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 ?
In cloud auditing schemes, the data files and homomorphic verifiable tags are uploaded once and for all.
Client-side embedding watermarking protocols can achieve a high level of efficiency in applying the watermark protection, since they adopt an enciphering scheme that only requires computations of modular additions, whereas the other schemes based on homomorphic encryption often require computations of modular exponentiations, which are much more expensive than modular additions.
After nine months of conducting research, progress is going well under the RAMPARTS program, but the two main issues with homomorphic encryption--of efficiency and usability--still have "a long way to go," Archer said.
The result of homomorphic filtering is depicted in Fig.
On inverse homomorphic images of deterministic ETOL languages.
Vaikuntanathan, "Fully homomorphic encryption over the integers," in Advances in Cryptology--EUROCRYPT 2010: 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, May 30-June 3, 2010.
Motivated by the three case studies the project will examine new design and implementation techniques for homomorphic cryptography, as well as a thorough security analysis.
Several classes of encryption technique are then discussed, including homomorphic image encryption, chaotic image encryption, and special discussion of the diffusion mechanism for the ECB mode.
Based on homomorphic encryption(1) which allows computations to be performed on confidential encrypted data without disclosure, Fujitsu has developed a new batch search method that accelerates the processing speed of searching for matches on the encrypted data.
While there are encryption technologies, such as homomorphic encryption, that make it possible to perform calculations on data in an encrypted state, in order for data in the cloud to be useful, statistical calculations alone are not enough.
Such an assumption allows us to obtain isotropic inflation in a rotationally invariant background if we take into account the homomorphic relation between SU(2) and 0(3) groups.