# 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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### Why is “semantically secure” important for cryptosystems?

The first question: what is the exact definition of semantically secure? Basically, a cryptosystem is semantically secure if given the public key and the ciphertext, an adversary cannot learn any ...
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### How to calculate Enc(-m) from Enc(m) in Paillier cryptosystem?

The encryption in Paillier cryptosystem is like this according to Wikipedia: Let $m$ be a message to be encrypted where $m \in \mathbb{Z}_n$ Select random $r$ where $r \in \mathbb{Z}_n^*$ Compute ...
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### Is there an additively homomorphic encryption scheme that supports calculating a square root on the ciphertext?

I need an additively homomorphic encryption scheme that satisfies: $D(\sqrt{E(m)}) \approx \sqrt{m}$. It seems that the lifted ElGamal satisfies this, but it is hard to do decryption if the message ...
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### How can I multiply an additively homomorphic encrypted value by a float number?

As we all know, if $E()$ is an additively homomorphic encryption, we can multiply $E(a)$ by an integer $b$, then we will get $E(ab)$. But what if $a$ is a float number? Can we still get $E(ab)$? Which ...
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### Designing Secure Multi-Party Computation Sub-Protocols Based on Homomorphic Encryption

When designing SMPC protocols using secret-sharing, it is a common approach to compose a protocol from several sub-protocols (each proven secure under the formal definition of security w.r.t. semi-...
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### Changing encryption key without revealing the original key

Say that Alice encrypts a $\text{plaintext}$ with $\text{key}_{m}$ and gives the $\text{ciphertext}_m$ to Bob. Alice wants to send several gigabytes of $\text{plaintext}$ to Eve but she is on a mobile ...
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### 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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### 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 ...
In the BGV paper [1], the authors say in ยง5.4 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 ...