Detectors in general semigroups Sample Clauses

Detectors in general semigroups. To be completed. Detectors are defined as range-dependent, depending very much on the ranges of the functions ki, whereas other attackers, such as watchers and distinguishers, are only concerned with images of the functions ki. The main definitions of subscheme and equivalent schemes were given as range-independent notions. Therefore, detectors do not translate as cleanly as other attackers, when translating to subschemes or between equivalent schemes. In particular, in the reduction of key agreement to semigroups, the issues of the range have been mostly ignored. Nonetheless, a range-aware reduction may be possible, by letting the semigroup have elements belonging to the ranges of the functions ki. These ranges are subsets of the semigroups, but there might not be a clean way to describe a detector without calling out these subsets. One artificial approach is to set the ranges to be the whole semigroup, and to also set the domains to the whole the semigroup. (Extending the domain should only the detector’s task more difficult). In this case, detectors T2 and T3, can be defined Ti : S → {0, 1} : a1a2 . . . ai '→ 1, and otherwise Ti(a) = 0. (Also, let T1 = T2 and T4 = T3.) In other words, a detector tests if a semigroup element can be factored into 2 or 3 elements.