Injective one-way trapdoor functions are one of the most fundamental cryptographic primitives. In this work we show how to derandomize lossy encryption (with long messages) to obtain lossy trapdoor functions, and hence injective one-way trapdoor functions. Bellare, Halevi, Sahai and Vadhan (CRYPTO ’98) showed that if Enc is an IND-CPA secure cryptosystem, and H is a random oracle, then x 7→ Enc...

For a number of locally finitely presentable categories K we describe the codensity monad full embedding all objects into K. We introduce concept D-ultrafilter on an object, where D is “nice” cogenerator prove that assigns to every object representing D-ultrafilters it. Our result covers e.g. sets, vector spaces, posets, semilattices, graphs and M-sets for finite commutative monoids M.

The pure-injective R-modules are defined easily enough: as those modules which are injective over all pure embeddings, where an embedding A → B is said to be pure if every finite system of R-linear equations with constants from A and a solution in B has a solution in A. But the definition itself gives no indication of the rich theory around purity and pure-injectivity. The purpose of this surve...

Semigroups S for which the Banach algebra ℓ 1 (S) is injective are investigated and an application to the work of O. Yu. Aristov is described.

We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring.

The local multiplier C*-algebra Mloc(A) of any C*-algebra A can be ∗-isomorphicly embedded into the injective envelope I(A) of A in such a way that the canonical embeddings of A into both these C*-algebras are identified. If A is commutative then Mloc(A) ≡ I(A). The injective envelopes of A and Mloc(A) always coincide, and every higher order local multiplier C*-algebra of A is contained in the ...

An injective $k$-edge-coloring of a graph $G$ is an assignment colors, i.e. integers in $\{1, \ldots , k\}$, to the edges such that any two each incident with one distinct endpoint third edge, receive colors. The problem determining whether $k$-coloring exists called k-INJECTIVE EDGE-COLORING. We show 3-INJECTIVE EDGE-COLORING NP-complete, even for triangle-free cubic graphs, planar subcubic gr...