It is known that every multigraph with an even number of edges has an even orientation (i.e., all indegrees are even). We study parity constrained graph orientations under additional constraints. We consider two types of constraints for a multigraph G = (V,E): (1) an exact conflict constraint is an edge set C ⊆ E and a vertex v ∈ V such that C should not equal the set of incoming edges at v; (2...

We study Lascar strong types and Galois types and especially their relation to notions of type which have finite character. We define a notion of a strong type with finite character, so called Lascar type. We show that this notion is stronger than Galois type over countable sets in simple and superstable finitary AECs. Furthermore we give and example where the Galois type itself does not have f...

We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Complex Multiplication. Furthermore, we demonstrate the efficiency of the algorithm in practice by giving practical running times. In addition, we present statistics on the number of cryptographically strong elliptic curves...

Recent theoretical a potential to signifi information-theoreti concerns, which we community that a s bits from a block o protected data. Even information bits can information-theoreti weak notion of secre ultimate secrecy ra namely one which b bridge the existing security, we present criterion. As in the formulation. The ex

New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutation representation, which in turn simplifies the computation of a strong generating set. In addit...

in this paper, the concept of {sl local base with  stratifiedstructure} in $i$-topological vector spaces is introduced. weprove that every $i$-topological vector space has a balanced localbase with stratified structure. furthermore, a newcharacterization of $i$-topological vector spaces by means of thelocal base with stratified structure is given.