Die Deprotonierung von Metallaquoionen II: Aquochrom(III)-ion. Zur Struktur aktiver Chromhydroxide

On alkalinization of solutions of the chromiun(III)-aquo ion simple deprotonation takes place first. The degree of hydroxylation n _OH however can be brought up to only about 1 (the exact value depending on the total concentration [Cr]_t), before the uncharged complex Cr(OH)₃(OH₂)₃ is precipitated. The structure of the very sparingly soluble complex (solubility ～10^?7M ) is held together by hydrogen bonds of type I between the molecules, so that its formula may be written as Cr(OH)₂H_6/2-lattice. The formation of the well ordered structure is extremely fast. On aging, the metallic centers become connected by μ-hydroxo-bridges (type II) and the substances become amorphous and very insoluble. The dinuclear (H₂O)₄Cr(OH)₂Cr(OH₂)₄⁴⁺ behaves similar on deprotonation. Concerning the various equilibria constants see Table 1.     

On complexity of round transformations

A modern block cipher consists of round transformations, which are obtained by alternatively applying permutations (P-boxes) and substitutions (S-boxes). Clearly, the most important attribute of a block cipher is its security. However, with respect to the hardware implementation, a good block cipher has to have a reasonable complexity as well. In this paper, we study complexity of round transformations satisfying some basic security criteria. There are several ways to define the complexity of a round transformation, and to choose “necessary” security criteria. It turns out, that for our purpose, it is suitable to view a round transformation as a single Boolean function, not separating it into S-boxes and P-boxes. We require that the Boolean function F possesses some fundamental properties imposed on each block cipher for security reasons; namely, we require that the function is a strictly non-linear bijection and that it has a good diffusion. The total number of variables in the normal algebraic form of the component functions of F is taken as its complexity. We find the minimum complexity of such functions, and this way we establish a lower bound on complexity of all round transformations. To show that the lower bound is the best possible, we construct a round transformation F^′ attaining the bound. We stress that it is not an aspiration of this paper to construct a round transformation which would be of practical use; F^′ is useful only from the theoretical point of view.     

On quasigroups with few associative triples

There are numerous application of quasigroups in cryptology. It turns out that quasigroups with the relatively small number of associative triples can be utilized in designs of hash functions. In this paper we provide both a new lower bound and a new upper bound on the minimum number of associative triples over quasigroups of a given order.     

On Non-Polynomial Latin Squares

It turns out that Latin squares which are hard to approximate by a polynomial are suitable to be used as a part of block cipher algorithms (BCA). In this paper we state basic properties of those Latin squares and provide their construction.