# Tag Info

Accepted

### What exactly is bootstrapping in FHE?

First off, from your question, it is not clear whether or not you understand the "circuit" part. So I'll start there. With (most) FHE schemes, you are evaluating circuits, or a bunch of gates hooked ...
• 38.7k
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### Noise in Homomorphic encryption

The noise is usually a small term added into the ciphertext while encrypting. This term may be a small integer (if the scheme is based on integers) or a small polynomial (if the scheme is based on ...

### Chinese Remainder Theorem and RSA

What really helped me understand RSA-CRT was Section 3 of Johann Großschädl: "The Chinese Remainder Theorem and its Application in a High-Speed RSA Crypto Chip" [1]. What follows is a summary of that ...
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### Representing a function as FHE circuit

The circuit term in the evaluation of functions with FHE is a coming from Electronics. In the notion of FHE circuit, we have almost the same problem; build a circuit of a function $f$ with available ...
• 48.9k
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### What is the link, if any, between Zero Knowledge Proof (ZKP) and Homomorphic encryption?

There are many. Homomorphic encryption implies ZK proofs for NP. This is simply because homomorphic encryption implies one-way functions, which imply ZKP for NP. Homomorphic encryption allows to ...
• 20.2k
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### How is Homomorphic Encryption secure (over integers)?

The use case for homomorphic encryption is that I encrypt my own data with my public key. I then ship this data to the cloud. The cloud can perform operations on those ciphertexts. But, since the ...
• 38.7k
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### Can Fully Homomorphic Encryption do comparisons?

This is simply not true. The above function can perfectly be homomorphically computed on FHE ciphertexts encrypting the inputs. There is no such "obvious limitation", and I wonder where your certainty ...
• 20.2k
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### Is there a way of maintaining malleability in a homomorphic encryption system while making it infeasible to perform chosen ciphertext attacks?

I know of two lines of work on this question. It is indeed possible to allow malleability but still make some guarantees in the presence of a chosen-ciphertext attack: Manoj Prabhakaran & Mike ...
• 13.5k
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### Homomorphic encryption - Why does addition not imply multiplication?

There are at least two problems; The $b$-times addition leaks the $b$. A semi-honest observer can see that you add the $a$ by $b$ times. However, in FHE, the $b$ is also encrypted with semantically ...
• 48.9k
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### Beavers Triple Vs BGW Multiplication on MPC

Yes, preprocessing Beaver triples in an offline phase leads to a faster online phase. The online phase of an AND gate requires just two openings plus local computations. But there are other ...
• 13.5k
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### Somewhat Homomorphic Encryption versus Fully Homomorphic Encryption?

PHE (partially homomorphic encryption) schemes are in general more efficient than SHE and FHE, mainly because they are homomorphic w.r.t to only one type of operation: addition or multiplication. SHE ...
• 656
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### Obfuscating functions that are mostly zero

I provide a summary below of what is currently known (to my knowledge) regarding obfuscation of various class of "mostly-zero" functions. From Indistinguishability Obfuscation What we can obfuscate: ...
• 20.2k
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### Difference between somewhat homomorphic encryption and leveled homomorphic encryption?

Let $\mathcal{C}$ be the set of allowed binary circuits. Then, a $\mathcal{C}$-evaluation scheme $(\mathsf{Gen}, \mathsf{Enc}, \mathsf{Eval}, \mathsf{Dec})$ that has (i) correct decryption and (ii) ...
• 116
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### "Power of one" as input to functions of a cryptosystem

The notation $1^\lambda$ means a string with $\lambda$ characters all of them equal to 1. For instance, if $\lambda = 3$, then $1^\lambda$ is $111$. And yes, it typically stands to the security ...
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