Loosely speaking, a T-function is a mapping from k-bit words into r-bit words such that each i-th bit of image depends only on low-order bits 0,…,i of the pre-image. For example, all arithmetic operations (addition, multiplication) are T-functions, all bitwise logical operations (XOR, AND, etc.) are T-functions. Any composition of T-functions is a T-function as well. Thus T-functions are natural computer word-oriented functions.

It turns out that T-functions are continuous (and often differentiable!) functions with respect to the so-called 2-adic distance. This enables one apply 2-adic analysis to construct wide classes of T-functions with provable cryptographic properties (long period, balance, uniform distribution, high linear complexity, etc.). We consider stream ciphers constructed out of T-functions as specific automata that could be associated to dynamical systems on the space of 2-adic integers and apply the theory of non-Archimedean dynamical systems to study important cryptographic properties of these ciphers.