Efficient zero-knowledge proofs of knowledge for homomorphisms are a key building block in a vast number of constructions in applied cryptography. Examples are: identification-, signature-, group signature-, anonymous credential-, and identity escrow-schemes as well as voting systems, e-cash, multi-party computations, and trusted computing. This dissertation studies efficient zero-knowledge pro...

We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an “almost folklore” general result, we present a purely algebraic proof of “étale implies exponentiable”, alternative to the topologically motivated proof given in one of our previous papers, in a different context. We prove that only isomorphisms are exponentiable homomorphi...

We study two natural models of randomly generated constraint satisfaction problems. We determine how quickly the domain size must grow with n to ensure that these models are robust in the sense that they exhibit a non-trivial threshold of satisfiability, and we determine the asymptotic order of that threshold. We also provide resolution complexity lower bounds for these models. One of our resul...

This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras. In this categorical model, from the point of view that we provide, the notions of observation and interaction are separate features. This is useful, for example, in the specification of process equivalences, which are obtained as kernels ...

The relations between evaluation of Ore polynomials and pseudo-linear transformations are studied. The behavior of these transformations under homomorphisms of Ore extensions, in particular with respect to algebraicity, is analyzed leading to characterization of left and right primitivity of an Ore extension. Necessary and sufficient conditions are given for algebraic pseudo-linear transformati...

3 Connection matrices 9 3.1 The connection matrix of a graph parameter . . . . . . . . . . . . . . . . . . . . 9 3.2 The rank of connection matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Connection matrices of homomorphisms . . . . . . . . . . . . . . . . . . . . . . . 12 3.4 The exact rank of connection matrices for homomorphisms . . . . . . . . . . . . 13 3.5 Extensions...

The algebraic theories of Lawvere are extended in a natural way to small complete categories. These categories exhibit not only the operations and identities, but some of the homomorphisms, functions, objects and constructions which are encountered when working within the algebraic categories associated with the theories. The category of extended theories is isomorphic to the original category ...

Abstra t. Let P be the set of all probability measures on R possessing moments of every order. Consider P as a semigroup with respe t to onvolution. After topologizing P in a natural way, we determine all ontinuous homomorphisms of P into the unit ir le and, as a orollary, those into the real line. The latter are pre isely the nite linear ombinations of umulants, and from these all the former a...

We investigate the profinite completions of a certain family of groups acting on trees. It turns out that for some of the groups considered, the completions coincide with the closures of the groups in the full group of tree automorphisms. However, we introduce an infinite series of groups for which that is not so, and describe the kernels of natural homomorphisms of the profinite completions on...

We, for any natural n, construct an אn-free abelian groups which have few homomorphisms to Z. For this we use “אn-free (n+1)-dimensional black boxes”. The method is hopefully relevant to other constructions of אn-free abelian groups. I would like to thank Alice Leonhardt for the beautiful typing. This research was supported by German-Israeli Foundation for Scientific Research and Development Fi...