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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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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164 views

What is this cryptosystem called?

From a paper Outsourcing Large Matrix Inversion Computation to A Public Cloud (IEEE Transactions on Cloud Computing, Vol. 1, N°1, 2013; alternate source requiring registration; preprint), I got to ...
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5answers
676 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
138 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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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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305 views

Is there an additively homomorphic encryption scheme that supports calculating a square root on the ciphertext?

I need an additively homomorphic encryption scheme that satisfies: $D(\sqrt{E(m)}) \approx \sqrt{m}$. It seems that the lifted ElGamal satisfies this, but it is hard to do decryption if the message ...
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66 views

Changing encryption key without revealing the original key

Say that Alice encrypts a $plaintext$ with $key_{m}$ and gives the $ciphertext_m$ to Bob. Alice wants to send several gigabytes of $plaintext$ to Eve but she is on a mobile 3G connection. So instead, ...
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808 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
117 views

Inner product with homomorphic encryption

I want to do a very simple thing: Given two vectors, I want to encrypt them and do some calculation, then decrypt the result and get the inner product between both vectors. I want to do this as fast ...
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1answer
142 views

What's the differences among Blind Computation, Secure Multi-Party Computation, Secure Circuit Evaluation and Homomorphic Encryption

We know that Blind Computation, Secure Multi-Party Computation, Secure Circuit Evaluation and Homomorphic Encryption all can process the encrypted data, but I am puzzled by them. What are their ...
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216 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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648 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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1answer
613 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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472 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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1answer
36 views

How to calculate Enc(-m) from Enc(m) in Paillier cryptosystem?

The encryption in Paillier cryptosystem is like this according to Wikipedia: Let $m$ be a message to be encrypted where $m \in \mathbb{Z}_n$ Select random $r$ where $r \in \mathbb{Z}_n^*$ Compute ...
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2answers
101 views

Formal security of recycled random blinding in a Paillier scheme

This question is a follow-up/variant on a previous question. Supposing that we are trying to generate a large number of (indistinguishable) ciphertexts of a given plaintext and want to avoid the ...
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91 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
316 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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3answers
451 views

Can we construct fully homomorphic encryption scheme based on non-circuit approach?

At present, all FHE scheme are be constructed based on circuit approach. Can we construct fully homomorphic encryption scheme based on non-circuit approach? Is Polly cracker non-circuit approach ?
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1answer
393 views

Why can't Homomorphic encryption schemes support algorithms with conditions/branching?

If it isn't already apparent from the title of my question, i should make clear that I have only a very basic understanding of homomorphic encryption. I would like to know why homomorphic encryption ...
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1answer
41 views

How to test an implementation of a homomorphic scheme?

I want to implement the following homomorphic encryption scheme from On-the-Fly Multiparty Computation on the Cloud via Multikey Fully Homomorphic Encryption by Lopez-Alt et al. I use C++ and I want ...
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115 views

cipher text only attacks on deterministic homomorphic encryption schemes

If we consider a set of numbers say a set $s=\{a,b,c,d\}$ , where $a,b,c,d>1$ and the numbers $a, b, c, d$ do not share any relation between them , i.e. for any two numbers, $n_1,n_2\in s$ the ...
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1answer
159 views

How to implement homomorphic multiplication for Elgamal?

I want to add the homomorphic property to Elgamal in libgcrypt. This is the core code I added to the library. ...
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80 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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342 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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171 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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254 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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138 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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452 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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483 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
49 views

Convert ciphertexts of one encryption scheme to another without decryption

I want to convert ciphertexts of one encryption scheme to another without decrypting them under the first scheme and then encrypting with the second scheme. For example convert OPE encryption to ...
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2answers
40 views

How can we define division operation by using Fully homomorphic encryption

Last fews months, I'm working with homomorphic encryption. Now I am dealing with some computational problems with integers or real-numbers (like arithmetic mean, standard deviation) where division is ...
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1answer
100 views

Is the ring of octonions “commonly” used in Cryptography?

I've recently read "Fully Homomorphic Encryption on Octonion Ring" by Yagisawa, which is based on octonion rings over finite fields. Personally I've never encountered octonion rings in cryptography ...
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72 views

Are all homomorphic encryption schemes not CCA secure? [duplicate]

Homomorphic encryption is hyped by computer sciences because it offers great potentials. For example you can perform cloud based calculation while nobody gets to know you data. I am wondering if ...
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186 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
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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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418 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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2answers
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Homomorphic encryption diagram and trouble about a paper

I'm reading a paper based on Homomorphic Encryption: “Fully Homomorphic Encryption over the Integers: From Theory to Practice” (PDF). Now, I need a diagram of this algorithm if possible with all the ...
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33 views

Are there any FHE-MPC schemes implemented?

I want to know if there are any publicly available multiparty computation schemes derived from fully homomorphic encryption schemes. An example would be the implementation of this scheme ...
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Can I expand the modular of an encryption scheme?

Take the lifted ElGamal as an example: suppose the original ciphertext is $<g^y ~mod~q,~g^m~mod~q>$. After some calculations, $m$ could be large enough to do modular. But I don't want $m$ to be ...
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How can I multiply an additively homomorphic encrypted value by a float number?

As we all know, if $E()$ is an additively homomorphic encryption, we can multiply $E(a)$ by an integer $b$, then we will get $E(ab)$. But what if $a$ is a float number? Can we still get $E(ab)$? Which ...
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49 views

Scale-Invariant DGHV Scheme - Decryption

I have just started reading the Scale-Invariant Fully Homomorphic Encryption over the Integers paper and I'm a bit confused about something: When decrypting the ciphertext: $c = r + (m+2r^*) \cdot ...
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Proving that a plaintext is the Paillier decryption of a certain ciphertext [duplicate]

Assume that Alice received 100 ciphertexts encrypted with additive homomorphic encryption, say Paillier, using the same public key that belongs to Bob. Alice added all of them, and wants to know the ...
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74 views

Exponentiation with fully homomorphic encryption [duplicate]

I have often heard that because a fully homomorphic encryption scheme allows for both additions and multiplications on encrypted data, most other operations can be simulated. I don't understand how ...
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119 views

Key Recovery Smart-Vercauteren SWHE

In the article (https://eprint.iacr.org/2009/571.pdf, pag 8) of Smart and Vercauteren, it is mentioned that the recovery of the private key is an instance of the small principal ideal problem. But I ...
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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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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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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 ...