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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Starting point on Fully Homomorphic Encryption and Proxy Re-encryption

I am new in this field. Can some one tell me where should I start for FHE and PRE reading ? Any papers where I can find Basic information on FHE and PRE ? Thank You in advance.
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+100

Key Size for Symmetric Homomorphic Encryption Over the Integers

In the paper Fully Homomorphic Encryption over the Integers, it mentions a symmetric key scheme on page 1 and 2. Key Generation: Pick a random odd number $p \epsilon [2^{N-1},2^N)$ Encrypt A Bit m: ...
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In DGHV FHE, why noise $r$ can be in $(-2^{\rho'}, 0)$?

"Fully Homomorphic Encryption over the Integer" described a simple FHE scheme based on the GACD assumption. Its encryption function (on page 6) has the form $c \leftarrow (m + 2r + 2*\sum_{i \in S} ...
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Hitting a counter example in homomorphic encryption over the integers

The paper Fully Homomorphic Encryption over the Integers talks about a super simple symmetric key implementation on page 1 and 2. It says that to generate a key, you pick a random odd number between ...
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39 views

Symmetric key in homomorphic encryption over the integers

Much like this question: Public key in fully homomorphic encryption over the integers I am also reading I'm reading Fully Homomorphic Encryption over the Integers, but I'm working on implementing the ...
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Additive homomorphic encryption scheme without change in operator

I'm looking for an additive homomorphic encryption that the addition operator (+) in its plaintext space be the same as addition operator in its ciphertext space. (Schemes like Paillier do addition in ...
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38 views

Why an upside down path on the evaluation of branching program on encrypted data?

Suggested by Ricky Demer in this post, I am reading the paper "Evaluating Branching Programs on Encrypted Data"(TCC 2007), which uses one-round strong OT protocol to implement homomorphic evaluation ...
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Are there any encryption schemes that enable to permute homomorphically?

According to the Barrington's theorem, any circuit in NC1 can be converted to a branching program, whose main operation is the composition of permutations (along with the choosing of permutations ...
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Is there a partially homomorphic quantum secure public key cryptosystem with IND-CCA1 security?

I recentely asked "IND-CCA1 RSA padding?" about whether there is a IND-CCA1 secure variant of RSA. The original version of the question also allowed usage of ECC which would allow usage of ElGamal, ...
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Question about OR operation in fully homomorphic encryption

This page (which won't let me post a comment, sadly!) describes how the original FHE paper by Craig Gentry describes FHE. (Other references to this stuff can be found on this question.) It mentions ...
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Is full Homomorphic encryption quantum resistant?

Since most of our asymmetric encryption algorithms are going to be out-of-date in a couple of year due to Shor's algorithm, I was wondering about the future of FHE schemes. I have found this paper, ...
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Are there simpler FHE methods than Craig Gentry's original paper?

Craig Gentry's 2010 paper on FHE is very cool, and I'm planning on implementing a basic proof of concept FHE. I was wondering though, are there any simpler methods that have been discovered since ...
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Generating random vector for Full Homomorphic Cryptography

The site below explains that part of doing homomorphic encryption, you need to generate a vector of random numbers that have the property that its dot product against a randomly generated bit vector ...
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What consequences do the plaintext space size has on the performances in the BGV scheme?

In the BGV paper [1], the authors say in §5.4 that you can have $\mathbb{Z}_p$ as plaintext size with a large $p$. What is the impact of the size of $p$ on the ciphertext size and computational work ...
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1answer
67 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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165 views

Fast attack on approximate GCD problem?

This question is about the approximate GCD problem which is defined as follows: Given any number of the approximate multiples $a_i = p \cdot q_i + r_i$ of $p$, where $p$, $q_i$ and $r_i$ are integers, ...
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AES-Paillier Homomorphic encryption [closed]

How can I implement following problem in java code for addition? (here I use Paillier homomrphic encryption): Input would be to generate a new AES key, encrypt the private data with that key, encrypt ...
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1answer
52 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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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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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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2answers
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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
55 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
48 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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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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90 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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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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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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67 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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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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151 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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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
120 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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99 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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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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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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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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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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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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182 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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118 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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110 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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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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240 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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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 ...