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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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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Why do fully homo-morphic constructions use 'ring' or 'lattice' structures?

Is there a significantly advantage to these data structures, or is it simply the status-quo and the easiest to use for describing constructions?
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Distributing blocks with validation and non-dependant list generation

Problem Suppose I have a system of nodes that can communicate with a parent node, but not among each other. Suppose then a file on the parent node is split up into blocks and divided among the ...
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472 views

Searching over encrypted data

Is there any library/tool available which can allow me to search over encrypted data? I would like to encrypt data on client side, send it to cloud and perform search in cloud. I've been reading ...
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233 views

DGK Cryptosystem Key Generation and Decryption Issues

I detailed here the DGK (Ivan Damgård, Martin Geisler and Mikkel Krøigaard) cryptosystem, and I managed to get it to work, most of the time... The BIG problem that I am facing at the moment is that ...
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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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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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105 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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472 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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3answers
473 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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372 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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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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318 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
82 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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210 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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140 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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56 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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137 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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80 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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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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121 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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386 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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163 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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94 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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348 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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339 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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Homomorphic proxy re-signature

Alice has a value $a$ and she signs it using her secret key $d_1$ as: $s_1 = (r_1 * g^a)^{d_1} \bmod p$, and Bob has a value $b$ and he signs it using his secret key $d_2$ as: $s_2 = (r_2 * g^b)^{d_2} ...
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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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80 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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70 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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105 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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131 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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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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416 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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178 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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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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Malleability of homomorphic encryption

El Gamal is a malleable homomorphic encryption system, so is Rabin. Are all homomorphic encryption systems malleable? Or are there any that are not malleable? Thanks!
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326 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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178 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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71 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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165 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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412 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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362 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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244 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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206 views

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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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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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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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 ...