Computationally infeasible definition

Computationally infeasible means that, with today’s state-of-the-art machines, this computation would take more time than is available, say, billions of years.
Computationally infeasible means that the "cost measured by either the amount of memory used or the running time is finite but impossibly large". So, the mathematical expression of the security conditions of electronic exchanges for cryptosystems induced to distinguish the security level of cryptosystems according to the kinds of attack which it has to resist to. And new concepts can still be defined, founded on the theory of algorithms and of complexity, such as authentication of the user, digital signature, backdoors.