homomorphism

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Related to homomorphic: Homeomorphic

homomorphism

[‚hä·mə′mȯr‚fiz·əm]
(botany)
Having perfect flowers consisting of only one type.
(mathematics)
A function between two algebraic systems of the same type which preserves the algebraic operations.

Homomorphism

 

a concept of mathematics and logic that first appeared in algebra but proved to be very important in understanding the structure and the area of possible applications of other branches of mathematics. The concept of homomorphism applies to a set of objects with prescribed operations (or relations). Thus, a homomorphism (homomorphic mapping) of a group G onto a group H is a mapping that associates to every element G∈G a definite element h∈H (the image of g) and satisfies the requirements that every element of H is the image of some element in G, and the image of the product (sum) of two elements in G is the product (sum) of their images. For example, the mapping that associates to an integer a the remainder when a is divided by a fixed positive integer m is a homomorphism of the group of integers (under addition) onto the group of residues modulo m. (The latter consists of m elements represented by the remainders 0, 1, . . . , m - 1.) The sum of two elements is represented by the sum of the corresponding remainders possibly diminished by m.

homomorphism

A map f between groups A and B is a homomorphism of A into B if f(a1 * a2) = f(a1) * f(a2) for all a1,a2 in A.

where the *s are the respective group operations.
References in periodicals archive ?
The project will focus on Somewhat Homomorphic Encryption (SHE).
In order to enhance the security, we propose a dynamic assignment of encryption algorithm for the data to be stored on cloud based on their file format such as Data Encryption Standard (DES) for low priority files, Advanced Encryption Standard (AES) for image files and Homomorphic Encryption schemes for high priority files.
Fujitsu Laboratories has developed a technology that matches encrypted text using an extension to the private calculation functions in homomorphic encryption.
Assuming that at least one party behaves in semi-honest model, they use threshold homomorphic encryption for malicious adversaries presented by Cramer et al.
We can now simply define that the hierarchical data model as a hierarchical structure system homomorphic (or even isomorphic) to an algebra including a PCR relation or a DEP relation.
There is particular excitement about the prospects for homomorphic encryption, which would allow processes to act on encrypted data, but practical challenges to implementing this approach remain significant.
2b, 3a); meiosis is achiasmatic, and bivalents are homomorphic, condensing gradually during prophase I (Figs.
Another common despeckling approach is the homomorphic Wiener filter where the speckle noisy image is first subjected to a logarithmic transform and then filtered with an adaptive filter for additive Gaussian noise.
A wide-sense homomorphic encoder is a machine M = (U, Y, S, [omega], v), where the input alphabet U, the output alphabet Y, and the state set S are groups, and the next state map v and the output(encoder) map [omega] are, respectively, surjective and injective homomorphisms defined on an extension U [?
In the homomorphic case, S = 0 holds, and the first equation in (6) reduces to
Our more recent constitutional history reflects this critique of law as applied: Equity's leaven is nearly homomorphic with our own category of due process.
Newline Software solves this problem using its own advancements in homomorphic computing to provide granular access inside encrypted data.