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homomorphic
homomorphic, a. (hɒməʊˈmɔːfɪk) [f. as prec. + -ic.] 1. Of the same or similar form. spec. a. Entom. Said of insects in which the larva more or less resembles the imago (Homomorpha); hemimetabolous or ametabolous. b. Bot. Applied to flowers or plants in which there is no difference in the relative le... Oxford English Dictionary
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Homomorphic encryption
Some common types of homomorphic encryption are partially homomorphic, somewhat homomorphic, leveled fully homomorphic, and fully homomorphic encryption See also Homomorphic secret sharing Homomorphic signatures for network coding Private biometrics Verifiable computing using a fully homomorphic scheme wikipedia.org
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GitHub - intel/he-toolkit: The Intel Homomorphic Encryption (HE ...
The Intel Homomorphic Encryption (HE) toolkit is the primordial vehicle for the continuous distribution of the Intel HE technological innovation to users. The toolkit has been designed with usability in mind and to make it easier for users to evaluate and deploy homomorphic encryption technology on the Intel platforms. - intel/he-toolkit
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Homomorphic image of a nilpotent group is nilpotent Is it true that an image of a nilpotent group under a homomorphic function is nilpotent? In that case, how am I going to show this? Thanks in advance.
You can think of a homomorphic image of $G$ as a quotient $G/N$. If $G$ is nilpotent then the lower central series terminates.
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Homomorphic equivalence
Homomorphic equivalence also comes up in the theory of databases. In fact for any category C, one can define homomorphic equivalence. wikipedia.org
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Homomorphic secret sharing
In cryptography, homomorphic secret sharing is a type of secret sharing algorithm in which the secret is encrypted via homomorphic encryption. Technique Homomorphic secret sharing is used to transmit a secret to several recipients as follows: Transform the "secret" using a homomorphism. wikipedia.org
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Isomorphic encryption or homomorphic encryption? Many encryption functions are said to be homomorphic: < As encryption functions are invertible, they can be considered one-to-one and onto on properly defined domains...
Now, consider a homomorphic encryption such as ElGamal cryptosystem: It takes a message from a cyclic group $G$, and outputs a pair $(c_1, c_2) \in G^2
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Homomorphic image if smaller fails to exist > Suppose a finite group $G$ has no homomorphic image of order $n$. Is it possible for $G$ to have a homomorphic image of order a multiple of $n$? My gut says "no", as the ...
**Hint:** There is no surjective homomorphism from $S_3$ to a group of order $3$ (do you know why?), but there is an obvious surjective homomorphism from $S_3$ to a certain group of order $6$.
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Unique homomorphic extension theorem
The unique homomorphic extension theorem is a result in mathematical logic which formalizes the intuition that the truth or falsity of a statement can From this lemma we can now build the concept of unique homomorphic extension. wikipedia.org
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$A_5$ as a unique homomorphic image Is there an infinite group whose only (nontrivial) finite homomorphic image is $A_5$ (the alternating group of degree $5$) ? **Edit** : I am interested in a group that is not the d...
I think the following will work. Let $M$ be an irreducible module for $A_5$ over ${\mathbb Q}$. For example, we could take $M = {\mathbb Q}^4$ to be the 4-dimensional deleted permutation module. Now let $G = M \rtimes A_5$ with the module action of $A_5$ on $M$.
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Query on homomorphism. If we say that $H:A\rightarrow B$ is a homomorphism from **A** to **B** , does it mean that **A is homomorphic to B** or **B is homomorphic to A**?. Are the two statements actually different? Wh...
homomorphic through the homomorphism mapping everything to the trivial element. The term "homomorphic image" just refers to the image under a given homomorphism $A \to B$ with the structure that comes with it.
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Homomorphic image of matrix ring Is that true that any homomorphic image of $M_n(R)$ ($R$ a ring with 1) is of the form $M_n(\overline{R})$, where $\overline{R}$ is an homomorphic image of $R$? It's clear for me that...
In particular, every ring of the form $M_n(R/I)$ is a homomorphic image of $M_n(R)$.
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Ciphertext-retrieval-based-on-Homomorphic-Encryption ... - GitHub
A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior.
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Show (R>0, x) is ismorphic to (R,+) I am trying to prove that these 2 groups are homomorphic first, since I know that isomorphic groups are isomorphic if they are homomorphic and bijective. My problem is that I don't ...
$\ln(xy) = \ln(x) + \ln(y)$ shows that the natural logarithm is a homomorphism from the multiplicative group of reals to the additive group. You also need to check that it is one-to-one and onto, to conclude that it is an isomorphism. As for how you would come up with this operation, I'm not sure th...
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Homomorphic Image If $N$ is any normal subgroup of $G$, then the factor group $G/N$ is abelian if and only if $G' \subseteq N$. In the proof I don't understand why $G/N$ is the homomorphic image of $G/G'$ $G\subsete...
$G/N$ being the homomorphic image of $G/G'$ means that there is a surjective homomorphism $\varphi : G/G' \to G/N$.
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