# Tag Info

0

No, this is not possible. The homomorphism only works at one layer. A ciphertext in Paillier is $g^m\cdot r^n\bmod{n^2}$. The plaintext space is the multiplicative group of integers modulo $n$. So, for it to even have a chance to work, first of all, the modulus of the outer encryption would have to be greater than $n^2$, where $n$ is the modulus of the ...

2

It can not do multiplication in the plaintext domain using two ciphertexts. In other words, given $E(m_1)$ and $E(m_2)$, you can not get $E(m_1\cdot m_2)$. You can only get $E(m_1+m_2)$. Given $E(m_1)$ and $m_2$, you can get $E(m_1\cdot m_2)$ however. But notice that $m_2$ in this case was not encrypted. On the site you reference, $C$ is not encrypted. It ...

1

I can’t remember having stumbled upon them in RealLife™ cryptography either, but I am well aware of a somewhat older, related patent by the same author. (Which might or might not violate your “Please don't mention the mentioned previous version of this scheme.” depending on what you’ve previously been reading. The patent is titled “Schemes for signcryption” ...

6

This doesn't address your question; however the algorithm in the paper is broken. The paper does show that recovering the key requires you to solve the approximate GCD problem (which may be difficult); what they don't show is whether recoverying the plaintext requires solving a hard problem. It turns out that it isn't that difficult at all (a bit of linear ...

1

By definition, homomorphic encryption cannot be CCA secure. Therefore when using homomorphic encryption, care must be taken to prevent chosen-ciphertext attacks in the constructed system. Sometimes this requires proving in zero knowledge that certain actions were followed correctly, for example. If you want to learn a bit more about what can be said about ...

4

You can use these schemes instead: “Evaluating 2-DNF Formulas on Ciphertexts”, or “A Simple BGN-type Cryptosystem from LWE”. These schemes enable you to do addition, a single multiplication, and more additions. For inner product, that's all you need (encrypt each item separately, multiply pairs, and add all together). Not everything needs FHE. In any ...

0

I think you must know what homomorphic encryption system can support inner product as you want. I hope that Dario Catalano, Dario Fiore - Boosting Linearly-Homomorphic Encryption to Evaluate Degree-2 Functions on Encrypted Data can help you.

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