Number systems are behind a lot of implementations. The role of representation is often underrated while its importance in implementation is crucial. We survey here some classes of fundamental systems that could be used in crypotgraphy. We present three main categories:
- systems based on the Chinese Remainder Theorem which enter more generally in the context of polynomial interpolation,
- exotic positional number representations using original approaches,
- systems adapted to operations like the exponentiation.
We stay at the level of the representation system, we do not deal with all the decomposition forms that can be used for accelerating the computation.