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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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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2answers
244 views

Which multiplicatively homomorphic encryption scheme supports encryption of 0?

I want a multiplicatively homomorphic encryption scheme that supports encryption of 0 (e.g. Elgamal doesn't support). I also want the multiplication to be operated on the ciphertext of 0, i.e., if ...
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Obliviously computing the Least common multiple of two poylnomials

Consider I have two polynomials $f_1$ and $f_2$ of the same degree. I want to secure them (using any kind of encryption except FHE) and outsource them to an untrusted server. I want him to compute the ...
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1answer
187 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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272 views

fully homomorphic encryption (FHE)

Please, I would like to find some hints or solution to my following problem, I would appreciate your assistance to walk with me throughout the solution Given fully homomorphic encryption (FHE) ...
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149 views

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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226 views

RSA or Paillier is good? [closed]

I want to implement file storage in cloud using homomorphic encryption. I want to use paillier encryption. Can you suggest the drawback of RSA to store and retrieving the files. Then only i can use ...
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1answer
169 views

practical use of homomorphic encryption

Are RSA and Elgamal partially homomorphic techniques? which one is better if one want to use it for practical purpose? and is there some FHE technique which can be used practically?
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can you suggest any applicayion for implementing threshold homomorphic encryption cryptosystem(Paillier cryptosystem) [closed]

I want to implement one project in multi party homomorphic encryption using paillier. Can you suggest any application for implementation.
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2answers
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Real life systems that use concepts of crypto computing [closed]

Are there any working cloud/internet solutions/products that operates on encrypted data such as systems using homomorphic encryption, secure multiparty computation, electronic voting, private ...
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1answer
153 views

Proving correctness of a decryption of a homomorphically summed ciphertext?

I would like to take some additively homomorphic cryptosystem - don't care much which one for now - and encrypt a series of numbers with it. I would then like to (in public) take these numbers, add ...
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1answer
198 views

Secure Multiparty Sum in malicious model using threshold encryption

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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4answers
263 views

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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What does “circuits” mean in Cryptography?

I am not a hardcore cryptographer so this might be a really stupid question. I am looking through some papers in homomorphic encryption and discovered they describe computation as "circuits", why do ...
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0answers
85 views

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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1answer
59 views

When homomorphic encryption goes wrong?

Consider I have two ciphertext $c_1$ and $c_2$ encrypted using RSA encryption. By definition if I multiply them I'd get $c_1.c_2 \ modN$. My question is what would happen if $c_1.c_2 >N$. Can we ...
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0answers
125 views

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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1answer
393 views

Homomorphic encryption based on XOR

Consider the values $a$ and $b$ are encrypted as $c_1=(a \oplus D)$ and $c_2=(b \oplus D)$. My question is: can we derive $b+a$ from any combination of $c_1$ and $c_2$? Note: I admit that the ...
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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 ...
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1answer
116 views

simple encryption scheme turns out to be “somewhat homomorphic”

In the paper Fully Homomorphic Encryption over the Integers in the introduction: How do I calculate $r$ and $q$ of this equation in the picture? $r \approx 2^{\sqrt{\eta}}$ and $q \approx ...
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1answer
208 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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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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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
170 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
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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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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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435 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
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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 ...
4
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1answer
159 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 ...
2
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1answer
381 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
239 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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3answers
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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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132 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 ...
4
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455 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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230 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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289 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
777 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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261 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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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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2answers
363 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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4answers
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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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290 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 ...
2
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1answer
147 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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153 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
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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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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? ...