product of two ciphertexts is the encryption of the sum of the plaintexts. The problem is that I need to ...
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2answers
295 views

Simple homomorphic crypto for 32-bit integers

I'm looking for a simple way to perform homomorphic crypto on 32-bit integers. My only requirement is that I can add and subtract from the plaintext value without actually decrypting it. The crypto ...
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2answers
79 views

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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1answer
179 views

Proof of correctness of a homomorphic ElGamal sum

Let's suppose we are using the exponential ElGamal as a public-key encryption scheme, so that we encrypt $g^m$ instead of $m$, for some generator $g$. Let $x$ be the private key, and $h=g^x$ be the ...
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1answer
161 views

What's efficient MPC protocol for determining if sum's bigger than y?

My secure multi-party computation (MPC) in need is simply to determine if a sum of two private variable is bigger than a given value $y$, as $f(x_0, x_1) = [(x_0 + x_1) > y]$ in which the value ...
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2answers
139 views

How to compare two datasets „anonymously”?

Ok, I hope this question makes some sense because I am not so sure how to word it any differently… Imagine the following situation: There are 10 defined colors (blue, orange, yellow etc.) There are ...
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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
116 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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1answer
70 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
202 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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120 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 ...
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1answer
369 views

Do companies like CipherCloud really have the option to use homomorphic encryption?

I was reading How is CipherCloud doing homomorphic encryption? and was wondering: Is there a technically feasible way for companies like CipherCloud to use homomorphic encryption (HE) while ...
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2answers
156 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 ...
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1answer
92 views

Why unit vectors should be encrypted bit per bit in that case?

At this work at section $2.2$ concerning a possible application for the BGN cryposystem the author points out that if you want to encrypt a unit vector $\overrightarrow{u_l}$ of size $l$ then the ...
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1answer
329 views

Is there difference between Algebraic Homomorphic Encryption and Fully Homomorphic Encryption Schemes?

Is there difference between Algebraic Homomorphic Encryption and Fully Homomorphic Encryption Schemes?
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1answer
330 views

DGK Cryptosystem Encryption Speedup

Following @poncho's nice clarification of the RSA speedup here, let's see if I'm able to do the same in the case of the DGK cryptosystem: We have pk = (n, g, h, u), sk = (p, q, $v_p$, $v_q$) which ...
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How to compute the decompositions used in fast FHE bootstrapping?

Leo Ducas and Daniele Micciancio's recent paper "FHE Bootstrapping in less than a second" gave an exciting result that one can compute the `atom operation' of Fully Homomorphic Encryption (i.e. ...
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73 views

Encrypted database: how to deal with general queries?

My question is quite related to the concept of homomorphic encryption, which is not practical at all nowadays. In short, I would like to know how to query encrypted databases. Simple queries which ...
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51 views

See any problems with this search-specific homomorphic encoding strategy?

I'm imagining this for use in the scenario of cloud-stored client-encrypted email, where, when seeking to do a string search across messages, you don't want to have to download every stored message in ...
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“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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100 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 ...
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62 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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2answers
353 views

Is it possible to subtract/multiply numbers using homomorphic encryption?

Most of the libraries I've seen allow you to add encrypted numbers. Is it possible to subtract and multiply them?
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1answer
170 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
581 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 ...
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1answer
119 views

Fully Homomorphic Encryption over the Integers - perform an operation on an encrypted data

In Fully Homomorphic Encryption scheme represented here Fully Homomorphic Encryption over the Integers In the Evaluate process (see section “3.1 The Construction” of the paper): $$Evaluate(pk, C, c1, ...
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112 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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249 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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164 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
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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1answer
146 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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378 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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335 views

Homomorphic Encryption

Homomorphic Encryption (HE) which supports any function on ciphertexts is known as Fully Homomorphic Encryption (FHE), while Partially Homomorphic Encryption (PHE) includes encryption schemes that ...
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229 views

Can Add and Multiply On Cipher Text achieve all operations?

A Fully homomorphic encryption scheme needs to support an evaluate function that can do add and multiply operations on cipher text. Can we do all kinds of complex operations on cipher text like ...
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homomorphic encryption special case of multi party computation?

I read that Fully Homomorphic Encryption schemes are special case of Secure MPC in page no 3. Especially , generalization of two party computation problems stated by Yao But is there any additional ...
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249 views

Are there any multiparty homomorphic encryption schemes?

Are there any multiparty homomorphic encryption schemes ? Most of the literature is about two party schemes . Is there any generalization made for n party ?
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1answer
98 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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123 views

Connections between Instance Hiding and Fully Homomorphic Encryption

Another approach taken by researchers for carrying out computations over encrypted data is Instance Hiding. In brief, If a user wants to outsource the computation of a function for a particular input ...
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291 views

Store hashed email and compare hash values

I have a number of different systems sending me email addresses, but I don't actually need the underlying email, just a hash of the email address. I know I can compare hash values to find matches ...
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1answer
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How can I do minus on plaintexts in the Paillier cryptosystem?

We have $E(a)$, $E(b)$ encrypted under the same Paillier key. As we all know, we can get $E(a+b)$ by calculating $E(a)*E(b)$. But can we get $E(a-b)$, by calculating $E(a)/E(b)$? I tried to ...
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103 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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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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What goals is homomorphic encryption aiming to solve?

As I understand from this article about homomorphic encryption, it mainly aims to enhance the security of cloud computing. We should be able to encrypt data and send it to the cloud. After it is send, ...