# Tag Info

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### breaking fully homomorphic encryption schemes

Even though all the operations you described can be performed homomorphically, the result remains encrypted, i.e., the attacker cannot "see" it. So homomorphic computation is not useful (on its own) ...
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### 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 ...
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### What does "circuits" mean in Cryptography?

Circuits can be expressed using very simple operations. For example, a boolean circuit consists of only two types of gates, addition and multiplication (where the input values are each 1 bit). ...

### Why is "semantically secure" important for cryptosystems?

Let me try to answer your second question, and hopefully shed some light on the first one in doing so. When we encrypt a message, it's because we want to keep something about that message secret. ...
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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 ...
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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 ...

### 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" . What follows is a summary of that ...

### difference between leveled FHE and normal FHE scheme

FHE should be able to evaluate any circuit. Leveled FHE can evaluate circuits which have a bounded depth. BGV was, I believe, the first to offer leveled FHE. The gain was in performance. By ...
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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 ...
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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 ...
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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 ...
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### Cipher text only attacks on deterministic fully homomorphic encryption schemes

Yes, your understanding is correct. It is well-known that homomorphic encryption schemes are vulnerable to cipher text attacks if they are deterministic. See, for example, the section 2.4 of the ...
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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 ...
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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 ...