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...

A theory of di erential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a Lefschetz-Pontrjagin Duality Theorem, which asserts that the pairing c IHk(X; @X) c IHn k 1(X) ! S1 given by ( ; ) 7! ( ) [X] induces isomorphisms D : c IHk(X; @X)! Hom1(c IHn k...

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.

We study the sofic tree shifts of A ∗ , where Σ∗ is a regular rooted tree of finite rank. In particular, we give their characterization in terms of unrestricted Rabin automata. We show that if X ⊂ A ∗ is a sofic tree shift, then the configurations in X whose orbit under the shift action is finite are dense in X , and, as a consequence of this, we deduce that every injective cellular automata τ ...

Abstract. Renner has defined an order on the set of partial injective functions from [n] = {1, . . . , n} to [n]. This order extends the Bruhat order on the symmetric group. The poset Pn obtained is isomorphic to a set of square matrices of size n with its natural order. We give the smallest lattice that contains Pn. This lattice is in bijection with the set of alternating matrices. These matri...

In a model-centric software development environment, a multitude of different models are used to describe a software system on different abstraction layers and from different perspectives. Following the MDA vision, model transformation is used to support the gradual refinement from abstract models into more concrete models. However, target models do not stay untouched but may be changed due to ...