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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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. Can you recommend me ...
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AES and Homomorphic Encryption

Is it possible to do the following? Input would be to generate a new AES key, encrypt the private data with that key, encrypt the AES key with the FHE key, and send the FHE-encrypted AES key along ...
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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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SQL-Like queries in CRYPTDB doesn't work [closed]

I have downloaded and built Cryptdb and it works well. Most of queries on encrypted database run without any issue but, the query with LIKE key word receives an ...
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1answer
47 views

Executing encrypted code? [closed]

I want a code 'black box' that receives data inputs, processes those inputs, then sends out the outputs. I want the code to be encrypted, or somehow obfuscated. Is there any known way to do achieve ...
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1answer
40 views

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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65 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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1answer
78 views

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 ...
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0answers
23 views

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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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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1answer
70 views

Paillier cryptosystem preserve ordering of sums for two integer sequences

According to Paillier cryptosystem the product of two ciphertexts will decrypt to the sum of their corresponding plaintexts. I have two separate integer sequences X and Y that have same number of ...
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1answer
63 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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81 views

Proving that a plaintext is the Paillier decryption of a certain ciphertext

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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1answer
97 views

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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0answers
51 views

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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1answer
96 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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1answer
82 views

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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1answer
161 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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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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78 views

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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2answers
91 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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1answer
65 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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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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1answer
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can anyone give the java code to encrypt files using paillier [closed]

I want to implement encryption on personal files using paillier encryption. Is it possible to encrypt files using this encryption..
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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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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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105 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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1answer
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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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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
230 views

Looking For Additively Homomorphic Encryption

I have a construction that requires as primitive an Additively Homomorphic Encryption scheme that does not rely on hidden group order, meaning I can't use Paillier. I now have two different ...
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1answer
129 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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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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1answer
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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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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
75 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
155 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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1answer
184 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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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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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
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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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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
124 views

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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1answer
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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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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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93 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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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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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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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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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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80 views

Partial Homomorphic Schemes that are probabilistic

As mentioned in wikipedia there are many Partial Homomorphic Encryption(PHE) scheme like RSA, Elgamal, Pailler etc. Pailler encryption scheme seems to be probabilistic Are there any other PHE ...