# Tagged Questions

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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### 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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### 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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### 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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### 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. NAND-...
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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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### 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 $D$...
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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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### 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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### 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 $q \approx 2^{\eta^3}$...
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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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### 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 ...
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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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### 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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### 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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### 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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### 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 6,...
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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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### 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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### 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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### 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 ...