In this paper, the continuity and strong continuity in domain-free information algebras and labeled information algebras are introduced respectively. A more general concept of continuous function which is defined between two domain-free continuous information algebras is presented. It is shown that, with the operations combination and focusing, the set of all continuous functions between two do...

Under the continuum hypothesis, there is a compact homogeneous strong S-space.

In this paper, we propose a simple scheme which produces a new S-box from a given S-box. We use the well-known conversion technique between the polynomial functions over F2n and the boolean functions from F2 to F2. We have applied the scheme to Rijndael S-box and obtained 29 new S-boxes, of which only one is a bijection with better algebraic expression than the original Rijndael S-box and has t...