Probabilistic watchers of subschemes Sample Clauses

Probabilistic watchers of subschemes. To be completed. Recall that a seclusive key agreement scheme K can have a non-seclusive subscheme k. The same failure can happen for π-seclusive schemes. A sub- schemes of a π-seclusive scheme can be fail to be π-seclusive. Recall that if scheme K has a seclusive subscheme k, then K is seclu- sive. In other words, seclusiveness is inherited from a subscheme. But π- seclusiveness is not inherited from a subscheme. A scheme K can have a subscheme k that is π-seclusive, even though K is not π-seclusive. For ex- ample, K could have the property that, outside of sessions drawn from k, all other sessions have the same non-secret agreed key, and furthermore, the number of these non-k session vastly outnumbers those k, with a probability of session of K being a non-k close to one. This observation about drastic differences between π-seclusiveness of a scheme and its subscheme weakens the strength of our reduction of key agree- ment to semigroups. In some sense, the observation shows how the difficulty of attacks hinges not so much on the whole semigroup, but rather special sets of inputs. However, as long as we keep this mind for the later, we can first attempt to solve semigroup problems as though the average difficulty did not vary with the inputs, and then later account the varying average difficulty as needed.