Search results
Results from the WOW.Com Content Network
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).The word homomorphism comes from the Ancient Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "form" or "shape".
Homomorphic encryption is a form of encryption that allows computations to be performed on encrypted data without first having to decrypt it. The resulting computations are left in an encrypted form which, when decrypted, result in an output that is identical to that of the operations performed on the unencrypted data.
Diagram of the fundamental theorem on homomorphisms, where is a homomorphism, is a normal subgroup of and is the identity element of .. Given two groups and and a group homomorphism:, let be a normal subgroup in and the natural surjective homomorphism / (where / is the quotient group of by ).
In cryptography, homomorphic secret sharing is a type of secret sharing algorithm in which the secret is encrypted via homomorphic encryption. A homomorphism is a transformation from one algebraic structure into another of the same type so that the structure is preserved. Importantly, this means that for every kind of manipulation of the ...
Monomorphism A group homomorphism that is injective (or, one-to-one); i.e., preserves distinctness. Epimorphism A group homomorphism that is surjective (or, onto); i.e., reaches every point in the codomain.
Let the equivalence class of a graph G under homomorphic equivalence be [G]. The equivalence class can also be represented by the unique core in [G]. The relation → is a partial order on those equivalence classes; it defines a poset. [28] Let G < H denote that there is a homomorphism from G to H, but no homomorphism from H to G.
Let f : R → S be a ring homomorphism. Then, directly from these definitions, one can deduce: f(0 R) = 0 S.; f(−a) = −f(a) for all a in R.; For any unit a in R, f(a) is a unit element such that f(a) −1 = f(a −1).
Homomorphic filtering is a generalized technique for signal and image processing, involving a nonlinear mapping to a different domain in which linear filter techniques are applied, followed by mapping back to the original domain.