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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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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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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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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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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78 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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278 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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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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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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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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139 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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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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Regarding NTRU homomorphic properties

NTRU has some homomorphic properties modulo q, supporting both addition and multiplication. Due to its nature, it cannot support many of them. My main focus currently is in the addition, so the ...
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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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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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157 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, ...
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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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Paillier Encryption: problems with double encryption

Given have two public keys $k1$ and $k2$, $E_{k1}(E_{k2}(m_1))$ and $m_2$. Is it possible to calculate $E_{k1}(E_{k2}(m_1 + m2))$? (or with multiplication instead of addition) At a first glance, I ...
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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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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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66 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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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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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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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 ...
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Encrypted Functions with Fully Homomorphic Encryption [duplicate]

While Fully Homomorphic Encryption schemes facilitate carrying out computations over encrypted data, can the function that has to be evaluated be encrypted too ? For example, if i have some programs ...
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Cipher text only attacks on deterministic fully homomorphic encryption schemes

If we have encryptions of additive and multiplicative identities in the corpus of cipher text of a deterministic fully homomorphic encryption (FHE) scheme, I guess we can break it. If the FHE scheme ...
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Cryptographical formalization of computational privacy

Yesteryears problems of communication privacy has been well defined in cryptography through Asymmetric cryptography. Due to rise in Cloud computational model , computational heavy tasks are being ...
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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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59 views

How bad would it be to reuse the random blinding factor in a scheme like Paillier?

A secure and somewhat fast way to "re-encrypt" (refresh? anonymise?) a Paillier ciphertext, $c$, is to multiply it by an exponentiated random value: $c \gets c \cdot r^n \mod n^2$ (with $r \in ...
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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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138 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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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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131 views

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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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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Noise bound in FHE over the integers

I'm studying the paper Fully Homomorphic Encryption over the Integers by Marten van Dijk, Craig Gentry, Shai Halevi and Vinod Vaikuntanathan. I have questions about the proof of Lemma A.1. In page ...
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How to perform homomorphic multiplication in ElGamal?

How can I compute homomorphic multiplication in ElGamal? That is: Given two ciphertexts $(R_1,c_1)$ and $(R_2,c_2)$ corresponding to plaintexts $m_1$ and $m_2$ under some public key; how can I compute ...
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38 views

Pailler encryption of small integers to 32-bit integers

I want to encrypt very small integers in the range 0-44 using the Paillier cryptosystem. Is there a way to select p, ...
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Does Paillier Cryptosystem work in different message space? [duplicate]

I have a question about Paillier Cryptosystem. Assuming we have $c = Enc(m) = g^m \cdot r^N \mod N^2$ as the output of encryption algorithm, where $N=p_1p_2$ and $m \in \mathbb{Z}_q \subset ...
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55 views

Key distribution and computation for homomorphic encryption

How can a system where the party performing a computation also possess the private key and still not know the answer of computation be designed ? Also the other party who does not have the private key ...
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Are there any noisy homomorphic encryption schemes?

Are there any Homomorphic Encryption(HE) schemes that result in noisy answers ? By noisy i mean , the answers could be approximately near the actual answers by noise factor $\epsilon$. For example , ...
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BGV FHE scheme parameters

In their paper presenting the BGV scheme, the authors mentioned in section 4.4 that, for the RLWE variant, the ring degree d, dimension n and noise distribution do not necessarily vary with the ...
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Mistakes in Jarecki-Liu use of Camenish-Shoup encryption?

I am implementing a protocol that uses Jarecki-Liu OPRF, which itself uses a simplification of Camenish-Shoup Encryption. Description of the way they do Camenish-Shoup is in section 2.3 of ...
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Don't Understand these Parameters

I don't understand section 3 of the paper Fully Homomorphic Encryption over the Integers. How can one calculate these paramters and make these equations in pictures into code?
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Perform general computation using a crypto algorithm as a building block

I have a somewhat special question. In our software we use a existing dongle which got cracked by our customers. The protection offered by the dongle isn't very sophisticated. For the moment I can't ...
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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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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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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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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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How difficult is homomorphic encryption? [closed]

I want to learn more about homomorphic encryption and eventually make a career from it. Currently, I'm thinking to have my bachelor degree in this field. What background should I have for this ? How ...