ABSTRACT: The security of asymmetric primitives typically relies on the hardness of a well-established mathematical problem and is then well accepted by the community. By contrast, the security of symmetric primitives is much less clearly established and the existing pseudo-security-proofs always rely on an ideal modelization that is far from realistic (for example, modeling a pseudo-random distribution by a truly random one). We are then often left with an empirical measure of the security, provided by a thorough, and even more importantly never-ending study of the symmetric primitives by cryptanalysts.
That is why confidence in symmetric primitives is always based on the amount of cryptanalysis they have received, and on the security margin that they have left. To react as quickly as possible when required, it is important to analyze the security thoroughly with respect to all currently available cryptanalysis tools (including quantum ones); and then keep it up to date as the tools evolve.