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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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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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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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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“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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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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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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Can we give access to controlled functionality in Fully homomorphic encryption schemes?

Homomorphic encryption schemes are PKE schemes with an additional special method Evaluate. Evaluate method takes input any function (as boolean circuit) and encrypted inputs of the function and ...
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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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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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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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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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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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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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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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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
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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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Which areas in CS will be (or have been) most affected by fully homomorphic cryptography? [closed]

I'm in the middle of planning a 5000ish word essay on fully homomorphic cryptography, the current practical implementations and their limitations. Which areas of CS as a subject have been (or will ...
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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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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
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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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3answers
426 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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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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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
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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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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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218 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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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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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 ...
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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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Is Porticor's “homomorphic” key encryption something that can really be done or is it just marketing hype?

Porticor has an interesting file encryption offering for encrypting and decrypting files in an MySQL database quickly. They are an Amazon AWS (Amazon Web Service) Partner Network technology partner ...
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2answers
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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
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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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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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Can any one explain Circuit Privacy using fully homomorphic encryption from Gentry's thesis?

Craig Gentry's thesis talks about circuit privacy being straight forward from fully homomorphic encryption in the last chapter. Can somebody explain in simpler terms what that means ? I have read it ...
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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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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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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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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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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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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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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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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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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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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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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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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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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 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 ...